Ecological Research Series
STUDIES OF CIRCULATION AND PRIMARY
PRODUCTION IN DEEP INLET
ENVIRONMENTS
Environmental Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Corvallis, Oregon 97330
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RESEARCH REPORTING SERIES
Research reports of the Office of Research and Development, U.S. Environmental
Protection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ECOLOGICAL RESEARCH series. This series
describes research on the effects of pollution on humans, plant and animal spe-
cies, and materials. Problems are assessed for their long- and short-term influ-
ences. Investigations include formation, transport, and pathway studies to deter-
mine the fate of pollutants and their effects. This work provides the technical basis
for setting standards to minimize undesirable changes in living organisms in the
aquatic, terrestrial, and atmospheric environments.
This document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/3-77-049
April 1977
STUDIES OF CIRCULATION AND PRIMARY
PRODUCTION IN DEEP INLET ENVIRONMENTS
by
Donald F. Winter
University of Washington
Seattle, Washington 98195
Grant No. R-801320
Project Officer
Richard J. Callaway
Marine and Freshwater Ecology Branch
Corvallis Environmental Research Laboratory
Corvallis, Oregon 97330
CORVALLIS ENVIRONMENTAL RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
CORVALLIS, OREGON 97330
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DISCLAIMER
This report has been reviewed by the Corvallis Environmental
Research Laboratory, U.S. Environmental Protection Agency,
and approved for publication. Approval does not signify that
the contents necessarily reflect the views and policies of
the U.S. Environmental Protection Agency, nor does mention of
trade names or commercial products constitute endorsement or
recommendation for use.
ii
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FOREWORD
Effective regulatory and enforcement actions by the Environmental Protec-
tion Agency would be virtually impossible without sound scientific data
on pollutants and their impact on environmental stability and human
health. Responsibility for building this data base has been assigned to
EPA's Office of Research and Development and its 15 major field installa-
tions, one of which is the Corvallis Environmental Research Laboratory
(CERL).
The primary mission of the Corvallis Laboratory is research on the effects
of environmental pollutants on terrestrial, freshwater, and marine eco-
systems; the behavior, effects and control of pollutants in lake systems;
and the development of predictive models on the movement of pollutants in
the biosphere.
This report concerns research conducted on a highly complex estuarine
(fjord) system as part of an attempt to assist regulatory agencies in
their management role. Results of the research have already been put
to practical use by federal, state and local government agencies as well
as by commercial engineering firms through utilization of computer programs,
the reports listed in the appendix, and consultation with the grantees. As
such, the work has formed one part of the base upon which criteria and
policy decisions are made and revised.
A. F. Bartsch
Director, CERL
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ABSTRACT
This report summarizes the results of a three-year grant from the U.S. Envi-
ronmental Protection Agency to investigate various aspects of circulation
dynamics and primary production in a deep inlet environment. Throughout the
course of the research, special attention has been given to Puget Sound,
Washington, although many of the findings are applicable to other deep inlet
waters.
The several tasks undertaken during the course of the project fall into three
general categories:
1) numerical modeling of gravitational convection and tidal motions in
deep estuaries,
2) hydraulic model studies of tidal circulation patterns and dye dis-
persal characteristics in Puget Sound,
and 3) numerical modeling of primary production in a deep inlet (in parti-
cular, the deep central basin of Puget Sound).
A list of all publications and reports resulting from the project are given
in Section 7 of this report.
This report was submitted in fulfillment of Project No. R-801320 by the Uni-
versity of Washington, Seattle, Washington, under the sponsorship of the U.S.
Environmental Protection Agency. Work was completed as of March 1976.
IV
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CONTENTS
Sections Page
1 INTRODUCTION 1
2 CONCLUSIONS AND RECOMMENDATIONS 3
3 CIRCULATION MODELING
3.1 STEADY GRAVITATIONAL CONVECTION:
TWO-LAYER ANALYSIS 7
3.2 STEADY GRAVITATIONAL CONVECTION:
SIMILARITY ANALYSIS 25
3.3 STEADY GRAVITATIONAL CONVECTION:
METHOD OF WEIGHTED RESIDUALS 36
3.4 PERIODIC TIDAL MOTION IN NARROW INLETS 40
4 HYDRAULIC MODEL STUDIES OF PUGET SOUND
4.1 MODEL DESCRIPTION AND LIMITATIONS 46
4.2 SURFACE TIDAL CURRENTS IN PUGET SOUND 49
4.3 DYE STREAM DISPERSAL CHARACTERISTICS IN THE
PUGET SOUND MODEL 57
West Point 61
Elliott Bay 62
Dredge Disposal Sites 66
5 NUMERICAL MODEL OF PRIMARY PRODUCTION IN
PUGET SOUND, WASHINGTON 75
6 REFERENCES 96
7 PUBLICATIONS AND TECHNICAL MEMORANDA 98
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FIGURES
No. _
— Page
1 Sketch of an inlet cross-section (a) and longitudinal
section (b), depicting the two major flow zones and
illustrating geometrical quantities. The horizontal
scale is compressed. 9
2 Sketch of an inlet longitudinal section, illustrating
zonal fluid sections used to derive equations of con-
servation of volume, mass, and horizontal momentum. 9
3 Map of Hood Canal, Washington. ^g
4 Bottom profile of Hood Canal, Washington, and salinity
isopleth configuration in mid-November 1954. 19
5 Idealization of Hood Canal bottom profile used in
model calculation ^
6 Principal drainage basins of Hood Canal. 21
7 Relative cumulative runoff rate in Hood Canal. 21
8 Axial variation of deep and near-surface zone salinity in
Hood Canal during October and November. 22
9 Calculated axial variations of mean horizontal current
speed (a), zonal depth (b), and upward transport function F
(c) in Hood Canal for October and November. 24
10 Comparison of measured and calculated isohaline configuration
in a longitudinal section of Hood Canal; the data were
acquired at the stations shown in the map. 33
11 Comparison of calculated depth profiles of salinity and
salinity measurements acquired in May 1966 at a mid-channel
station in the central basin of Puget Sound for (a) a
relatively high runoff rate: Ro = 455 m3 sec-1and (b)
a moderate runoff rate: RO = 220 m3 sec"1- Velocity profiles
for the high runoff period are also shown: (c) horizontal
component; (d) vertical component. 34
12 Comparisons of salinity profiles throughout Knight Inlet, B.C.,
as calculated by the weighted residual method and by the two-
layer analysis. Axial location is distance upstream of the
inner sill. 39
vi
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No. Page
13 Narrow inlet geometry. 41
14 Axial variation of velocity mode amplitudes for model inlet. 41
15 Hydraulic model coverage (outlined by dashed line) and the
locations of the dye discharge experiments. 47
16 Hand-drawn replication of part of the tidal mosaic for one
stage of the tide; direction and magnitude of surface tidal
current is indicated by orientation and length of streamline
segments. 50
17 Map of Puget Sound showing the measured model tides; dots
on the tide curves correspond to the time of the eight
streamline photographs. 51
18 Measured model tide at Seattle; the times correspond to the
beginnings of each of the eight streamline photographs. 53
19 Representative spring tides at Seattle (May 1973, days
1 through 10). 58
20 Representative neap tides at Seattle (October 1973, days
2 through 11). 58
21 Dye discharge locations near Seattle; solid triangles are
dredge disposal sites. 65
22 Dye discharge locations at two dredge disposal sites in
Commencement Bay. 68
23 Dye discharge location at the dredge disposal site near Everett. 72
24 Dye discharge location at the dredge disposal site in Dana
Passage. 74
25 Map of Puget Sound. 77
26 Variations of salinity, temperature, density, oxygen saturation,
phosphate, silicate, nitrate, chlorophyll a, and carbon uptake
rate at Station 1, April to June 1966. 79
27 Variations of salinity, temperature, density, oxygen saturation,
phosphate, silicate, nitrate, chlorophyll a, and carbon uptake
rate at Station 1, April and May 1967. 80
VI1
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No. Page
28 Flow diagram of numerical model showing relationship
amongst the several components of the model. 88
29 Comparison of measured and calculated integrated chloro-
phyll a from surface to Secchi disk depth and Secchi disk
depth at Station 1 in Puget Sound, April to June 1966;
arrows indicate endings of periods of rapidly rising
salinity in brackish zone. 90
30 Comparison of measured and calculated integrated chloro-
phyll a from surface to Secchi disk depth and Secchi disk
depth at Station 1 in Puget Sound, April and May 1967. 91
31 Comparison of measured and calculated chlorophyll a concen-
trations as functions of depth at Station 1 before, during,
and after algal bloom in 1966; dashed lines indicate
estimates of 1% light depths. 92
32. Depth variation of algal flux due to turbulent mixing,
upwelling, and sinking for standard run at noon on g^
28 April 1966.
viii
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ACKNOWLEDGMENTS
The writer wishes to acknowledge with appreciation the support of this
project by the Environmental Protection Agency under Grant No. R801320.
The contributions of all the research collaborators whose names appear
as authors in the publication list in Section 7 were essential to the
success of this project. Special thanks are due to Dr. Ronald K. Lam and
Mr. John H. Lincoln of the Department of Oceanography, University of Wash-
ington, who carried out and reported the hydraulic model studies of Puget
Sound described in Section 4.
The numerical modeling study of primary production in Puget Sound described
in Section 5 was supported in part by the Washington Sea Grant, which is
maintained by the National Oceanic and Atmospheric Administration, U.S. Depart-
ment of Commerce. Funds for the field effort in that study were provided
primarily by the United States Public Health Service and later by the Federal
Water Pollution Control Administration (Grant WB-00633). Minor assistance
was given by the Office of Naval Research, Contract Nonr-477(37), Project NR
083 012, and the U.S. Energy Research and Development Administration, Contract
AT(45-l)-2225, TA 26 (RLO-2225-T 26-21).
The two-layer analysis of steady deep inlet flow, as set forth in Section
3.1, is a recent modification of the method developed originally under
Grant No. R801320. The procedure described here was developed by Prof.
Carl E. Pearson and the author under the auspices of Program Research, Inc.,
with support from EPA, subsequent to the expiration of Grant No. R801320.
However, the modified approach is presented here inasmuch as it represents
an improved version of the original method.
Staff assistance in the University of Washington Department of Oceanography is
acknowledged in each of the publications, as appropriate. The writer expresses
special thanks to Ms. Betty Hardin for typing this report and preparing it for
publication.
ix
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SECTION 1
INTRODUCTION
In recent years, deep inlet waters have been subject to increasing environ-
mental stress associated with rising population densities and industrial
activity. In many areas, these developments have been accompanied by efforts
to improve and preserve inlet water quality through the institution of
rational water management and utilization programs. Such efforts have a
greater chance to succeed if the biological and chemical characteristics of
an inlet are known and if the hydrography and water movement can be described
in quantitative terms. Although in many respects the research described in
this report responds to the general need for such descriptions in deep inlets,
special consideration has been given to Puget Sound, Washington, in most phases
of the work.
Section 2 of this report summarizes the approach and conclusions in each of
three principal categories of the project and presents recommendations of
future research directions, where appropriate.
Section 3 presents descriptions of several different numerical models of deep
inlet circulation, including time-averaged flow and periodic tidal motions.
Section 4 describes two investigations with the hydraulic model of Puget Sound.
One study is concerned with a description of surface tidal current patterns
throughout the Puget Sound region. The other deals with dye-stream dispersal
characteristics in the model at various locations in the Sound which are sites
of potential pollution stress.
Finally, Section 5 presents a summary of field measurements in the central
basin of Puget Sound conducted over a period of several years and includes
both conventional hydrographic data and measurements related to biological
activity. Highlights are also presented of the results of a numerical model
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study of the relationship between primary productivity and the hydrodynamic
characteristics of a deep inlet environment, as exemplified by the central
basin of Puget Sound.
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SECTION 2
CONCLUSIONS AND RECOMMENDATIONS
The overall objective of this research has been to investigate various aspects
of deep inlet circulation with a view toward improving our ability to repre-
sent flow patterns and to explore relationships between circulation and phyto-
plankton growth (primary production) in a deep inlet environment. The tasks
undertaken in pursuit of this general objective fall into three categories:
1) numerical modeling of deep inlet hydrodynamics, 2) hydraulic model studies
of tidal circulation patterns throughout Puget Sound, and 3) numerical model-
ing of primary production in the central basin of Puget Sound, Washington.
The principal accomplishments, conclusions, and recommendations in each cate-
gory are as follows:
1) CIRCULATION MODELING
Circulation in deep, narrow inlets with appreciable freshwater input is gene-
rally dominated by two modes: quasi-steady gravitational convection and periodic
tidal motion. With regard to the first of these modes, it is characteristic
of deep, stratified inlet flow that the most vigorous circulation takes place
in a brackish water zone near the surface. During the course of the project,
three different types of approximation procedures were used to represent this
mode; the techniques included a similarity analysis, a two-layer representation,
and a weighted residual approach. Approximate descriptions were obtained for
time-averaged or quasi-steady state velocity fields and density distributions.
These representations have been applied to inlet segments in Puget Sound and
along the coastline of British Columbia. In each case, the procedures used
can be adapted to analyze distributions of dissolved and suspended pollutants.
The various steady-state models simulate the gross features of observed time-
averaged flow and density distributions where such comparisons have been made.
However, none of these models of steady inlet flow (or any other one, for that
matter) can be considered entirely satisfactory. Our experience in this
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research effort suggests that high priority ought to be given in the future
to i) carefully designed field studies with high data resolution in space
and time to identify and describe more precisely basic patterns of deep
inlet fluid motion and to allow more reliable quantitative descriptions of
the relevant physical processes, and ii) the development of more accurate,
economical procedures for solving the governing equations.
In connection with inlet tidal motions, a new and efficient procedure was
developed for computing periodic flow in deep, narrow inlets. The method is
based on a harmonic analysis in which accurate representations of the nonlinear
terms in the equations of motion are developed by successive approximation.
At each iteration, the modal coefficients satisfy a system of first-order
equations and boundary conditions which are combined in such a way as to
promote algorithmic efficiency. The method appears to be both accurate and
economical—typical computation times for deep inlets may be less than 10% of
that required by conventional time-stepping procedures.
The recommendations for deep inlet tidal dynamics follow somewhat the same
lines as those for the time-averaged circulation mode. More specifically, the
one-dimensional, time-dependent model developed under this grant should be
extended to two dimensions, thereby allowing representation of cross-channel
flows where they are important (in fact, that extension is now in progress
under sponsorship of the National Science Foundation). Beyond that, the
formulation should be modified to allow for effects of stratification, and
the method should be checked by applying it to a deep inlet region with a fairly
complicated shoreline.
2) HYDRAULIC MODEL STUDIES
The Puget Sound hydraulic model in the Department of Oceanography at the Uni-
versity of Washington was used to define detailed surface circulation patterns
throughout Puget Sound at various stages of the tide. Four sets of photo-
graphs of tidal mosaics were produced which give a qualitative description
of the surface flow configuration at different stages of the tide throughout
the entire Sound. In addition, a continuous dye injection study was performed
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with the hydraulic model to define deep water movement and pollutant path-
ways at depth for selected locations in Puget Sound near Seattle (at the
METRO sewage outfall site at West Point and in Elliott Bay), as well as at
seven dredge disposal sites indicated by the Region X office. An edited
set of 16 mm films of these studies was given to the Environmental Protec-
tion Agency, along with an informal report describing the work and our
interpretation of the results. The film and reports may be obtained by
contacting the project officer.
The techniques developed for the tidal current study have been satisfactory in
most respects, and the results are adequate for a description of the gross
surface features of the tidal circulation. Additional work along this line
should be aimed at improving the sampling scheme and, in particular, it
would be desirable to undertake some combination of the following for certain
locations in the Sound: increase the sampling frequency, improve the spatial
resolution, and shorten the averaging (exposure) times.
3) BIOLOGICAL MODELING
The overall purpose of the biological modeling effort was to examine relation-
ships between seasonal algal growth, nutrient availability, and gravitational
convection in the central basin of Puget Sound, using one of the aforementioned
hydrodynamic models and a numerical model of phytoplankton growth. By means of
"numerical experiments", the relative importance of various factors influenc-
ing algal standing stock in the central basin was assessed, particularly for
the spring and summer months. A detailed report was prepared describing not
only this aspect of the work, but also earlier phases, including field measure-
ments of central basin topography and biological activity over several years'
time.
It was concluded that phytoplankton growth in the central basin of Puget Sound
is governed by a combination of factors, including vertical advection and turbu-
lence, modulation of underwater light intensity by self-shading and inorganic
particulates, sinking of algal cells, and occasional rapid horizontal advection
of algae from the central basin by sustained winds. The high primary produc-
tivity of the Sound is due to intensive upward transport of nitrate by the
gravitational convection mechanism. It would appear that during the spring
and summer months the quantity and quality of freshwater runoff in the central
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basin is such as to maintain moderately intense gravitational convection
without producing an excessively turbid, brackish, surface zone. On occasions
of sustained winds, standing stock is limited by relatively short residence
time determined by horizontal advection. Episodic nitrate depletion of a few
days' duration, together with a succession of cloudy days, will discourage
vigorous growth and will cause blooms to decline in intensity. The effects of
grazing by zooplankton and cellular sinking appear to be of secondary importance
in the central basin. Because of the rather rare occurrence of nutrient limi-
tation during the spring and the light limitation that prevails during the fall
and winter months, nutrient addition from sewage treatement plants is not likely
to change the level of primary production in the main channel significantly;
perhaps species composition is altered, but no direct evidence of it is at hand.
