United States
Environmental Protection
Agency
Office of
Radiation Programs
Washington DC 20460
EPA 520/1-82-002
June 1982
Radiation
c/EPA
Analysis of Current Meter Records
at the Northwest Atlantic 2800
Metre Radioactive Waste Dumpsite
\
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EPA 520/1-82-002
ANALYSIS OF CURRENT METER RECORDS
AT THE NORTHWEST ATLANTIC 2800 METRE
RADIOACTIVE WASTE DUMPSITE
by
Peter Hamilton
June 17, 1982
Contract No. 68-01-6235
Submitted to: U.S. Environmental Protection Agency
Office of Radiation Programs
Washington, D. C. 20460
Project Officer: Robert S. Dyer
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ABSTRACT
In August 1976, four current meter moorings were deployed for a period of
three months at the Atlantic 2800 m radioactive waste disposal site as part of
a series of scientific surveys conducted by the Environmental Protection
Agency for the purpose of assessing conditions at dumpsites which had been
active in the past. The Atlantic 2800 m site covers an area of approximately
350 square kilometres on the Continental Rise of the Mid-Atlantic Bight and is
centered at 38°30'N and 72°06'W.. The four moorings were placed in a
rectangular array; each with a current meter 5.1 m off the bottom. The
southwest mooring also had an additional meter at 96 m from the bottom.
The current and temperature data from the meters were analyzed in terms
of the dynamic processes occurring on the Continental Rise and the
implications of these measurements for transport of radionuclides in the water
and attached to sediments discussed.
The principle findings are that substantial, 3-4 cm/s, southwesterly mean
currents were observed near the bottom and that the low frequency part of the
spectrum is dominated by fluctuations with about a 16-day period which could
be explained as bottom trapped topographic Rossby waves with horizontal
wavelengths of about 200 km. Bottom boundary layer effects on the low
frequency wave motions, measured by the lower current meters, have only minor
influences on the agreement of the observations with basic Rossby wave theory.
The implications are that long-term water mass transport is dominated by the
mean flow along the isobaths with excursions of about 300-400 km over three
months. The Rossby waves disperse dissolved radionuclides with an effective
/• o
horizontal diffusion coefficient of about 7 x 10 cm/s.
The high frequency motions superimposed on the low frequency currents are
dominated by inertial oscillations (period 19.3 hours) which are intermittent
and vary in amplitude. Maximum amplitude is about 10 cm/s. The passage of
Hurricane Belle close to the site on August 10, 1976 gave rise to large
amplitude inertial oscillations about 24 days later. Such inertial events
provide about as much mixing energy to the bottom boundary layer as do the
maximum low frequency currents (^ 20 cm/s). Based on the maximum speeds
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observed, the propensity for sediment transport during the measurement period
was judged to be very small. Measured internal wave motions were dominated by
the semi-diurnal internal tide, amplitudes 0.5-1.5 cm/s, which is generated
from the astronomical or barotropic tide in the region of the shelf break and
slope to the northwest of the site.
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TABLE OF CONTENTS
Section Page
—• • ' •' '—• ...-.— _„.. V •.