It is also concluded that the functions and parameters traditionally employed to
describe phytoplankton metabolism are marginally adequate for use in a short-
time scale numerical model of primary production. Our present ability to
describe quantitatively the response of phytoplankton to changing environmental
stimuli is too limited to permit the construction of predictive models of algal
growth which are both reliable and generally applicable to all deep inlets.
The clear indication from our work here is that additional studies of fundamental
biological processes at the base of the marine food web are essential. Improved
quantitative descriptions are needed of mechanisms by which cells take up, store,
and utilize nutrients, mechanisms of light adaptation, changes in cellular
chemical composition, and the respiration function. Zooplankton grazing, bacte-
rial activity, and algal response to deleterious substances are also topics which
require further study. So far as the central basin of Puget Sound is concerned,
it is recommended that biweekly field sampling of the sort described in Section 5
be maintained to monitor water quality on a long term basis. Occasional inten-
sive surveys during different seasons would be a useful supplement to such a
sampling program and would also provide additional insight into connections
between biological mechanisms and various environmental processes in Puget Sound.
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SECTION 3
CIRCULATION MODELING
The deep inlets along the coastline of the Northeastern Pacific Ocean are
typically a few kilometers in width, tens of kilometers long, and hundreds
of meters deep, except possibly for sills located near the mouth. It is also
typical that fluid motions in these deep inlets are dominated by two circu-
lation modes: quasi-steady state or time-averaged gravitational convection
and,periodic tidal motion. In the course of this project, three different
mathematical procedures have been used to represent the flow pattern and
density distribution associated with the gravitational convection mode: each
method is outlined in some detail in the next three subsections. In the last
subsection, a new procedure is described for computing periodic tidal flow in
deep, narrow inlets.
3.1 STEADY GRAVITATIONAL CONVECTION: TWO-LAYER ANALYSIS
In an inlet with appreciable freshwater runoff, time-averaged horizontal
currents characteristically form a two-zone circulation pattern variously
referred to as "gravitational convection" or "estuarine circulation". The
freshwater input to the inlet produces a longitudinal pressure gradient which
drives a brackish near-surface zone persistently seaward, while at greater
depth, a dense saline zone moves landward. The water in this deeper zone is
derived largely from sea water external to the inlet, although it may be
freshened somewhat by brackish water from above due to turbulent mixing be-
tween the zones. This is particularly the case if there is a sill near the
inlet mouth. It may also happen that a relatively shallow sill partially
isolates deep basin water from oceanic water external to the inlet, thereby
creating a third zone of relatively stagnant water in the inlet interior.
In this report, gravitational convection is treated on the basis of a two-
layer representation (with mixing), although the procedures outlined here
could be modified to deal explicitly with a three-layer formulation in which
an intermediate transition zone is included.
The discussion is restricted to time-averaged conditions with a view to pro-
viding a quantitative description of the quasi-steady state component of
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inlet flow. Consider a straight, deep, narrow inlet of length L. The
flow parameters and topographic variables are referred to a Cartesian system
where the coordinate origin is taken at the mean free surface level near the
inlet mouth. The ^-coordinate denotes horizontal distance along the inlet
axis, measured from the mouth and reckoned positive landward, and the 3-axis
is directed vertically upward, as shown in Fig. 1.
Fluid motion and density distribution in the inlet is described in terms of
a two-layer model, which is derived along lines similar to those used in
analyzing single-layer channel flow. Subscripts 1 and 2 are used to
denote variables in the lower and upper zones, respectively. It is assumed
that the fresh water in the inlet is introduced exclusively into the upper
layer with zero horizontal velocity (except at x = L ) at a cumulative volu-
metric rate given by R(x); (thus, R(x) denotes the total influx between x
and L ). Because of the typically small depth of the near-surface layer, its
breadth b(x) may be taken as constant over its depth. Let d~ be an
appropriate fixed reference depth, such as the zonal thickness at the inlet
head, and denote by h~3 h~ the displacements of the lower and upper surfaces,
J. Cl
respectively (Fig. 1). The cross-sectional area of the near-surface layer,
denoted by AC)(x)3 can be written as
2/
AJx) = b(x) [d, + hjx) - h.tx)}.
£i u £i J.
Next, suppose that the deep layer has cross-sectional area A(x) when the
fluid is at rest; the breadth of its top surface will be b(x). The actual
cross-section of the deep layer can then be represented as
AI(X) = A(x) + b(x) + b(x)h1(x).
It will be convenient subsequently to refer to a maximum depth dAx) of the
deep layer when the fluid is at rest. Finally, the horizontal velocities of
the deep and near-surface layers will be denoted by u1(x) and u~(x)s respec-
J. &
tively; each is positive when directed landwards. Equations expressing
incompressibility (or conservation of volume) and conservation of mass and
horizontal momentum in each layer can now be written down.
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(a)
Fig. 1. Sketch of an inlet cross-section (a) and longitudinal
section (b), depicting the two major flow zones and
illustrating geometrical quantities. The horizontal
scale is compressed.
ZONE 2
ZONE 1
Fig. 2. Sketch of an inlet longitudinal section,
illustrating zonal fluid sections used to
derive equations of conservation of volume,
mass, and horizontal momentum.
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In so doing, it is necessary to allow for (upward) convection motion
and for turbulent mixing between the layers. In models where flow parameters
are continuous functions of depth, vertical transport is described by ver-
tical flow velocities and turbulent fluxes, the latter involving eddy coeffi-
cients of viscosity and diffusion. Since turbulent exchange mechanisms in
estuarine flow are not at all well understood, the eddy coefficients are
usually assigned values or functional forms which are adjusted until calcu-
lated flow and hydrographic patterns are similar to those observed in
practice. In layered models of coastal plain and salt wedge estuaries, the
approach has not been much different; the traditional procedure is to assign
adjustable values to friction coefficients at a zonal interface until some
correspondence is achieved between computation and observation. In the
present work, convective and turbulent transfer between the layers is repre-
sented by two interzonal exchange flux rates denoted by F and Fj. The
symbol F represents the upward volume rate of flow of fluid from the deep
LAr
layer to the near-surface layer per square meter of inter facial area. Like-
wise, F, denotes the downward volumetric flux rate from the upper to the
lower layer .
Equations expressing incompressibility or volume conservation for each layer
are derived from considerations of volume flow rates in and out of sectional
"slices" of thickness Aa;, illustrated in Fig. 2. For the deep and near-
surface layers respectively, one obtains
- F) (1)
and
- V
where the subscript x denotes differentiation with respect to x. Similarly
the equations expressing conservation of mass in the lower and upper layers
are
v - « v ) (3)
10
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and
U2A2)]
(4)
where p denotes the mass density of fresh water. In writing down Eqs.
(3) and (4), it has been assumed that horizontal diffusion is negligible
compared with advective transport. This is a common assumption in deep inlet
studies and is validated by the findings of certain oceanographic field
studies of fjord waters (e.g., McAlister jit al. 1959; Dyer 1973). On the
other hand, it may not be justified in the vicinity of a long shallow sill
where tidally induced longitudinal dispersion of mass can become competitive
with advection .
To derive the momentum equations, we use the fact that the net force on each
slice of fluid, in Fig. 2, must equal the net rate of efflux of momentum from
that slice. Consider first the lower slice. The net force on it is made up
of a pressure imbalance across its two faces, the pressure force on the sides
due to changes in breadth, the horizontal component of the pressure force
acting on the interface, and the frictional stress i_p(x) acting on the
wetted perimeter C :
b(d
p $(x} z) dz
r -d,
+
i
P £
-Lds
3 + h«(x)
1 2
]x dz + 9
1
X
where p is the pressure, g the acceleration of gravity, and 3fa, z)
the breadth of the lower layer at vertical position z. The usual convention
of shallow water theory is adopted to the effect that p results from hydro-
static forces only, so that
P = 9
In carrying out the differentiation indicated for the first term of the
momentum conservation equation above, there is no contribution from the
x-dependence of the lower limit, since g 6r _, - [dg + d^\) = 0. Furthermore,
there is no contribution from this term if the channel has a flat bottom since,
in that case, the momentum equation contains an additional term of equal
11
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magnitude and opposite sign. The final result can be written as
A, - A
_ £
(i -
(5)
where y is defined by the relation
-d2~dl
Clearly, in the case of a rectangular channel, y = 1. A similar line of
argument leads to the equation of horizontal momentum applicable to the
near-surface layer:
U2(u2}x
A
- A
A
bF
u
(U., -
X
ib
R
+ P~«
(6)
o"2
• 6 6
where ^^x) i-s the stress exerted on the upper surface by wind.
Equations (1) - (6) can be regarded as a system of equations for the six un-
known dependent variables p-, p9J A** Ar>3 u13 and U0. Two integrals can be
J. to J. a J. tLt
obtained immediately by adding Eqs. (1) and (2), and Eqs. (3) and (4),
respectively:
u.JA1 + u^2 = ~R V)
and p^UiAi + pnu<>Ao = -p.J? . (8)
These two equations will be used subsequently to eliminate a pair of dependent
variables from the system.
All that remains is to specify appropriate boundary conditions. In situations
often encountered in practice, the mass density of oceanic water seaward of
the inlet mouth is presumed known. In fact, p^(0) is ordinarily the only
dependent variable that can be specified at x = 0. At the head of the inlet,
we take the horizontal velocity in the lower layer to be zero, i.e., U^(L) = 0.
Suppose now that a river flows into the head of the inlet, delivering fresh
water (of mass density p ) at the volume rate R(L). If d^ is taken to be
12
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the effective depth of the freshwater zone at x = L3 where the channel
breadth is b(L)3 then both h^ and h can be set equal to zero at
x = L. Then, since p^fL) = p , it is consistent with Eqs. (7) and (8) to
6 O
take Ur,(L) = R(L)/b(L)d~. The boundary value problem statement is now
6 6
complete since six conditions have been imposed.
According to the foregoing specification, all but one of the dependent vari-
ables are assigned values at the inlet head. Most standard integration
methods that might be used to solve the system of six differential equations
assume that starting values of all variables are given at the same point. In
practice, one could begin the calculations with a provisional value of p
estimated from data and adjust it iteratively until p JO) is approximately
equal to the prescribed value seaward of the inlet mouth.
Since not every inlet possesses a simple, well-defined headwater region, it
may be convenient to start the calculation at some distance downstream of the
landward terminus. For example, suppose that near the landward end (x = L)3
fresh water originates in streams that feed a number of small subsidiary embay-
ments where wind mixing of fresh and salt water takes place. In this situa-
tion, the total freshwater influx near x = L is still R(L) 3 but the mass
density P0(L) must be that appropriate to the brackish water contributed by
£i
the embayments. If the depth d~ is now the depth of the brackish zone,
LI
h^ and h0 are again set equal to zero. However, the velocity U- is no
J. 6 J.
longer zero at x = L3 since continuity implies movement of some saline water
into the embayments. The specification of both u~ and u~ follows from
L ci
Eqs. (7) and (8) after assignment of values to p and p 0 and x = L, As
J. 6
above, the estimate of £>«(L) could be regarded as provisional and could be
adjusted until agreement with a prescribed value of P7(0) is achieved.
In applying the model to a particular inlet, it would be desirable to follow
a definite procedure for estimating F and F ,. There is more than one
u a
course of action open at this stage and the choice that is made will depend
upon the special circumstances of the problem. For example, on the basis of
hydrographic information and other considerations, one might choose to assume
that specific transport or exchange mechanisms are dominant and assign appro-
priate functional dependence to F and F, when such dependence is believed
known or can be guessed at (from laboratory experience, for instance).
13
-------
However, when the main objective is to simulate representative flow in a
particular inlet, an attractive alternative is to establish the density distri-
butions by measurements and to express F and F-, in terms of the densities
£*t Ci
and unknown dependent variables by the procedure described below.
Consider a deep, narrow inlet for which the cumulative freshwater input is
known and where estimates of the mass densities p- and p? are available
from field data. Define auxiliary functions §«(x) and $p(x) by
**-'
and
*• - £^? • f
Since p7 and pp are prescribed, the functions 7 and p are known, and
can be used together with Eqs. (7) and (8) to express the layer cross-sections
A- and Ac, in terms of the unknown velocities u^ and u^'
A1 = b^^'1 (ID
and
A2 = -btjU^1 (12)
These expressions can be used to help eliminate 4- and A^ from Eqs. (5)
and (6). Next, it is shown that the factors bF^/A^ and bFu/A% can also be
expressed in terms of known (or estimable) functions and the unknown velocities.
Thus, Eqs. (1) and (2) may be used in Eqs. (3) and (4) to yield
and
bF
•
From these equations, together with Eqs. (9) and (12), it can be shown that
(13)
14
-------
and
u
(14)
where
61 =
x
(15)
and
(16)
67 and 6p are known, and A-, and
Since the two auxiliary quantities
A~ are given in terms of u., and u<> by Eqs. (11) and (12), the factors
j and F
are F i/A- and F /4_ given in terms of the unknown velocities.
It is now clear that the original system of six equations can be reduced to
two equations of the form
(17)
and
a21(ul)x
a22(u2)x
(18)
where
= g —
'
a
21
-2
a
22
-2
(19)
and where
-1
u.
!i
2
-i . (A
f
w
» -r
f b
u
A
b
1
2
-1
(20)
15
-------
123
48°h
HOOD CANAL '!
FLOATING BRIDGE:--
:.SOUTH PT.
PLEASANT
'HARBOR
40'h
20'
123
Fig. 3. Map of Hood Canal, Washington.
16
-------
and
U2
- T * p -r- u - 7— (21)
O D
The system (17) and (18) is readily solved for (w7J and (u0) 3 and the
J. CC & 3C
resulting equations can be integrated efficiently by the fourth-order Runge-
Kutta method.
For the purpose of illustration, the procedure just outlined has been applied
to Hood Canal, Washington. Hood Canal is a deep inlet nearly 100 km long and
1 to 3 km wide, on the western side of the Puget Sound system (see Fig. 3).
Puget Sound as a whole communicates with the Pacific Ocean by way of the Strait
of Juan de Fuca to the north. The principal entrance to the Sound is through
Admiralty Inlet, a relatively shallow channel with a 50 m deep sill, between
the Olympic Peninsula and Whidbey Island. Hood Canal opens into Admiralty
Inlet near Tala Point, about 15 km south of the sill. As can be seen from the
bathymetric profile in Fig. 4, Hood Canal itself has a 50 m deep entrance sill
near Vinland, about 20 km south of the inlet mouth near Tala Point. Landward
of the Vinland sill, the basin deepens to 160 m in the central segment. The
Hood Canal basin is characteristically steep-sided, with shelves which are
either very narrow or non-existent. Near the northern end is Dabob Bay, a
small, deep subsidiary inlet. At the southern terminus of the basin is a rela-
tively shallow appendage, Lynch Cove, whose axis forms an acute angle with the
main axis of Hood Canal.
Fresh water in Hood Canal is derived from land drainage, rainfall, and river
runoff. A large fraction of the land area adjacent to the Canal is drained by
five main rivers that are distributed along the inlet axis as shown in Fig. 3.
Freshwater input to the inlet is greatest during the early winter months when
rainfall is most intense. The seasonal river discharge cycle exhibits a peak
at that time and a secondary peak in the late spring due to snow melt in the
mountains within the watersheds on the western side of the Canal.
In considering this particular application of the model, we recognize that,
since Hood Canal is a relatively low runoff inlet, it is seldom strongly
17
-------
stratified (see Fig. 4) and, therefore, a two-layer representation is perhaps
only marginally appropriate. Despite its shortcomings, however, the results
of the two-layer analysis have been shown to be reasonably consistent
with alternative approaches (see Winter and Pearson, 1976). The two-layer
representation is most likely to be justified following the later summer
replacement of deep basin water and during the autumn period of heavy rainfall.
Figure 6 shows surface layer and deep zone salinities typical of this season
at nine different locations along the basin axis. (Salinity is defined here
as grams of salt per kilogram of sea water.) The data shown in the Figure
are averages of salinity measurements acquired in nine cruises conducted during
the months of October and November from 1953 through 1963.
Autumnal conditions in Hood Canal were simulated in the following way: first,
it can be deduced from a study by Friebertshauser and Duxbury (1972) that,
during the months of October and November, the average total volumetric fresh-
o
water inflow rate to Hood Canal is approximately 145 m /sec. Next, it is
assumed that the distribution of cumulative runoff along the inlet is propor-
tional to cumulative drainage area, which can be reconstructed from the water-
shed areas shown in Fig. 8. This reconstruction gives the data points plotted
in Fig. 7. The overall variation of R(x) is represented approximately by
the function
R(x) = 145, for 0 < x < 20 km
= 145 exp [- 50J' for x > 20 km' (22)
shown as a dashed line in Fig. 7. A plot of the approximate representation of
Hood Canal bathymetry is given in Fig. 5. The breadth of the main channel was
taken to be constant and equal to 2 km.
Next, in order to specify the auxiliary functions (f^, 4>^ 52J and 62
in Eqs. (9), (10), (15), and (16), respectively, it is necessary to
generate approximate representations of p^ and p^ from salinity measure-
ments acquired during the late autumn months. Inspection of profiles of
salinity at several locations along the axis of Hood Canal suggests that the
nominal depth of the near-surface layer is roughly 15 m over the greater part
of the inlet. Salinity data from nine stations in all were averaged over
two depth intervals, 0 to 15 m and 15 m to the bottom, with the results shown
18
-------
~ 50
X 100
Q.
g 150
200
DATE /£-//" NOV '54
Fig. 4. Bottom profile of Hood Canal, Washington, and salinity
isopleth configuration in mid-November 1954.
~ 50 -
E
QL
LU
O
100
150
200
DISTANCE FROM MOUTH (km)
50
100
Fig. 5. Idealization of Hood Canal bottom profile used in model
calculation.
19
-------
in Fig. 6. A consideration of the graphs in Fig. 6 indicates that, as a
first approximation, we may neglect the refluxing effect near the Vinland
sill and take p to be constant throughout the deep zone. If we assume
a linear equation of state, then p takes the value
P2 = 1000 + 0.775 = 1023.4 kg/m3
where S denotes salinity and where the coefficient of S is appropriate
to the autumnal water temperature range in Hood Canal. The longitudinal vari-
ation of salinity S in the near-surface layer can be approximated by a
&
Gaussian function of x, thereby providing a functional representation of
p? for substitution into the equations for the auxiliary functions.
In the model equations, the wind stress on the upper surface was taken to be
zero on the average. The boundary stress T,, was assumed to be related to the
horizontal speed u~ in accordance with the Chezy-type relation
rf= - 5 u2 \U2\ D~2/3 (23)
2 5
in newtons/m , if u- is in m/sec, and D in m. (One newton = 10 dynes.)
This last relation is one frequently used in the literature for frictional
stress; the coefficient 5 represents a mean value of typical reported coeffi-
cients. Actually, in most deep inlet applications, boundary stress will not
make an important contribution to the overall horizontal momentum balance.
In order to specify the boundary conditions, recourse is made to field data.
Consideration of representative salinity profiles for the region, the runoff
distribution in Fig. 7, and the topographical relation between Hood Canal and
Lynch Cove, suggests the desirability of starting the calculation near the
confluence of Lynch Cove and the southern end of the main basin. According to
the earlier discussion of boundary conditions, the nominal terminus of the
inlet can be taken to be at x = L = 90 km. R(L) will then be the river
discharge at 90 km as calculated from Eq. (26) (near the Skokomish and Tahuya
Rivers). Salinity profiles indicate that an appropriate value for dt) is
roughly 15 m. Next, the value of p at x = L can be obtained from the approxi-
-------
31
30
-------
Fig. 8. Principal drainage basins of Hood Canal.
22
-------
Eqs. (7) and (8). The system of differential equations for u^ and u^
was then solved by a fourth-order Runge Kutta procedure, for the domain
0 < x < 90 km, subject to the boundary conditions above. Calculated hori-
zontal speeds and the zonal interface depth are given in Fig. 9 along with
a graph of the depth longitudinal variation of F . Current speeds and the
(A-
calculated zone depths seaward of the Vinland sill are in rough agreement
with preliminary current meter results for that region (Applied Physics
Laboratory, University of Washington, unpublished). However, since no
tidal-average current measurements are available for other locations in the
inlet, no further comparisons can be made. Hence, an assertion that the model
has been validated on the basis of the existing data would be an overstatement
of the case. On the other hand, what has been done is to develop an approxi-
mate, self-consistent representation of horizontal currents and density
distribution believed to be characteristic of Hood Canal during the late
autumn months. The calculated results are in reasonable accord with the
limited amount of field data available for comparison purposes.
It should be clear from the foregoing illustration of the method that the
model can be applied with relative ease to an inlet with fairly complicated
bathymetry and distributed runoff. A model of this type could be conveniently
used in connection with pollution studies. Thus, if estimates were required
of soluble contaminant distributions in a deep inlet, the model can easily
be supplemented with equations of the type (3) and (4) describing pollutant
mass distributions in the near-surface and lower zones, with appropriate
terms appended to describe the source and (possibly) the loss of contaminant
throughout the inlet.
23
-------
100 km
-0.3L
100 km
20
(C)
40 60 80
DISTANCE FROM MOUTH Urn)
100
Fig. 9. Calculated axial variations of mean horizontal current speed
(a), zonal depth (b), and upward transport function FU (c)
in Hood Canal for October and November.
24
-------
3.2 STEADY GRAVITATIONAL CONVECTION; SIMILARITY ANALYSIS
Although the two-layer model is relatively easy to apply, it suffers from
several disadvantages: for example, 1) mass density and horizontal velocities
are represented as discontinuous functions of depth, 2) vertical transport
by advection and turbulent mixing is not represented in a straightforward way,
and 3) in contrast with the implications of a two-layer representation, it is
observed that the vertical scale associated with the horizontal current often
exceeds that of the mass distribution. On the other hand, it is very diffi-
cult to generate continuum descriptions of gravitational convection in deep
inlets. Two attempts to solve the problem by the use ot similarity analysis
have been reported [Rattray (1967), Winter (1973)]. The latter work was
performed under the sponsorship of the Environmental Protection Agency and is
summarized herein.
As mentioned at the beginning of this section, the flow in deep inlets with
appreciable freshwater input is characterized by a reversal in the direction
of horizontal current at depth. When most of the fresh water comes from river
discharge near the head of the inlet, and when winds are light-to-moderate,
the circulation tends to a two-layer system in which the uppermost layer moves
persistently seaward above a landward-moving deeper layer of saltier water.
Up-inlet winds retard the outflow and may sometimes exert sufficient stress
to reverse the direction of the surface current, causing outflow to occur in
an intermediate zone at several meters depth below the surface (Pickard and
Rodgers, 1959). Three-zone flow may also occur locally in fjord segments when
the longitudinal distribution of freshwater runoff increases fast enough in
the seaward direction to produce a landward-directed pressure head near the
surface. However, the present discussion is restricted to deep inlets with
runoff distributions which, in the absence of wind stress, produce a seaward-
directed mean surface current. Also, consideration is limited to inlet
segments which are narrow and sufficiently straight that cross-channel pressure
and velocity differences are small and Coriolis forces can be neglected. Under
these conditions, field accelerations in the upper regions of the flow may
contribute to the overall horizontal momentum balance as well as the horizontal
pressure gradient and the vertical gradient of the turbulent stress. As men-
tioned in the previous subsection, field studies in Silver Bay, Alaska,
25
-------
performed by McAlister et al. (1959) suggest that horizontal diffusion
plays a negligible role in the upstream transport of salt in fjords.
The steady-state equations are obtained by time-averaging the equations of
motion over a tidal cycle. In addition, the governing equations are
laterally averaged over the channel width. In this analysis, the spatial
dependence of all variables will be referred to a Cartesian coordinate
system whose origin is at mean sea level, located near the head of the
section under consideration. The positive ar*-axis extends horizontally
in the seaward direction and the s*-axis is taken to be positive downward.
Variables with asterisk superscripts are quantities with dimensions; variables
without asterisk are nondimensional.)
The usual assumption is made that the time-average of the turbulent stress
can be represented by the product of the horizontal velocity shear and a
suitably defined vertical eddy coefficient of viscosity N* . It is further
Z
assumed that the turbulent flux of salt can be adequately represented by the
product of a vertical eddy coefficient of diffusion K* and the vertical
%
gradient of the mean salinity S*.
It is convenient to express the governing equations and the final results in
terms of nondimensional variables. In the case of deep, stratified inlets,
an appropriate scale in the vertical direction is the thickness of the brack-
^
ish surface zone within which most of the fresh-water runoff is transported
to the sea. Field studies of the fjord-type inlets (see, for example, Tully,
1949; Pickard, 1961, 1971) suggest that the depth z* of the brackish surface
zone can remain within the decameter range over inlet segments which are tens
of kilometers in length. A measure of the total time-mean rate of outflow is
given by the ratio of the cumulative volumetric runoff rate fl* and the
fractional excursion 0 from great depths to the surface:
S* - S*
°o = ^S^ (24)
00
where S* is the salinity at great depth and 5* is the surface salinity.
oo S
(The subscript zero is used here and in the sequel to denote appropriate
reference station values in the inlet segment under consideration.) Since the
outflow takes place in a zone whose thickness is of the order of z* 3 by
26
-------
definition, an appropriate measure of the horizontal velocity is given by the
characteristic speed u* in the upper zone
u* = R* b*z*a 3 (25)
o o o o o
where b* is the reference channel width. It is appropriate to measure longi-
tudinal distance in units which reflect the fact that the horizontal scale
x* is determined by the balance between mixing and advective salt transport.
The turbulent transport of salt is described by a suitably defined vertical
eddy diffusivity of the order of K*3 say, near the surface. Estimates of
K* in fjord-type circulations place this parameter in the range of 0.1 to
° 2
10 cm /sec (Trites, 1955; Gade, 1968). When K* can be assigned a value
from field measurements or from estimates in comparable inlets, the vertical
velocity can be measured in units of
W* = u*z*/x* (26)
o o o o
where the horizontal scale is given by
x* = u*z
*2/K* . (27)
0000
The analysis is facilitated by replacing the salinity S* with- a nondimen-
sional salinity defect F(x3z) defined by the relation
- a F(x3z) (28)
where a is the dilution factor given by Eqn. (24). With this definition,
the salinity defect at the reference station is equal to unity at the surface
and approaches zero at great depth. It is also assumed that the vertical
eddy diffusivity K* is a constant fraction 6 of the kinematic eddy
H
viscosity N*/p*, where p* is a reference density; values of 6 inferred from
field studies lie in the range of 1 to 10 , with the smaller values corres-
ponding to stronger stratification (Trites, 1955). The nondimensional verti-
cal eddy diffusivity is denoted by K and is, in general, a function of the
nondimensional space coordinates, x and z.
The foregoing developments can be used to show that the nondimensional steady-
state velocity field (u3w) and the salinity defect F are determined by a
27
-------
system similar to the one given by Rattray (1967). In the derivation of the
equations, Coriolis accelerations are neglected, and the hydrostatic and
Boussinesq approximations are used:
Incompressibility:
(bu)x + (bw) = 0 (29)
Equation of Salt:
(buF) + (bwF) = (bKF ) (30)
X Z Z Z
Equation of Horizontal Momentum:
z
(31)
where t.(x) is the free surface height. The overall flux Richardson number
Rf is defined by
Rf = 8 g*c °oz*/u*23
where g* is gravitational acceleration and e is the differential density
parameter from the approximate equation of state
p* , . S*
-fi-= 1 + e j* .
o °°
Upon taking the s-derivative of Eq. (31), one obtains an alternative form in
which the free surface height does not appear:
6(uu + W)=(Ku) + Rf F (32)
a; z z z zz J x
A stream function can be defined in the usual manner, and is conveniently
measured in units of R* so that
i> and bw = i|> .
z •«•
The system is to be solved in the domain z >_ 0 and |a:| ±L*/x^3 say. The
boundary conditions at the surface require specification of the wind stress
T *
W
-Ku =
K*u*p*
O 0 O
= T at 2 = 0
W
28
-------
and the integral mass flux
ty(xaO) = R(x) (33)
At great depths, the velocity components, the vertical salt flux, and the
salinity defect approach zero. The problem statement is supplemented by the
requirement that the integral of the horizontal salt flux over each section of
the inlet is zero. This leads to integral salt flux constraint whose non-
dimensional form is
buFdz = R(x),
where the integral mass flux has been equated to the cumulative runoff.
Now, consider an inlet segment in which the channel breadth b(x) and the
cumulative runoff rate R(x) can be represented approximately as powers of
exponential functions
R(x) = exp (ox) and b(x) = exp ($x).
Introduce new independent variables by
£ '= exp (x) and r\ = z exp (\x) .
Then, the expressions for the equations of motion and the integral salt flux
constraint suggest a search for solutions of the form
ifi = ^f(r)) and F =
provided the eddy viscosity can be expressed as
x. =
A similarity solution is appropriate when the exponents y, v, and X are such
as to permit cancellation of all factors involving £ in the governing equa-
tions. According to Eq- (33) for the integral mass flux, similarity would
require the longitudinal variations of cumulative runoff and surface velocity
to be the same. Since this is not always characteristic of inlet flow, it is
convenient to replace Eq. (33) with an approximate condition. According to
Rattray (1967) , when the freshwater runoff is a small fraction of the total
circulation,
Ka:,o; = 0. (34)
29
-------
With the approximate condition (34), it can be shown that a similarity solu-
tion can be sought when the several exponents of 5 satisfy the relations
v = f (a - 3) - | K
A = -|(a - 8) - j K (35)
and the nondimensional wind stress is given by
T =
0)
N*u*
o o
where the constant T is calculated from the prescribed wind stress at a
central station in the inlet.
In order to proceed, a further assumption is made concerning the spatial
dependence of the eddy viscosity coefficient. The depth variation of turbu-
lent stress inferred in the aforementioned Silver Bay study (McAlister et a1.3
1959), considered together with the observed horizontal velocity shear,
implies that the eddy viscosity coefficient decreases with depth through the
halocline and then may increase somewhat at greater depth. The same trends
have been reported in a study of Olso Fjord by Gade (1968) who observed a
2
minimum in K* (-0.05 cm /sec) in the lower part of the brackish phase. The
2
coefficient K* was observed to increase nearer the surface where it attained
Z 2
values of 1 to 10 cm /sec. Both Gade (1968) and Trites (1955) report a ten-
dency of K* in fjords to increase in the seaward direction. Near the
surface the eddy viscosity may depend in some way upon the wind stress
(Kullenberg, 1971) or upon the character of the flow and density distribution
through the local Richardson number; however, dependence is not determined at
this writing. Since the present study is concerned only with the upper layers,
a simple exponential dependence on depth is assumed
D = exp (-r\).
When the exponent conditions expressed by Eq . (35) are satisfied, the govern-
ing equations reduce to a definite integral and two coupled nonlinear ordinary
differential equations for f and g:
30
-------
f*g dr\ = -1,
and
Hfa' - v/'gr =
where the prime indicates differentiation with respect to n. The boundary
conditions at the surface are
f(0) = 0, gr(O) = 1
and the stress condition gives
The conditions at great depth require
/(-; = /'(«>; = o.
In the paper by Winter (1973), an approximate solution for the stream-function
and the salinity defect is developed from series representations of / and
gs valid in the upper zone:
f = e-" I o /
o m
and
-2r\ _ j m
g = e I, d^n .
o
The reader is referred to Winter (1973) for details of the derivation.
For the purpose of illustration, the aforementioned approximate similarity
solution was applied to segments of Hood Canal and the central basin of Puget
Sound, Washington. Since the main purpose was to demonstrate the method of
analysis, the overall flux Richardson number was set equal to one-half, a
value appropriate to conditions of moderate to high stability (Bowden and
Gilligan, 1971) . Trites (1955) used current and density data in several
British Columbia inlets to estimate Richardson numbers and found large vari-
ations of Ri with depth. However, average values were generally in the range
10 to 50. This finding suggested the assignment of a value of 25 to the over-
all Richardson number Ri = Rf/&. This implies a value for 6 of 1/50, which
31
-------
is consistent with estimates in comparably stratified waters. Trites (1955)
also observed that the width of inlet flow was usually smaller than the
geographical width of the estuary. Hence, in the calculations, values of
b* were estimated by reducing the geographical widths by 25 percent. The
variations of channel width in Hood Canal were judged to be unimportant
(3=0). In the central basin of Puget Sound, the bathymetric charts suggest
a slight general widening in the seaward direction. The longitudinal varia-
tions in cumulative runoff for the central segment of Hood Canal and the
Puget Sound central basin were inferred from the distribution of drainage
basin areas as done in the previous subsection. Values of a and B
appropriate to each inlet segment and a segment of Knight Inlet, British
Columbia, are given in the paper by Winter (1973).
Data from various field studies were adopted for comparisons with the compu-
tations [estimated values of the paramaters b*3 R*3 and K* appropriate
to the midsegment station and time period of each field study are also pre-
sented by Winter (1973)]. The vertical and horizontal length scales can be
calculated from these parameters when the appropriate dilution factors a
are specified. The down-inlet variations in eddy viscosity were inferred
from observed longitudinal variations of surface salinity in Hood Canal. In
the case of Puget Sound, longitudinal variation of surface salinity over the
central basin segment is usually rather slight: about 0.5 parts per thousand
over 40 km, on the average. This value can be used to infer K when runoff
is low to moderate, but leads to small, negative values of K when river
discharge is high. Therefore, K was set equal to zero in the latter
instance.
Figure 10 shows a comparison of the calculated isohaline distribution in Hood
Canal with that observed during the month of April 1953, as reported by
Barlow (1958). Figure 11 shows salinity measurements acquired during two
three-day periods at a mid-channel station in the central basin of Puget
Sound in the spring of 1966. The periods shown correspond to runoff episodes
of high and moderate intensity, respectively. The solid lines in the figure
show the salinity distributions derived from the present theory. Theoretical
horizontal and vertical velocity profiles for the high runoff case are also
shown in the figure. Unfortunately, simultaneous measurements of salinity
32
-------
HOOD CANAL
STATION QP
LO
U>
DUCKABUSH;
RIVER
HAMMA HAMMA
RIVER ;t>
EAGLE
CREEK
'SKOKOMISH
RIVER
Fig. 10. Comparison of measured and calculated isohaline configuration in a longitudinal
section of Hood Canal; the data were acquired at the stations shown in the map.
-------
SALINITY
25 26 27 28 29 30%
HORIZONTAL VELOCITY (CM SECT1)
-10 -50 5 10 15 20
20
M
40
R
-------
and horizontal velocity are unavailable for this particular station and time
of the year. However, rough comparisons can be made with current data
acquired at other central basin stations by Paquette and Barnes (1951) and,
more recently, by Cannon and Laird (1972) during the month of February 1971.
In both sets of measurements, the time-mean surface outflow is of the same
order as that which was calculated, but the measured depth of no mean motion
exceeds the calculated depth by 10 to 15 meters. This latter discrepancy is
probably due to effects associated with an underwater promontory near the
sites of the measurements.