ABSTRACT i
TABLE OF CONTENTS iii
I INTRODUCTION 1
II LITERATURE REVIEW 5
2.1 Introduction 5
2.2 Deep Current Measurements in the Mid-Atlantic
Bight 7
2.3 Topographic Rossby Waves 11
2.4 Surface Currents over the Continental Rise 12
2.5 Hurricane Belle 15
III DATA COLLECTED 17
IV LOW-FREQUENCY CURRENTS 20
4.1 Zero Order Statistics 20
4.2 Time Dependent Motions 22
4.3 Spectra 29
4.4 Spatial.Structure 38
4.5 Dispersion by Low-Frequency Currents 44
V INERTIAL CURRENTS 63
VI TIDAL CURRENTS 77
VII HIGH-FREQUENCY INTERNAL WAVES 83
VIII THE NORTHWEST ATLANTIC 3800 m RADIOACTIVE
WASTE DUMPSITE 84
IX SUMMARY 86
X RECOMMENDATIONS 89
ACKNOWLEDGEMENTS 91
REFERENCES 92
m
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I. INTRODUCTION
Ocean dumping of low level radioactive wastes by the Unites States mostly
occurred between 1946 and 1962. On the Atlantic coast two deep water sites
received the majority of these wastes (Dyer, 1976; Luedecke, 1959). This
report is concerned with the 2800 m dumpsite centered at 38°30IN, 72°06'W on
the upper Continental Rise of the Mid-Atlantic Bight. The 2800 m dumpsite
covers an area of approximately 350 square kilometres. Figure 1.1 shows a
chart of the region with the dumpsite position marked. The Continental Rise
slopes gently away from the junction of the steep Continental Slope with the
Rise, at approximately 2000 m depth, towards the deep Sargasso Sea Abyssal
Plain with depths greater than 4000 m. The Continental Rise and Slope are
frequently dissected by steep-sided canyons. The reader is referred to the
bathymetric chart of the Wilmington Canyon (NOS NJ 18-6) and Figure 4.1 for
detailed topography of the dumpsite region. The Wilmington Canyon chart's
eastern boundary is 72°W, thus detailed topography to the east of the dumpsite
is lacking.
Other dumpsites in the region which have been the subject of scientific
studies are the 3800 m radioactive waste dumpsite situated at 37°50'N, 70°35'W
(Dyer, 1976) in the lower reaches of the Hudson Canyon, and the 106 mile Ocean
Waste Disposal Site, a 1500 square kilometre area just off the Continental
Shelf centered approximately at 38°45'N, 72°15'W, about 30 km NNE from the
2800 m dumpsite.
The 106 mile site has been studied as part of the NOAA dumpsite
evaluation program (Ingham et al, 1977; Devine et al, 1981). These studies,
however, are not particularly relevant to the radioactive waste dumpsites, as
the primary focus was to examine the dispersion of industrial and chemical
wastes within the surface layers as they are discharged from a barge. The
physical oceanography of the surface waters of the 106 mile site region was
also studied as part of this program.
The fate of radioactive waste packages dumped at U.S. dumpsites needs to
be assessed before there is consideration of further ocean disposal of low
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42° -
LEGEND
STORM PATH
CURRENT METERS
WIND DATA
crT SECTIONS I0600GMT)
1 8/10/76
STORM CENTER
ivtf-i/-h/^
6 V 2oOOlTl
(RIMAX RELATIVE TO
P STORM LOCATION AT
(0000 GMT) 8/10/76
36'
Figure 1.1. Chart showing storm track of Belle and stations
from which all data were obtained (from Mayer et
al. 1981). Positions of the two deepwater
radioactive waste dumpsites (2800 m and 3800 m)
are marked by large triangles.
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level radioactive wastes. As part of a survey program of U.S. dumpsites, the
EPA made near bottom current measurements at the 2800 m dumpsite for a period
of three months in 1976. The measurements were made in order to evaluate the
current regime at the site and its effects on the dispersion of radioactive
nuclides. The current speeds measured would also indicate whether transport
of sediment could occur. As part of the evaluation of physical mechanisms of
dispersion, it is necessary to analyze the currents in terms of the physical
processes occurring at the site. Physical dynamics of deep ocean currents
often have a large range of characteristic length and time scales. Thus, the
purpose of this report is to analyze the EPA current measurements in terms of
physical processes occurring at the most energetic parts of the spectrum from
very low frequencies (periods ^ 1-week to 1-month), through inertial (^ 19
hours) and tidal O 12.5 hours) to high frequencies O 1 hour). The
characteristic motions at different frequencies are placed in the context of
western North Atlantic circulation and dynamics and the physical processes
evaluated, as far as is able with limited data, in terms of dispersion and
transport of radionuclides.
The surface waters of the Continental Rise in the mid-Atlantic Bight are
dominated by the north (cold) wall of the Gulf Stream, which meanders over the
region offshore of the shelf break. It is also thought that the Gulf Stream
is a source of the energetic low frequency motions observed below 1000 m. The
surface waters are often dominated by anticyclonic eddies, which are pinched
off meanders from the Gulf Stream, which propagate west and southwest along
the Shelf Slope before dissipating or being reabsorbed into the Gulf Stream.