In the two cases examined here, different sets of parameter values might
possibly bring theory and observation into even better agreement. However,
the comparisons in the figures are good enough to indicate that similarity
analyses may be useful when approximate analytic descriptions are needed of
the principal features of flow and density distribution in deep, stratified
inlets.
35
-------
3.3 STEADY GRAVITATIONAL CONVECTION: METHOD OF WEIGHTED RESIDUALS
Despite some limited success achieved with similarity techniques, the proce-
dure suffers from at least two important disadvantages: 1) restrictive
interrelationships are imposed on variables which are normally unrelated, such
as the longitudinal variation of width, runoff, and wind stress,and 2) it is
necessary to solve coupled, nonlinear ordinary differential equations. The
series solutions obtained by Rattray (1967) and Winter (1973) are valid only
in the near-surface zone and are first approximations, at best. An attempt
was initiated in this project to circumvent the aforementioned disadvantages
by using weighted residual techniques. Since the effort is still in progress
at the time of this writing, only the highlights of the approach will be out-
lined here.
The starting point of the analysis is the set of equations describing steady-
state gravitational convection in inlets, as given by Eqs. (29), (30), and
(31). The dependent variables are the salinity defect F(x3z) and the hori-
zontal and vertical velocity components u(x,z) and w(x3z)3 respectively.
These variables are referred to a Cartesian coordinate system whose origin is
near the free surface, and where x is positive seaward along the inlet axis
and z is positive downward. As before, the governing equations are solved
subject to the appropriate boundary conditions at the free surface expressing
continuity of volume, horizontal stress, and salt flux. In the present work,
the flux boundary conditions were applied at 2=0, although the free sur-
face height C(x) was retained in the Equation of Horizontal Momentum. Again,
when the primary interest is in the near-surface circulation, one may neglect
the effects of bottom topography and friction by assuming the inlet to be
infinitely deep, as is done in the similarity analysis:
F3 U3 u j w -*• 0 as z -»• °° . (36)
3
Of course, the assumption of infinite depth is not essential to the applica-
tion of the method. Finally, starting conditions are imposed at an appro-
priate inlet station x.
It is convenient to employ an alternative form of the Horizontal Momentum Equa-
tion when the inlet is infinitely deep. In view of the conditions expressed
by (36), one may take the horizontal gradient associated with the
36
-------
free surface slope to be balanced at great depth by that associated with the
mass density distribution, so that
dz, (37)
where a is a reference value of the fractional salinity excursion from great
depth to the surface. It follows from Eq. (31) that
CO
&(uu + wu ) = (Ku ) - Rf f F dz. (38)
X S Z Z j X
z
The boundary value problem just described can be solved by the weighted resi-
dual method as outlined briefly below. First, the horizontal velocity u(x3z)
and the salinity defect F(x3z) were approximated by trial function expansions
of the following forms:
N
u(x3z) = Ey .(z)f.(x)
2 3 3
F(x3z) = g(x)$(z)
where y . and are prescribed functions of z3 chosen to satisfy the boun-
3
dary conditions at depth. The functions /. and g are undetermined coeffi-
3
cients in the expansions and depend only upon x. An expression for the
vertical velocity w(x3z) is obtained at once by integrating the incompressi-
bility condition:
w(x3z) = v.fsj If. + b~2b'fj
where b(x) is the inlet breadth, the prime denotes differentiation with
respect to X3 and where
z
v .(z) = y .(z)dz.
3 ) 3
00
Next, the above representations of u} W3 and F are substituted into Eqs.
(30) and (38) (Conservation of Salt and Horizontal Momentum, respectively) to
give equations of the general form
37
-------
N
X [/' . (x)A. (fk,g;x, z) ] + g\z)B f/fcj g;x, z)
1 N
•/• y D (T n * *P s*) — J3& ( "r 5>)
1 " is • \ J i j y J***j &/ IltS •* \ ***j &/
•j (7 *C /C
If 4>j Vjj f • and 0 satisfied the equations of motion exactly, the right-
hand side of this last expression would be equal to zero. Since this is not
the case, the combination on the left is equal to some "residual function"
which has been denoted by Re,(x3z). The essence of the method of weighted
residuals is to determine the functions /. and g in such a way that the
3
residual Re is small in some sense. Possible procedures for doing this are
the Method of Moments, Galerkin's Method, Collocation, etc.
In summary, it is necessary to determine N + 1 unknown functions; specifi-
cally, N functions /. and the function g. The unknown free surface
J
height t,(x) can be subsequently obtained from Eq. (37) . For this determi-
nation, we require N + 1 equations. Boundary conditions and the integral
salt flux constraint provide three independent equations. The remaining N -2
equations are obtained by one of the procedures mentioned above. The impor-
tant observation to be made is this: although one is dealing with coupled,
nonlinear, first-order differential equations, the equations are nevertheless
linear in the x- derivatives and can be solved accurately and efficiently
by, say, the Runge-Kutta method; the solution of nonlinear algebraic equations
for derivative values is not necessary. Moreover, it can be shown, after
some algebraic manipulation, that this statement also holds true if turbulent
mixing coefficients are functions of the local Richardson number. This
feature makes the method of weighted residuals particularly attractive as a
mathematical technique for solving deep-inlet flow problems. Figure 12 pre-
sents the results of a sample calculation using the method of weighted
residuals, with inlet parameters appropriate to Knight Inlet, British Columbia.
A Galerkin procedure was used to establish the equations governing the unknown
functions, as described above. Coefficients of eddy viscosity N and diffu-
sion K were assumed to decay exponentially with depth N , K ^ exp(-z/z );
d-1
also Vj = exp(-z/ZQ) (Z/ZQ) and ^ = exp (.Z2/Z2J where z is the
38
-------
AXIAL LOCATION
u>
20km 40km 60km 80km
C
0
20
40
m
60
) 20 30 0 10 20 30 0 10 20 30 0 10 20 3(
- ^
-
^v
SALINITY PROFILES
^^s~
• JI-TI i/^r> ^M- mi-i/^ii-rr
ivii_ i r\\ju ur vision i t
'^— ^
:D RESIDUALS
cvru AMI^C
UP-INLET
Fig. 12. Comparisons of salinity profiles throughout Knight Inlet, B.C., as calculated by
the weighted residual method and by the two-layer analysis. Axial location is
distance upstream of the inner sill.
-------
vertical scale of the gravitational convection zone (Winter, 1973). Starting
conditions were chosen to simulate conditions near the seaward end of the deep
inner basin in Knight Inlet. Computed results over a 60 km segment of the
inner basin are shown in Fig. 12; these results compare favorably with field
observations, as reported by Pickard and Rodgers (1959).
3.4 PERIODIC TIDAL MOTION IN NARROW INLETS
Consider a deep, narrow inlet in which the tidal motion may be analyzed in
terms of one-dimensional shallow water theory. The relevant equations express
conservation of volume, mass, and horizoiital momentum. Because of the periodic
nature of tidal phenomena, a harmonic analysis of the equations of motion
seems particularly attractive. However, the presence of nonlinear terms
introduces complications, so that some kind of approximation is necessary.
In this phase of the modeling work, a new approach was developed to harmonic
analysis of tidal motion based on an iterative numerical expansion of the non-
linear terms into frequency components. The inlet geometry may be fairly
arbitrary, so long as cross-channel motions are relatively unimportant (an
extension to two-dimensional time dependent tidal flow is in progress).
The coordinate system as used in this analysis is illustrated in Fig. 13. The
distance x is measured upstream from the mouth, and the upstream direction
is taken as positive. The velocity u(x3t) (where t is time) is assumed
constant over each cross-section; the height of the water surface above
reference level is denoted by h(x3t). The cross-sectional estuary is A(x)
and we take the effective top breadth as b(x)3 so that the net cross-sec-
tional area at any value of x and t is given by (A + bh) . From shallow
water theory, the equations of motion can be written in the form
Uf + gh + Fu = f (39)
j x J.
h. + b~1(Au) = f (40)
where g is the acceleration of gravity, and where the quantities f^ and
/ represent the effects of friction, wind stress, lateral drainage, and
6
convective acceleration.
F is an appropriately-chosen positive constant, and the term Fu may be
thought of as an artificial friction term, introduced for purposes of
40
-------
Fig. 13. Narrow inlet geometry.
.2
u
0>
U)
LU .1
Q
ID
\-
°
LJ
-I
20 40 60
x (km)
80
100
Fig. 14. Axial variation of velocity mode amplitudes for model inlet.
41
-------
computational stability. The same term is included in f , so that the term
Fu has no net effect, once iterative convergence is complete.
To illustrate the calculation of f^ and / , consider a situation in which
the estuary density p is approximately constant and in which there is no
freshwater inflow. Df
by T ~j one then has
freshwater inflow. Denote the wind stress by T and the frictional stress
w
V
= Fu - uu + + -2-
"1 fu x p(A+bh) pR
/„ = - -r (bhu) (42)
2 b x
where R is the hydraulic radius. As mentioned earlier in Section 3.1, !„
J
may be given by an expression that might be of the Chezy-Manning type:
_c
/
where C is a constant.
Denote the fundamental period by T and the angular frequency by GO = Sir/21.
In the case of some estuaries, a particular sequence of tidal patterns may not
repeat itself for several weeks. Nevertheless, in a great many applications,
it will be adequate to choose T to be some small multiple of the dominant
tidal constituent, such as the period of the M0 tide. (It might be noted
Ct
that competitive time-stepping methods must address a similar question in that
it is necessary to decide how long a time history is to be included in the
calculation.) If the first N modes are of primary interest, then u(xst}
and h(x3t) are approximated by
u (x) N
u(x3t) = ° z- + £« [u (x) oos nut + T (x) sin nut] (43)
Ci Yt~* -L tk i*
h (x) N
h(x3t) = -2-s — + Z [h(x) cos nut + s(x) sin nut] (44)
& n=l n n
where u (x), r (x) 3 h fa), sn^-x^ for n ~ °> 1> 2»"-->^ are x-depen-
dent expansion coefficients. These coefficients are determined by use of
Eqs. (39) and (40), together with f^ and f^ defined as in Eqs. (41) and
(42).
42
-------
The method used is one of successive approximation, and proceeds as follows,
Suppose that at any stage of the iteration approximate values for these
expansion coefficents have been determined. Then, by use of Eqs. (43) and
(44) each of u and h can be calculated, and can in turn be used to compute
/- and / (within the current degree of approximation) for any chosen
values of x and t. But if one can calculate /7 and /_, then these
quantities can also be expanded in a Fourier series, via
a (x) N
f~(x3t) = —5— + z [a (x) cos nut + b (x) sin nut]
J- ft n—J. n n
a. (x) N
f9(x,t) = —-— + Z [a (x) cost n®b + B (x) sin nu>c]
& u n—j. n YI
For least mean square error, we require, for n = 0, 1, 2,...,N3
2 (T 2 (T
anx) = ? f^x,*) cos nwt dt and bn(x) = - f1(x,t) sin nut dt
O' o'
with analogous formulas for a (x) and B (x). These coefficients, a (x),
b (x)3 a (x)3 B (x) are determined by direct numerical integration (for
/fr fL ft
periodic functions, the trapezoidal rule is optimal) for those values of x
which occur as mesh points in the sequel. It is, of course, only necessary
to evaluate /? and /„ for those values of t which arise in this numeri-
cal integration.
Having now determined a (x)3 b (x)3 a (x)3 B (x)3 all terms in Eqs.
(39) and (40) are replaced by their Fourier expansions, and terms of the
same frequency are equated to obtain a system of coupled first-order diffe-
rential equations for the unknown variables u , ~h , u , h , r, and s .
^ o o n' n n n
So far as the boundary conditions are concerned, some conditions are given at
one end of the inlet, and some at the other end. Thus, at x = 0, the tidal
fluctuation is imposed, so that each of h (0)3 s (0) is known for n = 0,
1, 2,..., N. At the upstream limit x = L3 we take the total flow rate Q
as prescribed, where
Q = u(L3t)[S(L) + b(L)h(L3t)] (45)
Since h(L3t) is unknown, it is necessary to include the determination of
u(L3t) as part of the iterative process. At each iteration stage, the
43
-------
current value of h(L3t) is used to compute a best value for u(.L3t).3 which
is again expanded in Fourier terms to give current values for u (L) 3 v (.L) 3
fi III
n = 0, 1,.,,, #, and so to provide upstream boundary conditions for the
modal equations. For a complete discussion of the modal equations and the
method of solution, the reader is referred to a paper by Pearson and Winter
(1976). In that paper, it is shown that a particular combination of the first-
order modal equations yields second-order equations, which may be discretized
so as to result in tridiagonal coefficient matrices, making two-sweep elimi-
nation feasible.
The calculation of the modal coefficients is now repeated iteratively until
the mesh-point values of the coefficients no longer change significantly. If
nonlinearities are weak, one or two such iterations may be adequate; if
strong, as many as 15 or more may be required. It is only in the latter case
that we need assign to F a value different from zero.
In the paper by Pearson and Winter (1976), the procedure is illustrated by an
application to a 100 km segment of a river in communication with the sea.
Since nonlinearities were large in that example, the problem posed consider-
able challenge to the method. An accurate result was obtained (a comparison
was made with results from a time-stepping solution) and convergence was
complete after 10 iterations (90 seconds on a CDC 6400).
As another example, consider a deep inlet with a sill, where the bathymetry is
described by
b(x) = 2000 - 0.015* (x in meters)
and A(x) = b(x){200 - 0.0016*} [l - 0.75 expf K" 000°°°
r]
for 0 < x < 100,000 meters. Suppose that all of h (0) and S(0) are set
— Yl fl
equal to zero, except that s^O) = 1; also, set Q = -315 m3/sec. The time
profiles of h(x3t) for various values of x are now not too dissimilar to
that of h(03t)3 only the first two modes are significant. The effect of the
sill (at x = 30,000) is seen most clearly in a plot of the modal components
of u(x3t) as given in Fig. (14), For this problem, only 1 iteration (5
seconds on a CDC 6400) was required; the value of F was set equal to zero.
Finally, it should be pointed out that the method can be applied to situations
44
-------
in which the inlet is branched. A description of the necessary modifications
of the procedure is given by Pearson and Winter (1976).
45
-------
SECTION 4
HYDRAULIC MODEL STUDIES OF PUGET SOUND
Puget Sound is a system of fjord-type inlets with complicated tidal circula-
tion patterns induced by irregular bathymetry and shoreline. Since its
dynamic tidal behavior is so complex, reliable qualitative and quantitative
descriptions are often very difficult to obtain by field observations alone
without intensive and costly effort. This suggests that studies of tidal
motions with the Puget Sound hydraulic model could provide a valuable guide
for efficient design of field studies and/or monitoring activities that may
be indicated. Tidal flows are important in Puget Sound because they are com-
parable with (and in some regions greater than) the mean flow (Cannon and
Laird, 1972). In nearly all parts of the Sound, a large fraction of the
energy associated with the fluid motion is contained in the tidal mode.
Previous studies have demonstrated that hydraulic model tidal currents,
circulation, and water exchange are generally representative of the prototype
and will provide a reliable means of investigating gross dynamic characteris-
tics within a relatively short time (Rattray and Lincoln, 1955). Before
proceeding with a discussion of the model studies, however, a brief descrip-
tion of the model itself is in order.
4.1 MODEL DESCRIPTION AND LIMITATIONS
The "Puget Sound Model" is a small working model of the entire system of
inland waterways extending south from the junctions with the Strait of Juan
de Fuca and Rosario Strait (see Fig. 15). The model has a horizontal scale
of 1:40,000 or 25 mm per m (1.82 in./naut. mile, 1,58 in. per stat. mile) and
a vertical scale of 1:1152 or 1 meter - 0.868 mm (1 foot = 0.0087 in.). The
model thus has a vertical exaggeration of 35:1. These scales correspond to a
time scale of 1:1,178 or 3.056 seconds per hour.
46
-------
45' 122 °3O' 15'
15' I23°00'
n EVERETT
f) SHILSHOLE
WEST POINT
FOURMILE ROCK
ELLIOT BAY
DUWAMISH HEAD
DUWAMISH RIVER
COMMENCEMENT
DANA PASSAGE
I23°00 45'
I22°30 15'
Fig. 15. Hydraulic model coverage (outlined by dashed line) and
the locations of the dye discharge experiments.
47
-------
Tides in the model are controlled by a Kelvin-type mechanical tide computer
that provides continuous summation of six cosine functions representing
the six major tide constituents. This analog computer controls the vertical
motion of a plunger which generates the tides by displacement of the appro-
priate volume of water in the model headbox, which is located in the inner
end of the Strait of Juan de Fuca. The tide computer provides the capability
of generating model tides for any specific calendar time period which agree
with predicted tide heights to within 0.15 scale meters (0.5 scale foot).
The model operates as a stratified system to provide a representation of the
natural density gradients within Puget Sound which drive the net circulation.
An ocean-tank provides a source of constant salinity water that is recircu-
lated between the ocean tank and the headbox. Fresh water is introduced at
appropriate rates at the sites of the eleven major rivers discharging into
Puget Sound. River discharge is manually controlled and indicated by indivi-
dual precision flow meters.
Not all physical phenomena can be adequately scaled in the model, and there
are a number of constraints on the interpretations of the results. These
limitations are as follows:
1) Wind stress effects cannot be scaled properly, thus model observa-
tions are representative of calm wind conditions only. This is
perhaps the most important limitation because surface transport and
mixing of the water by winds can be significant factors in dispersal
processes. In the prototype, winds will induce wave action and
exert stresses on the free surface that will modify near-surface
flow characteristics.
2) Surface tension cannot be eliminated or even appreciably reduced.
This effect distorts representation of flows just at the surface,
close to the shoreline, and in very shallow areas.
3) Water viscosity cannot be reduced to scale. This results in a
reduction of small-scale turbulence and mixing, and slightly retards
flow through small channels at times of strong currents. Various
considerations, such as. the requirement of representative density
gradients, make the use of a lower-viscosity fluid impractical.
48
-------
4) Because of the vertical exaggeration of 35:1, required for dynamic
similitude, horizontal flows are quantitative but vertical motion
is only qualitative.
Two types of studies were performed with the hydraulic model in this phase
of the project. The first study was an attempt to define tidal current
patterns throughout the Sound, and was carried out by photographing the
hydraulic model water surface motions as revealed by styrofoam powder.
The second was a model study of dye-stream dispersal characteristics in
selected locations throughout the Sound, with special attention given to
dredge spoil disposal sites. These studies are described in separate sub-
sections below.
4.2 SURFACE TIDAL CURRENTS IN PUGET SOUND
Eight mosaic photographs of the entire Puget Sound model surface were
assembled to indicate the surface current distribution for eight stages of
a hypothetical, but representative tide. The direction and magnitude of the
flow were indicated in the photographs as white "stream lines", with the
length of the line proportional to the speed. Graphs were affixed to each
photograph showing the stage of the Seattle tide at the time of the photo-
graph. Copies of the mosaic photographs were provided to the Region X office
and the Project Officer of EPA. For the purpose of this report, a hand-drawn
replication of a part of the mosaic for one stage of the tide is provided as
Fig. 16. A complete set of such surface tidal current patterns is being pre-
pared for publication at the time of this writing under the sponsorship of
Washington Sea Grant.
In the present studies, recording was done photographically on 35 mm Plus-X
black and white film. To obtain the tidal current flow lines, white or light-
colored particles were photographed against a dark background. The dark
background was achieved by coloring the water an intense red with Congo Red
dye and attaching a green filter (X-l) to the camera. The dye-filter combi-
nation resulted in the water photographing as. black, giving high contrast with
the white floating particles.
49
-------
Fig. 16. Hand-drawn replication of part of the tidal mosaic for one stage
of the tide; direction and magnitude of surface tidal current is
indicated by orientation and length of streamline segments.
50
-------
Fig. 17. Map of Puget Sound showing the measured model tides;
dots on the tide curves correspond to the time of the
eight streamline photographs.
51
-------
To mark the surface movement, we experimented with aluminum dust, lycopodium
powder, pollen, and finely divided styrofoam. Of these materials, the pow-
dered styrofoam appeared to be most suitable for the surface floating
particles.
To simplify the experimental procedures, repeating tides with semidiurnal
and diurnal frequencies were used in the model. The amplitudes and phases
of these two tidal components were computed to produce a representative mixed
tide at Seattle. The resulting tide heights, as recorded in the model for
Seattle and other locations around Puget Sound, are illustrated in Fig. 17.
Photographs of the model were taken vertically from a height of about 2 m
above the water level. Because of the limited spatial coverage of the photo-
graph, fourteen separate camera locations were required to cover the entire
area of the model. At each location, 2-second time exposures were made
(corresponding to 40 minutes of model time) for each of eight stages of the
tide. The beginnings of the exposures were chosen to correspond to the
times of highs, lows, and maximum slopes of the tide curve at Seattle. These
times are shown in Fig. 18, Because tides at other sites within Puget Sound
are slightly out of phase with respect to Seattle, the exposure times are not
synchronized to local lows, highs, and maximum flows. The choice of repeat-
ing tides allowed us to run the model continuously and to take the eight tidal
sequence photographs at each of the different locations without restarting
the natural tide sequence in the model.
All river outflows were adjusted to model yearly mean discharge rates and
were held constant for the duration of the study. The "ocean" salinity was
held constant at 16%; previous experience has indicated that the vertical
salinity profile better approximates the prototype when the model "ocean"
salinity is maintained at this reduced level.
As mentioned earlier, the photographs showing the streamlines for each of the
eight stages of the tide were assembled to produce eight mosaics of the tidal
currents in Puget Sound, The original negatives for these photographs are on
file at the Department of Oceanography, University of Washington, and enlarged,
detailed prints of selected locations and specific tide stages can be supplied
at cost. Some of the major flow features which emerged from this study are
described below.
52
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SEATTLE TIDE
4 r-
3
m 2
I
0
3.7 7.4 10.0 12.6 15 17.3 21.1
hrs
Fig. 18. Measured model tide at Seattle; the times correspond
to the beginnings of each of the eight streamline
photographs.
-------
During the two high tides and the two low tides in the cycle, numerous eddies
are present in many areas of Puget Sound. Some are formed behind the minor
points, and others which were formed during the preceding flows around the
major projections, are carried into mid-channel by the time of slack water.
At slack water, a few of the channels still show evidence of residual flows.
With the ebbs and the floods, major eddies exist only behind the larger
promontories, and most of the remaining streamlines are directed nearly para-
llel to the shorelines of the channels. At the heads of some of the embay-
ments and inlets, there is little indication of motion even during the major
floods and ebbs. Other areas—such as the stretch between Deception Pass and
Possession Sound—show motions which are less during the floods and ebbs than
during the high and low tides at Seattle, indicating a phase lag in the flow
characteristics.
One very important characteristic of the model is that the major circulation
features—such as the dominant eddies and the direction of magnitude of the
stream lines—are remarkably repeatable. This result was to be expected, of
course; otherwise it would not have been possible to conduct a study of the
periodic tidal circulation. It is encouraging, though, that the flow features
which are random and would be expected to vary with each successive
identical tide stage, are of a smaller scale than the dominant features in the
tidal flow charts.
One of the objectives of this study was to identify areas in the model where
there was very little tidal flow. For practical purposes, these areas were
considered to be the ones where a two-second time exposure of the styrofoam
particles did not produce an image with an obvious direction of movement.
It appears, then, from the results that in areas such as Penn Cove, Holmes
Harbor, Elliott Bay, Carr Inlet, the heads of Case Inlet and Dabob Bay, and
the southern part of Hood Canal from the Great Bend to Lynch Cove, there is
relatively sluggish flow at any stage of the tide. The results from very
shallow areas may be in doubt because of experimental difficulties due to
capillary action.
As for the remainder of Puget Sound (i,e., the major portion where we find
significant water movement), we were interested in distinguishing regions
54
-------
with flow characteristics which are similar across the channel from regions
where the flow changes across the width of the channel. There are few loca-
tions that appear to have flows that are uniform across the channel at all
stages of the tide. One of these locations is the central portion of Hood
Canal. Another is the middle portion of Saratoga Passage. By far the larger
part of the Sound is characterized by tidal flows which are not uniform across
the channel. These latter flows fall into two categories: 1) those which
are non-uniform at any instant of time across the channel but which might be
more uniform if the higher frequency variations are removed, and 2) those
which vary across the channel even if high frequencies are filtered out.
One major source of cross-channel variation is the system of eddies which
covers much of Puget Sound during periods of slack water. Some of these
eddies are obviously associated with nearby physical features in the shore-
line or bathymetry, while other appear to be more randomly distributed.
Quite possibly, if the motions of these eddies were averaged over a tidal day,
some of them would show cross-channel uniformity, while others would show a
variation in mean flow from one shore to the other.
There are two other obvious sources of cross-channel variability in the flow:
curvature in the channel configuration and physical features which cause the
ebb and flow patterns to be different. A striking example of the latter is
seen in the portion of the Central Basin just north of Vashon Island. In that
region, the channel configuration is such that floods tend to be directed into
East Passage. Ebbs into this channel from Colvos Passage have greater flow
speeds than the component coming from East Passage. The result of this higher
velocity flow through Colvos Passage is that during slack water following an
ebb in the rest of the system, a northward flowing core of water persists
through the central portion of the channel west of Alki Point. This tends to
bias the flow in that region to the north and, therefore, creates a flow which
is not uniform across the channel. Similar results are likely to be found in
other confluent regions with high flow velocities.
Three other features which were observed in the photographs of tidal currents
are worthy of Special mention. These include an apparent asymetric flow
around Vashon Island, a noticeable difference in the timing of the tidal
currents between Deception Pass and Possession Sound as compared to the
55
-------
currents in the rest of the area, and an interesting feature in the surface
currents in Elliott Bay. As to the first of these, floods tended to be
directed towards East Passage on the east side of Vashon Island, while
stronger currents were found in Colvos Passage during ebbs (as already
mentioned). The observations indicate that, during floods, southerly speeds
in East Passage and Colvos Passage are comparable; during ebbs, the northerly
speeds in Colvos Passage are larger; at high tide there is residual flood
movement in East Passage; and at low tide there is residual northward ebb flow
in Colvos Passage. The obvious interpretation of these results is that there
is a clockwise flow around Vashon Island. Release of dye into the water around
Vashon Island appears to confirm this interpretation.
Another flow feature that emerges from the photographs is that the timing of
tidal currents in the Skagit Bay channel and in Saratoga Passage appear to be
different from those in the principal channels of Puget Sound. The Deception
Pass and Skagit Bay areas show little movement at times when flows in the main
channels are near their maxima. This difference with respect to the major
portion of the system is caused by a phase lag between tides in Rosario Strait
and those in the vicinity of Skagit Bay. The phase lag is due to the greater
transit time of the tide around Whidbey Island and produces a difference in
water level between those two areas. Consequently, the currents are the
result of a hydraulic head, which is not directly related to the current be-
havior of the main channel. Furthermore, these currents are strongly affected
by the changing character of the tidal sequences.
Finally, it appears that, during floods, water is being drawn out of Elliott Bay
around Duwamish Head and, during ebbs, water flows into Elliott Bay via the
same route. Since the tide height in the bay is increasing during a flood and
decreasing during an ebb, water must be flowing into and out of the bay at
depth during those times. In the study described in the next section, it was
found that surface waters do indeed exit via Duwamish Head during floods and
enter there during ebbs. It was also found that there is inward transport of
deep water during floods and that there is a small amount of surface water
flowing into Elliott Bay during a flood along the east side of the bay. This
flow is not evident in the tidal current photographs because of its low velo-
city.
56
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4.3 DYE STREAM DISPERSAL CHARACTERISTICS IN THE PUGET SOUND MODEL
In these studies colored dye was Injected continuously into the water at
various locations, and the movement of the dye was recorded photographically
on 16 mm motion picture film. Surface flows were observed by using a low
specific gravity dye solution that initially would be retained in the near-
surface layer. For locations at which dye was injected at depth or near
bottom, the specific gravity of the dye solution was adjusted to be as nearly
neutrally buoyant as possible. In many cases, vertical movement and mixing
caused dye to be dispersed over an appreciable depth range. Vertical disper-
sion, however, is not readily apparent on the photographic record because the
photographs were taken vertically from above the model. Where vertical move-
ment is subsequently described, it is the result of visual observations made
during the course of the run.
The motion of the dye was photographed with a Bolex 16 mm movie camera mounted
directly above the model. Photographs were taken at approximately one frame
per second, or with reference to the model time scale, one frame every 20
minutes of model time. Runs were continued for at least ten model days. For
time reference, a moving tape showing the tide marigram, date, and time was
also included in the photograph. The tide stage can be determined from that
marigram which moves past an index mark at a rate equal to the model tirce scale.
Because of anticipated changes in the rate of mixing of water in Puget Sound
as the tidal amplitudes change, studies were made during periods representing
spring and neap tides. The period of May 1 through May 10, 1973, was chosen
for spring tides, and that of October 2 through October 11, 1973, was selected
for the neap tides. The tide marigrams at Seattle for these two periods are
shown in Figs. 19 and 20, respectively. The tides for each complete month are
included to illustrate the manner in which the tide character progressively
changes.
To investigate the effect of different river discharge rates, runs for selected
locations were made with rivers set at the lowest monthly average discharge
and the highest monthly average discharge. Discharge rates for the eleven
major rivers included in the model are listed in Table 1. These flows have
been adjusted to compensate for smaller streams and ungaged discharge into
57
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MAY 1973
Ui
00
Fig. 19. Representative spring tides at Seattle (May 1973, days 1 through 10).
OCTOBER 1973
Fig. 20. Representative neap tides at Seattle (October 1973, days 2 through 11)
-------
Table 1. Discharge rates for the major Puget Sound rivers.
Discharge Rate
River Highest Month Average Lowest Month Average
, 3 -1.
(m sec )
361
113
42
149
50
78
39
31
10
6
8
Note: These values are 15-year averages and have been adjusted for both
ungaged flow and for discharge of the smaller streams flowing into
the basins receiving the major rivers.
Skagit
Snohomish
Stillaguamish
Puyallup
Duwamish
Nisqually
Skokomish
Cedar
(Lake Washington)
Dosewallips
Hamma Hamma
Duckabush
( 3 -IN
(m sec )
1045
685
241
264
139
213
125
85
34
20
30
59
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areas contiguous to the river drainage basins. It should be noted that short-
period variation can result in both higher and lower rates than used in the
study. Also, yearly variability may affect peak and minimum flows.
The locations for these studies were chosen partly because of practical con-
siderations (potential pollution sites) and partly to obtain representation
of different types of systems. West Point and Elliott Bay were chosen for
intensive study; the first represents a deep inlet channel with bathymetrically
induced mixing, and the other represents a quieter embayment at the head of an
estuary. Both are potentially sites of environmental stress. In addition,
studies were conducted at a number of bottom locations in Puget Sound because
of their importance as dredge spoil sites. The locations of these sites are
also shown in Fig. 15.
Because of the complexity of the bathymetry and channel configuration in Puget
Sound, it is difficult to generalize about the dynamic behavior within the
whole system. Even though one observes outward net transport in the upper
layer and inward net transport at depth in most areas, local exceptions do
exist. Although the details of circulation patterns depend upon locations,
certain dominant features are observed for locations with similar topography.
Except for areas very close to river mouths with freshwater plumes, tidal
currents usually are larger than the density-driven circulation in the model.
The principal factors determining the characteristics of these strong tidal
currents are shoreline configuration and bathymetry; their effects on the
water movement may extend for distances of several kilometers. In a number of
places, promontories or "points" extend into the main channel (Bush Point, West
Point, Alki Point, Pulley Point), and tidal flow past these promontories
results in the formation of large-scale eddies or gyres that alternate with
ebb and flood currents. These eddies are very effective in promoting cross-
channel transport of water. For example, an eddy formed downstream of a point
may be carried toward midchannel when the tidal currents reverse. Usually
this behavior will occur during each flood and ebb, and, while the basic
pattern tends to repeat, the size of the eddy and it subsequent behavior will
be influenced by the variable ranges of the successive tides. Occasionally,
during periods of very small tides, such as may occur during neap tides, eddy
formation may be weak or may not occur. This effect, somewhat modified, also
60
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occurs at depth since surface features are reflected in the deeper bathymetry.
The direction and mean speed of flow at a fixed depth has been observed to
vary with the magnitude of river discharge. Furthermore, the behavior of the
mean flow appears to depend to some extent on the tide type.
In the following paragraphs, we describe the general results from West Point,
Elliott Bay, and the dredge disposal sites. The interested reader should
refer to the 16 mm motion picture record for critical details.
West Point
At West Point, dye was injected into the water from three near-bottom loca-
tions on the eastern side of the channel. These positions, situated on the
ridge or buttress extending into the water from West Point and at the surface,
73 m, and 165 m were chosen to simulate discharges above, at, and below the
depth of the existing sewage treatment plant outfall (see Fig. 21). Studies
were conducted for both spring and neap tides and at high and low river dis-
charge over a total of 12 runs.
It was found that in most instances dye released at all three depths dispersed
across the channel within a longitudinal distance from the injection site equal
to two channel widths. This dispersion is due to the lateral motions induced
by the protrusion of West Point into the channel and depends on the magnitude
of the tidal currents. Spring tides result in greater lateral motions than
neap tides. Dispersion near the surface was essentially in a horizontal plane;
the large vertical density gradients effectively inhibited vertical mixing.
At depth, the dominant mixing was roughly parallel to equal density surfaces,
but mixing across density interfaces also occurred. Mean transport of the dye
over 10 days was seaward at the surface and even at 73 m, but it was directed
landward at 165 m. Daily mean transport deviated from the long-term mean
pattern on some occasions possibly because of slow changes in the volume of
water in the fjord from long period variables. For instance, there was no
northerly surface transport during the first part of the neap tide period with
low river runoff due to an apparent accumulation of water in the basin. There
were also occasional variations in the transport which are presently unex-
plained. Qualitatively, larger mean transports were observed during high
river discharge than during low river discharge.
61
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The sharp protrusion of West Point into the channel, along with the relatively
large tidal currents at the surface, result in frequent formation of clock-
wise and counter-clockwise eddies behind the point during ebb and flood tides,
respectively. Upon reversal of the tide, these eddies would be advected into
mid-channel. Also, because of the configuration of West Point and its asso-
ciated bathymetry, which tends to accelerate the flows on the east side of the
channel, the currents on that side were stronger than those on the west during
both ebb and flood. Even though cross-channel mixing occurred regularly dur-
ing the spring tides, the weaker currents accompanying neap tides were often
insufficient to disperse the dye across the width of the channel before the
dye concentration diminished to the point where it was no longer visible.
There were also occasions during small tide ranges when the slower flows did
not produce back eddies behind the point, but merely produced much slower
flowing water in place of the eddies.
At 73 m, the combination of lower tidal velocities and more gradual curvature
of the West Point buttress results in less turbulent flow along the sides.
Whereas the point frequently sheds eddies in the surface currents, at 73 m a
reverse flowing eddy is rarely developed. Even though the flow is apparently
less turbulent at this depth because of the smaller channel width, dye was
consistently mixed across the channel. The mean transport at this depth was
northward, as in the surface, but it appears to be of lower magnitude.
The deepest discharge site at 165 m also showed apparent cross channel motions;
though, here, like the runs made at mid-depth, distinct eddies were not found.
Unlike the two shallower discharge sites, the mean transport of dye released
at this depth was landward to the south.
Elliott Bay
Elliott Bay, in contrast to West Point, is a relatively quiet body of water,
closed at one end with a river discharging into its head. The circulation
in this bay is complicated due—among other things—to the fact that it is
joined to the side of a major channel, has two distributaries of the Duwamish
River discharging into it, and has a pair of submarine canyons located on
either side of it. In order to describe some of the features of the circu-
lation and to study the residence time of water in Elliott Bay, dye discharges
62
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were injected into six different locations within the bay (see Fig. 21).
Three near-bottom sites were chosen: one in each of the two submarine canyons
and one at a slightly greater depth (Duwamish Head dredge disposal site). In
addition, three near-surface discharge sites were also chosen: one in the
Duwamish River, one at the southern end of the Seattle waterfront, and a third
one at Smith Cove on the northern end of the waterfront.
The results of the studies at these sites, which were conducted for a combi-
nation of river states and tide types, provide a set of descriptions showing
dye distributions of some complexity. On the average, dye injected at depth
was carried inward and upward until it reached to within about 37 m of the
surface; whereupon, it turned seaward and was ultimately dispersed either
past Smith Cove or around Duwamish Head. Dye which upwelled through the
West Waterway was always dispersed around Duwamish Head. Dye injected in the
eastern submarine canyon and that introduced at the waterfront normally was
removed via the Seattle waterfront even though it did disperse throughout
Elliott Bay and exit via Duwamish Head on some occasions. Dispersal of dye
within Elliott Bay can be rather slow with observed residence times of up to
3.5 days for dye flowing north along the waterfront. Once the dye in the bay
passes an imaginary line extending roughly from Smith Cove to Duwamish Head,
it was dispersed more rapidly by the strong tidal currents in the Central
Basin of Puget Sound. As expected, the accumulation of dye in Elliott Bay
was greatest during low river runoff.
The limited number of observations, the variability in the rate of dye dis-
charge, and the differing distribution of water between the east and west
channels of the Duwamish River preclude our making definitive statements
about circulation patterns in Elliott Bay. One possible description of the
circulation in the bay, which is consistent with the observations, is as
follows: Generally, we observe a standard estuarine gravitational convection
pattern with saline water intruding at depth and a brackish zone flowing out
near the surface. Because of the distributed source waters and the width of
the bay, the surface zone in Elliott Bay consists of two flows, with the core
of the discharge from the higher runoff West Waterway flowing along the west
side of the bay and the core of the much lower discharge East Waterway moving
along the Seattle waterfront. Superimposed on the mean circulation is a
63
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tide-induced circulation. On flood tides, the circulation is clockwise with
water moving into the bay in the east and flowing out around Duwamish Head.
During ebb tides, the directions are reversed, and a counter-clockwise flow
prevails. Because of the configuration of Elliott Bay relative to the
Central Basin, the flow in Elliott Bay is stronger during flood, and there is
net clockwise, mean tidal flow. The resultant of the tidal and gravitational
flow is a net outward flow at the surface with more water flowing out around
Duwamish Head than past Smith Cove. Whether water from the eastern part of
the bay flows north along the Seattle waterfront or is incorporated into the
flow past Duwamish Head depends upon the relative magnitude of the river
discharges and tidal flows. Water is most likely to flow out past Smith Cove
for combinations of low tidal currents and high river discharges. Conversely,
for high tidal currents and low or no river discharge, there is most probably
no outward transport past Smith Cove.
The results from the near-bottom injection sites in the eastern canyon (Elliott
Bay 1, 119 m), in the western canyon (Elliott Bay 2, 82 m), and at depth
(Duwamish Head dredge disposal site, 137 m) are consistent with the general
features of the circulation as proposed in the last paragraph. Observations
from the Duwamish Head disposal site showed an upwelling of the dye and subse-
quent dispersion from the outer parts of Elliott Bay into the Central Basin.
Because of the low dye concentrations, it was difficult to describe the sur-
face behavior of the dye from this injection site. The two sites in the
submarine canyons .showed the expected upwelling of water from the bottom into
the near surface layer. The dye appeared routinely to reach to within 37-55 m
of the surface before being transported outward in the surface flow. Dye that
remained in Elliott Bay for extended periods of time had the chance to adjust
further its density to that of the near surface water and was observed within
7-11 m of the surface. Dye originating in the western canyon was consistently
swept outward past Duwamish Head. Dye injected into the eastern canyon was
removed along the Seattle waterfront during high river runoff and was observed
to disperse throughout Elliott Bay and to be dissipated around Duwamish Head
during neap tides and low river discharge. Similarly, for low river discharge
and spring tides, the dye which reached the surface was swept around the bay
and out past Duwamish Head.
64
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Fig. 21. Dye discharge locations near Seattle; solid triangles
are dredge disposal sites.
65
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The near-surface discharge sites, like the near-bottom ones, corroborated
the proposed description of the circulation. Dye introduced into the
Duwamish River and dye injected along the southern end of the Seattle water-
front behaved in a predictable manner. In all cases, river water discharging
from the West Waterway of the Duwamish into the western half of Elliott Bay
flowed along the western shore and was dispersed around Duwamish Head. For
neap tides with the related weaker tidal currents with both high and low
river discharge, water from the East Waterway flowed along the waterfront
and past Smith Cove. With spring tides and low river discharge, the average
tidal current was stronger along the eastern shore than the river-induced flow;
so, water from the East Waterway which migrated north along the waterfront was
incorporated into the tidal flow and was swept back into the bay until it
merged with that from the West Waterway and ultimately dispersed around
Duwamish Head. With spring tides and high river discharge, there was not
enough dyed water flowing from the East Waterway to determine whether the river
water flowed out past Smith Cove or Duwamish Head. Given the other observations
of the Duwamish flow, either case would seem reasonable. Water injected at
the Seattle waterfront behaved in a similar manner. For neap tides, dye was
transported north along the waterfront and past Smith Cove. For spring tides
and low river discharge, as with Duwamish River water, the northerly moving
dye was incorporated into the clockwise flow and finally carried around the
bay and out past Duwamish Head. In this case, the results from the spring
tide, high river discharge run showed dye moving north and out past Smith Cove.
Near surface injections were made at Smith Cove for both tide types and low
river discharge. This dye was mainly swept along by the stronger currents of
the Central Basin and was dispersed both around Alki Point and around West
Point. However, there was some dye intrusion part-way into the central part
of Elliott Bay. Since the core of the river discharge mainly held to the
sides of the bay, it is reasonable to find that water from Smith Cove intruded
most strongly into the central part of the bay.
Dredge Disposal Sites
Model studies of the dredge spoil disposal sites were designed to investigate
x
the currents in the vicinity of the sites as well as the pathways taken by the
66
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water after it leaves the immediate area. At each of the sites, dye was
injected into the water close to the bottom. It must be stressed that these
studies do not address the question of movement of the spoils themselves.
However, any attempt to predict the movement of the dredge spoils, both as
they were settling towards the bottom and after incorporation into the
sediment, must be based on a knowledge of the water movement nearby.
The results of the near-bottom dye injections may be separated into three
categories. Sites located on the sides of the channels, such as Fourmile
Rock, Shilshole, and Everett, have circulation patterns parallel to the bottom
contours. Duwamish Head and the two locations in Commencement Bay display a
more typical estuarine-type circulation with a tendency for the bottom water
to flow landward before being incorporated into the near-surface layer and
dissipated. Finally, the site at Dana Passage shows high dispersal of the
dye because of the turbulent flows through that narrow passage. There, even
though the accumulation of dye at the discharge site is negligible, traces of
dye could be seen in all of the nearby inlets. Because of the small effects
of changing river discharge on the near-bottom flows, the studies at the
dredge disposal sites were conducted for high river discharge only but for
both spring and neap tides.
Results of the study at Duwamish Head have already been discussed briefly in
the description of Elliott Bay. The two sites in Commencement Bay (Fig. 22)
located in the inner (110 m) and outer (165 m) parts of the Bay differ from
Duwamish Head (and other Elliott Bay locations) most notably in having larger
tidal excursion and mixing. There, especially for spring tides and the outer
site, dye from the injector was often drawn into the main channel and dispersed
within one tide cycle. This enhanced circulation and mixing is due to the
bathymetry and shoreline of the area adjacent to Commencement Bay. Transport
in East Passage, just outside of the Bay, is unusual in that it is southward
both at depth and at the surface.
During floods, water in East Passage moved south as surface water in Commence-
ment Bay, and deep upwelled water in this area moved into and through the
Tacoma Narrows. Only very weak southerly currents developed in Colvos Passage
at this time. During ebbs, the circulation became more complex because the
67
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VASHON •.•:'
ISLAND
DA
COMMENCEMENT
BAY
Fig. 22. Dye discharge locations at two dredge disposal sites
in Commencement Bay.
68
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configuration of the Narrows directed flow from that channel toward the
southern end of Colvos Passage. During the first part of large ebbs strong
turbulence from the Narrows was diverted eastward around the southern end of
Vashon Island. This turbulence was carried into Commencement Bay where it
resulted in strong mixing within the entire water column. As the ebb con-
tinued, a strong northerly flow in Colvos Passage developed that carried the
major part of the discharge from the Narrows. The strongly turbulent flow
eastward into Commencement Bay decreased as the flow through Colvos Passage
increased. Water in Commencement Bay rarely was carried north in East
Passage for more than a mile or two beyond Browns Point. The result of these
flow characteristics was a net clockwise circulation around Vashon Island.
Dye injected during spring tides at Commencement Bay—Site One, located near
the head of the bay, produced a filamentous cloud that reached inward to the
head of the bay at depth and outward toward the mouth opposite Browns Point.
The outward edge of the cloud was rapidly distorted by flood flow past the
shoulder of Browns Point and to a greater extent by the turbulence resulting
from the strong outflow from the Narrows during the previous ebb. Periodic
upwelling along the steep slope at the head of the bay was observed and
appeared to reach its maximum excursion at the end of the flood. During ebbs,
the upwelled water tended to subside and move away from the head of the bay.
Horizontal excursion during the large tide ranges was about one mile. The
upwelling behavior was primarily oscillatory rather than continuous. Upwell-
ing of deep water along the shoaling bottom leading to the Narrows occurred
during floods and carried dye from the outer portions of the accumulated cloud
into the channel, and the dye was subsequently dispersed by the turbulent flow
through the Narrows.
In contrast to spring tides, neap tides were markedly less efficient in dis-
persion and transport of dye at this site. Dye tended to accumulate as an
irregular cloud at depth near the injection site, with small oscillations of
about 0.5 km occurring during the larger ranges of the early part of the period.
A small amount of turbulence and upwelling resulted in some dispersion toward
the head of the bay and outward to form an elongated cloud about 2.3 km long.
69
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Appreciable outward transport toward the Narrows did not occur until later
in the time period when the character of the tidal cycle produced more nearly
equal semidiurnal ranges. By October 7 or 8, a filament of dye began to be
carried outward at depth along the southwest side of the bay toward the Nar-
rows during flood tide. By October 11, a thin filament and low concentra-
tions were visible about 5.5 km from the site. Visible amounts of dye were
not observed reaching the north entrance to the Narrows by the end of the
observation period. The principal accumulation was still present as an
irregular cloud extending about 1.4 km from the site.
Commencement Bay—Site Two is located at the mouth of the bay so that the
major difference between it and Site One is the increased mixing at this outer
location. During spring tides, dye from this site was dispersed much more
rapidly than that from Site One. Movement inward toward the Narrows and up-
welling at the head of the bay was quite evident during the flood tides at
the beginning of the period. Onset of rapid dispersion by the turbulent front
associated with ebb flow from the Narrows was usually sudden.
In general, during neap tides the dye formed a small filamentous cloud that
oscillated between the head of the bay near Site One and the base of Browns
Point. During the first few days of this period, the dye cloud was about 2 km
long and 0.5 km wide, with its major axis along the axis of the bay. At the
time of high tide, it was centered on the injection site. A very thin and
faint filament was carried around the base of Browns Point where it was dis-
persed rapidly by the main channel flow during flood tide.
Dispersion of the dye was so intense, even with neap tides, that dye was
almost undetectable more than about 2.5 km from the site towards Point Defi-
ance. Upwelling of dispersed dye near the head of the bay occurred but was
most evident during the latter part of the period when the character of the
tides had changed to more nearly equal ranges.
As mentioned earlier, dredge disposal sites located on the sides of relatively
straight portions of the main passages had current patterns which tended to
carry the injected dye along a uniform depth contour line. In actuality, the
dye was carried along the contour lines, undisturbed, for some distance, and
then was dispersed as it became mixed into more turbulent flow. At Fourmile
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Px>ck (Fig.19), dye was injected at a depth of about 121 m and formed a narrow
band at this depth which extended from West Point to near Smith Cove. During
ebbs, dye which reached West Point was dispersed by the turbulence generated
there. On floods, dye reaching the vicinity of Smith Cove was subjected to
mixing and continued on as a much lower concentration dye cloud. This cloud
continued southward until it was ultimately dispersed by mixing around Alki
Point. On some occasions, part of this cloud drifted into the eastern canyon
of Elliott Bay where it became sufficiently diluted such that it could not be
traced further. In general, the difference between spring and neap tides was
only in the larger excursions which were associated with spring tides.
The dredge disposal site at Shilshole (Fig. 21) is located in about 79 m depth.
The main concentrations of dye were observed between Meadow Point to the north
and West Point on the south. Because of the eddies formed behind those two
points, there was more vigorous mixing even in this region so that there was
less buildup than at Fourmile Rock. During spring tides, the dye was normally
transported toward the south where it was dispersed around West Point. For
neap tides, there was a more northerly transport with dispersion around Meadow
Point. However, during the later stages of the neap cycle, the mean transport
swung to the south.
For spring tides, the largest dye accumulation remained between Meadow Point
and the entrance to the Lake Washington Ship Canal. Dye was carried by floods
as much as two miles south of West Point. During ebbs, dye was transported
about 3 km north of Meadow Point. At the same time, the eddy forming off West
Point carried filaments of diffuse dye closer inshore in the Shilshole bight.
During the neap tide period, the principal accumulation was in the area between
the injection site and the deep shoulder of Meadow Point. Although successive
ebb tide ranges during this time were small, the flow picked up portions of
the dye cloud and carried them 4 km northwest of the injection site. Dye could
be traced nearly 5.5 km beyond Meadow Point. Late in the neap tide period,
with the tides changing to more nearly equal semi-diurnal, there was increased
flow to the south and dye was dispersed around West Point.
Of the three sites located on the sides of passages, Everett (Fig, 23) at 110
m had the least local mixing. The dye, discharged at depth, moved slowly in
71
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Fig. 23. Dye discharge location at the dredge disposal site
near Everett.
72
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the low tidal currents and slowly rose to about 37-55 m. During ebbs, the dye
was carried to the southwest and some of it was dispersed around Elliott Point.
During floods, dye was carried into Port Gardner, around the outer edge of
the Snohomish River delta and across the mouth of Port Susan. Turbulence
associated with flow across the Snohomish River delta and at the mouth of
Port Susan slowly dispersed the dye before it was finally transported into
Possession Sound. In general, the flow characteristics were similar for
spring and neap tides, with the expected lower mixing and lesser tidal excur-
sions being associated with neap tides.
Of the dredge disposal sites studied, Dana Passage (Fig. 24) with a bottom
depth of about 18 m was by far the shallowest site as well as the location
with the strongest tidal currents. Because of this, there was no accumulation
of dye at the injection site, and shreds of dye were carried on floods into
Henderson, Budd, and Eld inlets. During ebbs, the dye was generally trans-
ported toward the Tacoma Narrows though some of it was deflected into Case
Inlet. There was no noticeable difference in the distribution of the dye
between spring and neap tides since the currents were very strong in both
cases.
73
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Fig. 24. Dye discharge location at the dredge disposal site in
Dana Passage.
74
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SECTION 5
NUMERICAL MODEL OF PRIMARY PRODUCTION
IN PUGET SOUND, WASHINGTON
The overall objective of this phase of the project was to conduct a quanti-
tative investigation of relationships between the growth of phytoplankton,
and climatic and hydrodynamic conditions in a deep, temperate inlet with
marked tides, as exemplified by Puget Sound, Washington. A fully detailed
paper describing the results of the investigation has already been published
(Winter et al., 1975) so that only the highlights of the primary production
model need be summarized here.
As mentioned in Section 3, gravitational convection in a deep inlet, such as
the central basin of Puget Sound, is characterized by a near-surface brackish
water zone of many meters thickness flowing seaward over a deeper, landward-
moving zone of salt water from the sea. Early qualitative observations of
primary production in deep inlets suggest that phytoplankton growth is closely
coupled to estuarine circulation as well as to the physical and chemical prop-
erties of the water. Under conditions of moderate stability, when insolation
is adequate and the brackish zone of the inlet is not excessively turbid,
algae may grow with sufficient vigor to exhaust the surface zone temporarily
of plant nutrients. However, turbulent entrainment of nutrient-rich oceanic
water from depth will tend to replenish the supply of these ions. On the other
hand, cells growing near the surface are only temporary residents of the near-
surface zone since they are advected persistently seaward, on the average.
At the same time, the estuarine mechanism will resupply the near-surface zone
with viable cells from depth. Some fraction of this "seed stock" may originate
external to the inlet, entering the inlet with the intrusion of oceanic water
at the mouth; the remaining fraction may consist of cells formerly growing in
the surface zone, which have sunk or" were mixed to depth in the vicinity of
a sill and were subsequently carried landward with intruding saline water.
75
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The principal objective of this work was to examine quantitatively the
relationships between gravitational convection and other environmental
factors and primary production in deep inlet environments. The central basin
of Puget Sound, Washington, was used as an example. Puget Sound, as a whole,
consists of a complex system of deep inlet basins and channels which consti-
tutes the southern terminus of a more extensive system along the northeastern
Pacific coastline from Washington northward to Alaska. The Sound as a whole
communicates with the Pacific Ocean by way of the Strait of Juan de Fuca to
the north (Fig. 25). The principal entrance to the Sound is through Admiralty
Inlet. The intensity of the incursion of oceanic water through the channel
at Admiralty Inlet is determined partly by tidal characteristics and partly
by the rate of fresh water input to the Sound.
Throughout all seasons of the year, the principal basins of Puget Sound exhibit
some degree of stratification. The density structure is determined primarily
by salinity differences between brackish near-surface zones and deeper zones
of more saline oceanic water.
The tides in Puget Sound are of the mixed type with a progressive increase in
range from Admiralty Inlet to the inner regions. In the vicinity of Seattle,
the mean and diurnal tidal ranges are 2.5 m and 3.5 m, respectively. In the
neighborhood of the sill at Admiralty Inlet, strong turbulence and high tidal
currents (up to 5 knots) are the rule. Elsewhere, throughout the open water
of the Sound, tidal current speeds are usually less than 1 knot.
The principal nontidal circulation mode in Puget Sound is gravitational con-
vection, induced by freshwater runoff. The greatest amounts of fresh water
are supplied to the Sound by rivers along the northeastern shore. During the
spring and early summer, runoff into the central basin is derived largely from
melting snow in the surrounding mountains rather than local rainfall.
3
Phytoplankton is found in appreciable concentrations (usually > 0.2 mg Chi a./m
even at depth) in nearly all parts of Puget Sound throughout the year, but the
algae proliferate during the spring and summer months. Although field studies
of phytoplankton production have been performed in a few locations in Puget
Sound and the San Juan Archipelago, the present investigation is based largely
upon hydrographic and biological data acquired during a Puget Sound field study
76
-------
123" 00'
20'
20'
48°
00'
40
201
1
PLANKTON STATIONS
MAJOR SILLS
I23'00'
40'
122° OO'
Fig. 25. Map of Puget Sound.
77
-------
initiated in 1963 by G. C. Anderson and K. Banse. The field work was moti-
vated partly by the fact that in the early 1960fs the municipality of
metropolitan Seattle (METRO) began the construction of a central sewage
treatment plant with a large outfall at West Point on the eastern shore
of the central basin (Fig. 25). The observational program was undertaken
to establish baseline conditions of environmental and biological variables,
as well as to investigate primary production in Puget Sound.
Measurements were taken at two stations, one near midchannel in the central
basin off Seattle, the other one located in the southern part of the Sound
(Fig. 25). From September 1963 through December 1965, the stations were
visited approximately biweekly to observe insolation, standard physical and
chemical water properties, and concentrations of chlorophyll _a and zooplankton.
Measurements were also made of the rate of carbon uptake by phytoplankton in
water samples drawn from several depths. The carbon uptake rates above the
1% light depth at the northern (central basin) station were 460 and 470 g C
-2 -1
m yr in 1964 and 1965, respectively, which is extraordinarly high for an
unpolluted temperate site. In contrast, the uptake rates in the southern
-2 -1
Sound for the same years were 270 and 280 g C m yr , respectively.
The data indicated that primary production at the southern station was fairly
uniform from March through September. However, the observations in the cen-
tral basin showed that the annual cycle of phytoplankton growth was dominated
by a number of intense blooms between early May and September. Moreover, the
algal concentrations were changing drastically within time periods shorter
than the sampling interval. Therefore, during some of the spring months of
1966 and 1967, the same parameters were studied on an almost daily basis at
the central basin station.
The results of observations acquired at the central basin station during
the springtime cruises in 1966 and 1967 are summarized in Figs. 26 and 27,
respectively. The figures present the data in the form of isopleth diagrams
showing the time and depth variations of salinity, temperature, density,
oxygen saturation, phosphate, silicate, nitrate, chlorophyll a_, and carbon
uptake rate from April to June 1966 and in April and May 1967. A detailed
account of the field measurements and methods, together with a description of
supplementary observations, is available in Winter jrt a^L. (1975).
78
-------
APRIL. 1966
10 2O
1 1 1 T
MAY. 1966
10 20
~i r
JUNE. 1966
31 IO 20 3O
—I 1 1 1 1 1 1
H^^^DS0^1
H2JJ.8
22.0 21.0 21.0 22.0 210
Fig. 26. Variations of salinity, temperature, density, oxygen
saturation, phosphate, silicate, nitrate, chlorophyll a,
and carbon uptake rate at Station 1, April to June 1966.
79
-------
APRIL .1967
10 20
MAY. 1967
IO 20
2T?8,
¥U»* lS
<30
^
r
1
u
CT>
E
5O
IOO
ISO
2OO
250
22
<20 IP
/:^20
\----\\r
9 9
9 §_
Fig. 27. Variations of salinity, temperature, density,
oxygen saturation, phosphate, silicate, nitrate,
chlorophyll a, and carbon uptake rate at Station
1, April and May 1967.
80
-------
The quantitative investigation of deep inlet primary production processes was
concerned specifically with the dynamics of springtime phytoplankton blooms
and the variation in productivity, as exemplified by the central basin data.
The principal investigative tool was a numerical model in which the hydro-
dynamical conditions were represented by an approximate similarity analysis
of the gravitational convection mode of inlet circulation. Algal concentra-
tion was represented as a continuous function of space and time in the model,
which ascribed changes in phytoplankton density to variations in photosyn-
thetic and respiratory activity, algal sinking, grazing by herbivores, and to
mixing and advection. As shown below, computations adequately reproduce the
principal features of phytoplankton concentrations observed during 75 days
and 35 days in the springtime months of 1966 and 1967, respectively. More-
over, by means of numerical experiments, it was possible to assess the relative
importance of various processes which govern the level of primary production
in Puget Sound.
The analysis of gravitational convection in the central basin has already been
described in Section 3 of this report. However, some amplification may be in
order before describing the numerical model of primary production. It is
appropriate to begin with a presentation of certain additional hydrographic
information relevant to the nontidal circulation mode. Consideration is
restricted to a segment of the central basin which is 30 km in length, bounded
at its southern end near Blake Island and at its northern end near the southern
tip of Whidbey Island (Fig. 25). This choice of segment boundaries reflects
the fact that different sections of the Sound north of the Tacoma Narrows are
characterized by different flow patterns. The central basin, as defined here-
in, constitutes an inlet segment characterized by the same general type of
circulation pattern and hydrography. On the average, a significant fraction
of the freshwater discharged from southern Puget Sound and the Puyallup River
appears to enter the central basin near Blake Island, via Colvos Passage. The
northern terminus of the segment marks the confluence with Possession Sound
which carries freshwater from three of the largest rivers in the Puget Sound
region.
The coordinate used in this discussion has its origin at the surface at the
location of Station 1 near Seattle. The x-axis extends horizontally along the
81
-------
axis of the central basin and is positive seaward; the z-axis is directed
positive downward. The main channel of the central basin is idealized as
a deep inlet segment sufficiently narrow and straight to preclude the occur-
rence of large cross-channel variations in the average flow. Although the
width of the segment is somewhat variable due to irregularities in the coast-
line, the effective main channel breadth at Station 1 is taken to be
approximately 5 km.
Fresh water introduced into the central basin segment at its southern end
consists of runoff from the Puyallup River drainage basin and the drainage
basins south of the Tacoma Narrows. In addition, the central basin receives
fresh water directly from the Duwamish and Lake Washington drainage basins,
and distributed runoff from coastal land along the length of the segment.
Daily gaging station data for the spring months of 1966 and 1967 were used
to estimate the temporal variations of the cumulative fresh water runoff rate
3
R (m /sec) in the central basin. Three-day averages of the hydrographs were
performed to simulate the smoothing effect of mixing in the vicinity of the
river mouths. The gaged discharge from each of the drainage basins was
corrected to account for ungaged area. Finally, as in the case of Hood Canal,
described in Section 3, the longitudinal distribution of cumulative runoff R
was assumed proportional to cumulative drainage basin area. In the absence of
turbulence measurements in Puget Sound (and hence direct descriptions of the
turbulent transport of momentum and salt), it was necessary to draw upon esti-
mates of turbulent processes in other deep, stratified inlets (Winter, 1973).
It was speculated that in Puget Sound tides play a more important role than
winds or river discharge in providing energy for turbulent mixing in the cen-
tral basin. For Canadian fjords, Trites (1955) suggested that changes in
mixing intensity might be related to changes in the mean tidal velocity or its
gradient in some nonlinear fashion (for example, to its square). Average
values of the vertical eddy diffusion coefficient K* in the surface zones of
2
several inlets were estimated to be in the range of 1 to 10 cm /sec. Thus,
for the central basin, the simple working assumption was made that the day-to-
day change in the mean intensity of turbulent salt flux was proportional to
the square of the maximum tidal range, with an average value of about
ey
2 cm /sec between spring and neap tides. Comparisons of calculations based
82
-------
on this assumption and hydrographic data from the field tend to support the
notion of a general dependence of mixing processes on tides, although the
exact nature of the dependence is probably not accurately represented.
In the case of the central basin of Puget Sound, the seaward increase in
surface salinity S is rather slight and is sometimes obscured by the
s
presence of partially unmixed lenses of fresh water which originate from
river mouths, following freshets. On the average, however, the salinity S
S
over the segment will be determined by mixing of fresh water runoff at the
river mouths in the major embayments, and by the cumulative runoff rate R .
In practice, the latter can be regarded as the principal factor determining
the fractional salinity excursion defined by Eq. (24)
a = (S - S )/S
Q CO g 00
where S is the salinity at depth in the incursion zone. As a first approx-
imation, the fractional salinity excursion a can be expected to vary in
time primarily in response to temporal changes in P , and secondarily to
changes in wind-induced mixing, turbulence at depth, and mode of introduction
of the runoff.
A study of the salinity changes at depth at Station 1 showed that between the
lower boundary of the euphotic zone (which varies from 15 to 30 m) and the
sill depth (50 m), the seasonal increase in salinity was fairly small over
the observation periods, being somewhat less than 0.5 parts per thousand.
In the numerical study of phytoplankton growth described below, the lower
boundary L of the model domain is 30 m. This value was chosen since it
corresponds to the greatest euphotic zone depth and also lies within the
upper portion of the deeper saline incursion zone most of the time. For
the purpose of calculating the velocity field of the gravitational convection
mode by the similarity analysis described in Section 3, it is sufficient
to assume that the salinity at sill depth (about 50 m) is constant and equal
to the approximately seasonal averages of 29.4 and 29.25 in 1966 and 1967,
respectively.
83
-------
With the aforementioned hydrographic data and topographic idealizations, self-
consistent quantitative estimates were generated of gravitational convection
in the central basin for the spring months of 1966 and 1967, by means of the
approximate similarity analysis described by Winter (1973) and summarized in
Section 3. Calculated results were compared with measured salinity profiles
at various times during the springs of 1966 and 1967. The data periods were
chosen to cover the broad range of runoff conditions encountered during the
observation periods. It should be noted that the idealized circulation analy-
sis implies that changes in the non-tidal circulation component reflect
variations only in tidal amplitude and runoff intensity. Since time-smoothed
runoff data and day-to-day changes in tidal amplitude excursions constitute the
input data to the analysis, the calculated density structure and velocity
fields over the basin segment do not show large changes on consecutive days.
In most cases, fair agreement was achieved between the calculated salinity
profiles and the observed salinity at Station 1.
The velocity components u and w are calculated from the same analysis;
the calculated time-mean outflow at the surface agrees well with data from the
few available measurements in Puget Sound made by Paquette and Barnes (1951)
and by Cannon and Laird (1972). It is difficult to determine experimentally
the depth at which the horizontal component of current reverses sign because
the non-tidal velocities above and below that depth are small compared with
tidal velocities. As noted in Section 3, the calculated depth of no mean
motion in the central basis is somewhat more shallow than that inferred by
Paquette. and Barnes, but is the same order as that observed by Cannon and Laird
when runoff is low or moderate.
A convenient measure of phytoplankton standing stock is the amount P of
chlorophyll a. in a cubic meter of water. In the model, P is taken to be the
dependent variable of a partial differential equation which expresses the time
rate of change of P as the resultant of changes due to transport by turbulent
mixing and advection, photosynthesis and respiration, sinking, and grazing by
herbivorous zooplankton. Although the effects of certain short-time scale flow
phenomena on algal dynamics are neglected, the option is retained of examining
the response of the algal community to diurnal and day-to-day changes of
84
-------
available light. For this, reason, the time variation of light intensity is
included explicitly in the expressions for photosynthetic and respiration
rates.
Under the hydrographic conditions described above, changes in momentum and salt
concentration produced by longitudinal mixing are small compared with variations
associated with vertical mixing and advection. The assumption is made that the
turbulent transport mechanisms of suspended and dissolved substances are the
same, and, therefore, the turbulent flux of phytoplankton can be represented
by the product of the eddy diffusion coefficient K* and the vertical gradient
of the mean algal concentration P, Also, it is assumed that on the average
the advective flux of chlorophyll a^ can be represented adequately by the quasi-
steady state velocity components u and w.
Under these assumptions, a laterally-averaged equation for the concentration of
plant chlorophyll P(x,z3t) can be written as
z)z - [(buP)x + (bwP)z + (bwP)z] + Pr(x,z,t) P - grH (46)
where w is a representative vertical sinking speed of algal cells, P is
the net specific production rate, g is the specific grazing rate, and H is
the herbivore concentration.
In principle, Eq.(46) is to be- solved in a specified space-time domain, subject
to appropriate boundary conditions and an initial condition. The relevant
space domain in the present instance is defined by
(0 <_x <_ L3 -10 km <_ x <_ + 20 kn] ,
where L is 30 m. The bounds on x correspond to the mid-channel distances
from Station 1 to Blake Island and the southern tip of Whidbey Island, respec-
tively. The time domain is April 15 through June 30 for spring of 1966 and
April 25 through May 30 for spring of 1967- The starting dates are chosen so
as to be near the beginning of daily observations and to lie well within a
time period when algal blooms were absent.
The boundary condition at the free surface requires that the flux of phyto-
plankton is zero:
-K*P + w P = 0. (47)
& O
85
-------
An appropriate boundary condition at depth is suggested by the observation
that a low-level concentration of phytoplankton is maintained by the advection
of cells into the basin with salt water intrusion. The deep chlorophyll con-
centration was assigned an average value for the observation period:
P = 1. 5 mg Chi a/m3 at z = 30 m. (48)
Boundary conditions at x = -10 km and +20 km could be specified on the basis
of observations (see, e.g., Munson, 1970) that longitudinal gradients at the
ends of the central basin segment are small on the average. In fact, a numeri-
cal study of the three-dimensional (xsz}t) problem was performed with such
conditions. As expected from field observations, a slight relative increase
in pigment was predicted in the down-inlet direction, but the chlorophyll
distributions with depth were similar at all stations along the inlet axis.
Since calculated phytoplankton concentrations at the central station differed
by only a few percent from those predicted by a simpler, more economical two-
dimensional (depth—time) model, the latter was subsequently used in the
investigation. Thus, the ^-derivative of P was assumed negligible through-
out the length of the inlet segment, and the original three-dimensional problem
was transformed to a two-dimensional one. Boundary conditions (47) and (48)
are still applicable, and the two-dimensional analogue of Eq. (46) was solved
for the two springtime intervals of 75 days and 35 days in 1966 and 1967,
respectively. Initial conditions for the two periods were the observed verti-
cal profiles of chlorophyll a. at Station 1 on April 15, 1966, and April 25,
1967. The starting profiles actually used in the computations were adjusted at
depth to pass smoothly through the seasonal average concentration of 1.5 mg
Chi a./m3.
The coefficients K* and W are obtained from the similarity analysis
summarized in Section 3. For the purpose of calculating the dynamical response
of phytoplankton to changes in circulation, the salinity distribution and the
non-tidal flow field were calculated daily in response to (usually modest)
changes in cumulative runoff rate and in the intensity of turbulent mixing (as
related to tides).
The net specific production rate P is a complicated function of several
environmental variables and physiological parameters; the reader is referred
86
-------
to the paper by Winter et_ al, (1975) for a full diacuss.ion of the specification
of P and also of the grazing rate g , In an effort to avoid biasing the
results of the simulation, somewhat traditional descriptions of photosynthetic
processes were used in the model, except when the conventional formulation of a
particular process was clearly inadequate and a better alternative could be
identified. In any event, the paper by Winter et al. (1975) presents the
relevant formulations including the dependence of the production rate on nutri-
ent availability, underwater light intensity, and parameters such as the
cellular carbon-to-chlorophyll ratio, the maximum specific photosynthetic rate,
P , and the optimum light intensity T . So far as sinking of algal cells
7TICL2C TfiCCtC
is concerned, it was assumed that the sinking speed was a fixed constant except
during those episodes when cellular activity was expected to decline due to
prolonged nitrate depletion; at which times the sinking rate was increased.
Finally, a single grazing function, independent of size of the grazers, was
applied to the herbivorous zooplankton.
The relationships among the various components of the model are depicted in
the diagram in Fig. 28. The hydrographic and climatic inputs, which include
runoff intensity, tidal range, and insolation, were supplied on a daily basis.
Observed nitrate distributions and estimated herbivore concentrations were also
provided each day, and, therefore, these variables act as "forcing functions"
in much the same way as the environmental inputs. The several model parameters,
such asP jJ 3 K*3 g 3 S , algal density at depth, etc., play a
TilCtvC j? G®
somewhat different role, inasmuch as they are of the nature of input constants,
most of which are fixed throughout the course of a calculation. The feedback
shown in the model diagram between the phytoplankton concentration submodel and
the submodel for underwater light intensity is a consequence of the effect of
self-shading on water transparency. Feedback also occurs between the phyto-
plankton submodel and the grazing submodel due to the dependence of the herbi-
vore ration upon food concentration.
The numerical integrations carried out with the "best available" functional
forms and parameter values were referred to as "standard runs" and were used in
fact as standards for comparison with experimental simulations. In considering
the standard run results, it is important to note that because the model in its
present form does not include explicitly the effects of sustained winds, it was
87
-------
HYDROGRAPHIC AMD
CLIMATIC INPUTS
insolation
00
00
NITRATE
CONCENTRATION
ZOOPLANKTON
CONCENTRATION
Circulation
Submodel
•Underwater Light
Intensity Submodel
Net Specific Primary
Production Submodel
Algal Sinking Speed
Grazing
Submodel
•^Phytoplankton
Concentration
Submodel
Circulation
Description
• Phytoplankton
Distribution
Fig. 28. Flow diagram of numerical model showing relationship amongst the several components of the model,
-------
necessary to perform the 1966 computation in two stages. In an open inlet,
such as Puget Sound, occasional episodes of strong, persistent winds will
drastically retard or accelerate seaward adyection in the upper zone, simul-
taneously altering its density structure and phytoplankton content. Such an
occurrence is exemplified by an abrupt change in surface salinity around mid-
May 1966. Beginning on 12 May, an episode of high runoff due to snow melt
was followed immediately by sustained strong southerly winds, which rapidly
moved the relatively fresh surface water to the north and, at the same time,
removed from the central basin the algal blooms which had previously been
extant in the surface zone. The reduction of the freshwater fraction in the
surface zone was accompanied by upwelling of saline water from depth and the
occurrence of low rates of specific algal production. Therefore, the calcula-
tion for 1966, which began on April 15, was terminated on 15 May, which was
the third consecutive day on which the average wind speed was near or exceeded
3
10 knots. The algal density was reset at 1.0 mg Chi a/m near the surface,
in accord with observations, and the computation continued without further
interruption to the end of June. Although there were episodes of winds during
the 1967 period, they were of shorter duration and lesser intensity, and, as a
consequence, the enti-re calculation for 1967 was performed without interrup-
tion.
The day-to-day variations of the computed Secchi disk depth and the integrated
chlorophyll values of the standard computer runs are shown together with the
observed values for the springtime periods of 1966 and 1967 in Figs. 29 and 30.
The comparison of the computed and observed results indicates that the model
reproduces satisfactorily not only the general pigment level but also many of
the details of the springtime phytoplankton dynamics in both years. Moreover,
the explanations for the periods of divergence between calculated and observed
values are set forth in the paper by Winter et al.(1975). The reader is also
referred to that paper for a discussion of various numerical experiments which
were performed and the conclusions to be drawn from each one.
Observed and calculated (standard run) depth distributions of chlorophyll before,
during, and after the first intense algal bloom in 1966 are compared in Fig. 31.
It is evident that-the near-surface concentrations are fairly well represented,
although the predicted profile is smoother than that inferred from the
89
-------
VO
O
Fig. 29, Comparison of measured and calculated integrated chlorophyll a from surface to Secchi
disk depth and Secchi disk depth at Station 1 in Puget Sound, April to June 1966;
arrows indicate endings of periods of rapidly rising salinity in brackish zone.
-------
Q.
UJ
O
I
O
O
1U
60
50
ui
O
ol
I
a.
o
tr
o
ol
-,~
Z 30
o
20
10
20
30
10
APRIL
20
MAY
I6
ui
o
x 8
o
_ 4
i
o
uj 0
31
1967
I
20 30
APRIL
10
20
MAY
31
1967
Fig. 30. Comparison of measured and calculated integrated
chlorophyll a from surface to Secchi disk depth
and Secchi disk depth at Station 1 in Puget Sound,
April and May 1967.
-------
P (mg Chi a/m3)
£ 20
UJ
Q
30
26 APR 66
8
8
8 10 12
28 APR 66
2 MAY 66
NJ
0
10
20
30
P
6
8
12 MAY 66
10
12
301-
14 MAY 66
Fig. 31. Comparison of measured and calculated chlorophyll a concentrations as functions of depth at
Station 1 before, during, and after algal bloom in 1966; dashed lines indicate estimates of
1% light depths.
-------
observations, I" is also apparent that the model fails to reproduce concen-
trations near and below the euphotic zone when the bloom is in progress. This
particular shortcoming was anticipated in view of the crudeness of the boun-
dary condition at depth. In addition, minimal phytoplankton concentrations
are predicted by the model below the halocline in the region around 20 m depth,
possibly as a result of low net in situ production, combined with an under-
estimate of mixing, resulting in insufficient downward transport of near-surface
algal material and upwelled seed stock from depth.
In summary, the calculations of the standard run reproduced most of the general
features of data acquired during the springtime cruises in 1966 and 1967. The
results of the standard runs and the numerical experiments with the model con-
firm the existence of a close relationship between the circulation and the
physical and chemical properties of the water, climatic (light) conditions, and
the level of primary production in Puget Sound. The model is general enough to
be applicable to other deep temperate inlets where the general constraints on
the physical submodel are satisfied and where nutrient exhaustion is not a
major feature. Incorporation of nutrient regeneration by zooplankton would be
necessary in the Strait of Georgia and in inlets subsidiary to the central
basin of Puget Sound where nitrate levels are low over prolonged periods of
time.
The model study lends further support to the notion that gravitational convec-
tion supplies the euphotic zone with algal seed stock from depth and replenishes
exhausted supplied of essential nutrients during vigorous flowering. A complete
quantitative verification of these hypotheses is somewhat beyond the present
state-of-the-art, since it would require the development of fjord circulation
models which include the influence of bathymetry (especially sills), the
effect of winds, and changing hydrographic conditions in external source waters.
Nevertheless, various results of the model computations, such as the flux
component profiles shown in.Fig. 32, indicate that the high productivity of
Puget Sound is due to strong, persistent upwelling of nutrients and algal cells
from depth. During the spring and early summer, the quantity and quality of
freshwater runoff in the central basin is apparently such as to maintain mode-
rately intense gravitational convection without producing an excessively turbid
brackish surface layer.
93
-------
vo
0
~ 10
N
X
h-
& 20
30
PHYTOPLANKTON FLUX
(mg Chi j./m2/day)
•4-20 2 4
} I
SECCHI DISK DEPTH
TURBULENCE
SINKING
28 APRIL 66
Fig. 32. Depth variation of algal flux due to turbulent mixing,
upwelling, and sinking for standard run at noon on
28 April 1966.
-------
In contrast with the situation in the open sea, the mixing processes in the
main channel of Puget Sound do not create a deep mixed layer within which
primary production is light-limited. Instead, algal growth in the central
basin is limited by a combination of hydrodynamic factors (as illustrated
in Fig. 32) and modulation of the underwater light intensity by self-shading
and by inorganic particulates. On occasions of sustained winds, standing
stock is limited by relatively short residence times determined by horizontal
advection. Evidently, the late occurrence of spring blooms in deep inlets
like Puget Sound is not explainable in terms of the critical depth concept.
In the central basin of the Sound, several consecutive days of bright sunshine
are sufficient to promote massive development of phytoplankton. Given the
right combination of weather, water stratification, and flushing characteris-
tics in the upper brackish zone, blooms might also occur earlier in the year,
but apparently these instances are somewhat uncommon and have not been observed
during 1964 and 1965. As noted above, horizontal advection by sustained
winds will remove blooms from the central basin; prolonged nitrate depletion
and a succession of cloudy days will discourage vigorous growth and will cause
a bloom to decline in intensity. By means of numerical experiments, it was
demonstrated that the effects of grazing by herbivorous zooplankton and
cellular sinking are of secondary importance. Because of the rather rare
occurrence of nutrient limitation during the spring and the light limitation
that prevails during the fall and winter months, nutrient addition from
sewage treatment plants is not likely to change the level of primary produc-
tion in the main channel significantly.
95
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SECTION 6
REFERENCES
Barlow, J.P., 1958. Spring changes in phytoplankton abundance in a deep
estuary, Hood Canal, Washington. Journal of Marine Research 17, 53-67.
Bowden, K.F., and R.M. Gilligan, 1971. Characteristic features of estuarine
circulation as represented in the Mersey estuary. Limnology and Oceanog-
raphy JL6, 490-502.
Cannon, G.A., and N.P. Laird, 1972. Observations of currents and water prop-
erties in Puget Sound, 1972. NOAA Technical Report ERL 247-POL 13,
National Oceanic and Atmospheric Administration, Boulder, Colorado.
Dyer, K.R., 1973. Estuaries; _A Physical Introduction. Chapter 5. John Wiley
and Sons, New York.
Freibertshauser, M.A., and A.C. Duxbury, 1972. A water budget study of Puget
Sound and its subregions. Limnology and Oceanography 17(2), 237-247.
Gade, H.G., 1968. Horizontal and vertical exchanges and diffusion in the
water masses of the Oslo Fjord. Helgolander Wissenschaftliche 17, 462-
475.
Kullenberg, G., 1971. Vertical diffusion in shallow waters. Tellus 23, 129-
135.
McAlister, W.B., M. Rattray, Jr., and C.A. Barnes, 1959. The dynamics of a
fjord estuary: Silver Bay, Alaska. Department of Oceanography Technical
Report No. 62. University of Washington, Seattle, Washington.
Munson, R.E., 1970. The horizontal distribution of phytoplankton in a bloom
in Puget Sound during May, 1969, 13 pp. Non-thesis masters report.
Department of Oceanography, University of Washington, Seattle, Washington.
Paquette, R.C., and C.A. Barnes, 1951. Measurement of tidal currents in Puget
Sound. Department of Oceanography Technical Report No. 6^. University of
'Washington, Seattle, Washington.
Pearson, C.E., and D.F. Winter, 1976. A numerical model of steady two-zone
flow in deep stratified inlets. Interim report on Grant No. R801320 with
the Environmental Protection Agency. National Environmental Research
Center, Corvallis, Oregon.
Pickard, G.L., 1961. Oceanographic features of inlets in the British Columbia
mainland coast. Journal of_ the Fisheries Research Board of. Canada 18,
907-989.
Pickard, G.L., 1971. Some physical oceanographic features of inlets of Chile.
Journal of Fisheries Research Control Board of Canada 28, 1077-1106.
96
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Pickard, G.L., and K. Rodgers5 1959. Current measurements in Knight Inlet,
British Columbia. Journal of_ the Fisheries Research Board of Canada
18, 635-678.
Rattray, M., Jr., 1967. Some aspects of the dynamics of circulation in
fjords. In, Estuaries (Lauff, G.H., ed.). American Association for the
Advancement of Science, Washington, D.C., pp. 52-62.
Rattray, M., Jr., and J.H. Lincoln, 1955. Operating characteristics of an
oceanographic model of Puget Sound, Trans. AGU, _36(2), 251.
Trites, R.W., 1955. A study of the oceanographic structure in British Columbia
inlets and some of the determining factors. Ph.D. thesis, University
of British Columbia, Vancouver, British Columbia.
Tully, J.P., 1949. Oceanography and prediction of pulp mill pollution in
Alberni Inlet. Bulletin Fisheries Research Board of Canada, No. 83.
Winter, D.F., 1973. A similarity solution for steady-state gravitational
circulation in fjords. Estuarine and Coastal Marine Science 1, 387-400.
Winter, D.F., K. Banse, and G.C. Anderson, 1975. The dynamics of phytoplank-
ton blooms in Puget Sound, a fjord in the northwestern United States.
Marine Biology 29, 139-176.
Winter, D.F., and C.E. Pearson, 1976. Computation of steady circulation in
stratified fjords. Proceedings Fifth Technical Conference, Estuaries
of the Pacific Northwest.April 1 and 2, 1976. Oregon State University,
Corvallis, Oregon.
97
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SECTION 7
PUBLICATIONS AND TECHNICAL MEMORANDA
RESULTING FROM EPA GRANT NO. R-801320 (TO APRIL 1976)
1. Lam, R. and J. Lincoln 1975. Model Study of Surface Tidal Currents in
Puget Sound. Project Report on EPA Grant No. R801320. Ref. No. M75-109,
October 1975. Department of Oceanography, University of Washington,
Seattle.
2. Lincoln, J. and R. Lam 1975. A Hydraulic Model Study of Dye-Stream
Dispersal Characteristics in Some Parts of Puget Sound. Project Report
on EPA Grant No. R801320. Ref. No. M75-108, October 1975. Department of
Oceanography, University of Washington, Seattle.
3. Pearson, C. E. and D. F. Winter 1974. A Numerical Study of Time-Dependent
Shallow Water Motion in Stratified Inlets. Interim Report on EPA Grant
No. R801320. Department of Oceanography, University of Washington,
Seattle.
4. Pearson, C. E. and D. F. Winter 1975. Analysis of Stratified Inlet
Flow by the Method of Weighted Residuals. Symposium on Modeling of
Transport Mechanisms in Oceans and Lakes. Canada Centre for Inland Waters.
Burlington, Ontario. October 6-8, 1975.
5. Pearson, C. E. and D. F. Winter 1976. Computation of Tidal Flow in
Well-Mixed Estuaries. Journal of the Hydraulics Division, ASCE3 Vol. 102,
No. HY3, p. 367-377.
6. Pearson, C. E. and D. F. Winter 1976. Summary of Efficient Computa-
tion of Tidal Currents in Estuaries. Proceedings of the Technical
Conference on Estuaries of the Pacific Northwest. Oregon State University.
p. 39-41.
98
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7. Pearson, C. E. and D. F. Winter 1976. A numerical Model of Steady
Two-Zone Flow in Deep Stratified Inlets. Interim Report on EPA Grant
No. R801320. Department of Oceanography, University of Washington,
Seattle.
8. Winter, D. F. 1973. A Similarity Solution for Steady-State Gravita-
tional Circulation in Fjords. Estnavine and Coastal Marine Science
1:387-404.
9. Winter, D. F., K. Banse, and G. C. Anderson 1975. The Dynamics of
Phytoplankton Blooms in Puget Sound, A Fjord in the Northwestern
United States. Marine Biology 29:139-176.
10. Winter, D. F. and C. E. Pearson 1976. Computation of Steady Circulation
in Stratified Fjords. Proceedings 5th Technical Conference on Estuaries
of the Pacific Northwest. Oregon State University, p. 55-58.
11. Winter, D. F. and C. E. Pearson 1976, A Numerical Model of Time-Depen-
dent Two-Zone Flow in Stratified Inlets. Interim Report on EPA Grant
No. R801320. Department of Oceanography, University of Washington,
Seattle.
99
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TECHNICAL REPORT DATA
(Please read iNUrtictioits on the reverse before completing)
\. REPORT NO.
EPA-6nn/^-77-n/,Q
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
""Studies of Circulation and Primary Production
in Deep Inlet Environments."
5. REPORT DATE
April 1977
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Dr. Donald F. Winter
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of Oceanography
University of Washington
Seattle, WA 98195
10. PROGRAM ELEMENT NO.
1BA608
11. CONTRACT/GRANT NO.
R-801320
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency - Corvallis
Con/all is Environmental Research Lab
200 S. W. 35th Street
Con/all is, Oregon 97330
13. TYPE OF REPORT AND PERIOD COVERED
Final Report, 1973-1976
14. SPONSORING AGENCY CODE
EPA/600-02
15. SUPPLEMENTARY NOTES
None
16. ABSTRACT
This report summarizes the results of a three-year grant from the U.S.
Environmental Protection Agency to investigate various aspects of circula-
tion dynamics and primary production in a deep inlet environment. Through-
out the course of the research, special attention has been given to Puget
Sound, Washington, although many of the findings are applicable to other
deep inlet waters.
The several tasks undertaken during the course of the project fall into
three general categories:
1) Numerical modeling of gravitational convection and tidal motions
in deep estuaries.
2) Hydraulic model studies of tidal circulation patterns and dye
dispersal characteristics in Puget Sound.
3) Numerical modeling of primary production in a deep inlet (in
particular, the deep central basin of Puget Sound).
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
ecosystem modeling
hydraulic modeling
circulation
diffusion
fiords
b.lDENTIFIERS/OPEN ENDED TERMS
estuaries
modeling
c. COSATI Field/Group
08A
08C
08J
20D
Z. DISTRIBUTION STATEMENT
Release to public
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
110
20. SECURITY CLASS (This page)
Uriel assified
22. PRICE
EPA Form 2220-1 (9-73)
100
ft U.S. GOVERNMENT PBINTING OFFICE- 1977-797-5901100 REGION 10
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