There is no direct evidence that these eddies affect the circulation below
1000 m on the Continental Rise.
The present report is divided into the following sections: Section II
presents a review of the literature and physical oceanography of the region as
it is relevant to EPA's current measurements. This section also includes a
brief review of relevant theories. Sections III-VII give a detailed analysis
of the data. These sections assume some knowledge of physical oceanography,
modern time series analysis techniques and wave kinematics and is written
primarily for the scientific reader. However, the conclusions which follow
(Sections IX and X), summarize the important findings of the analysis
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and recommendations are made for future studies. Where possible the relevance
of the 2800 m dumpsite current meter data as well as data in the literature
related to the 3800 m radioactive waste dumpsite will be discussed. No
current meter measurements have been made at this latter dumpsite.
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II. LITERATURE REVIEW
2.1 Introduction
The dispersion of radionuclides by bottom currents occurs over long time
periods by transport by the mean currents and by eddy diffusion by the
fluctuating or time varying components of the current and pollutant fields
(Csanady, 1973). In most ocean environments the fluctuating components are
greater than the mean, and energy of the fluctuating components varies with
frequency. The physical processes which result in fluctuating currents
include planetary wave motions (Rossby waves), eddies, inertial motions, and
internal tide and high frequency internal waves. All these time varying
motions can be regarded as turbulence which disperses natural (such as
temperature and salinity) and man-derived constituents (such as
radionuclides).
An idea of the distance parcels of water, on the lower Continental Rise
below 1000 m, may travel in the course of a year and also an estimate of the
scales of the eddy motions in the northwestern Atlantic is shown by the tracks
of isobaric Lagrangian deep ocean floats. These floats are tracked by shore
based acoustic listening stations (Figure 2.1, from Schmitz et al, 1981).
Float LRl was launched on 9 October 1977 (modified Julian day number 3425)
with a nominal depth of 1300 m and was tracked for 476 days. Float LR2 was
launched on 29 July 1978 (modified Julian day number 3718) with a nominal
depth of 1300 m and was tracked for 281 days. The floats are approximately
isobaric; i.e., remain on a pressure surface and so remain at approximately
the same depth as they move, and therefore do not track an exact water
particle path, since a water particle may change depth by advection along
density surfaces. Float LRl passed close to the 2800 m dumpsite on day 3725,
traveled eastwards undergoing some large cyclonic circulations, passed under
the Gulf Stream and ending up 175 days later in the Sargasso Sea more than 8
degrees of longitude east of the dumpsite. Thus the Gulf Stream appears to
have little effect on these deep float motions though some of the intermediate
mesoscale cyclonic fluctuations are visually coherent with surface Gulf Stream
meanders (Schmitz et al, 1981).
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Figure 2.1. Trajectories for floats LR1 and LR2, as indicated (nominal depth 1300 M), Numbers
next to the tracks denote time as a modified Julian day number. The quality of the
position fixes for LR1 varied considerably: solid lines indicate good quality;
solid squares, intermediate quality; dashes, poor quality (from Schmitz et al. 1931)
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The long time periods and large scales of the fluctuating motions
illustrated by the float tracks are appropriate for the dispersion of the
radionuclides from a source on the bottom because of the time scales
associated with the radioactive decay of some of the waste constituents
(100-1000 years). Both slow leaks from the waste packaging and catastrophic
instantaneous release of radionuclides in deep water would be dispersed by the
same physical processes.
2.2 Deep Current Measurements in the Mid-Atlantic Bight
Apart from the recent employment of deep lagrangian floats to study the
deep northwestern Atlantic circulation, most of the circulation studies on the
Continental Shelf, Slope, and Rise of the Mid-Atlantic Bight (Figure 1.1) have
used moored current meters. The analysis of these measurements reported in
the literature have concentrated on the low frequency motions with periods
ranging from a few days to several months, because the large scale
circulations have most of their energy at these periods. There have been a
few studies on internal tide and internal wave motions associated with the
Continental Slope, but discussion of these phenomena is deferred to the
appropriate analysis sections since they play a much smaller role than the low
frequency currents in the long term dispersal of radioactive waste.
Some early deep water current measurements were made in this region,
including the studies of Volkmann (1962) and Zimmerman (1971), but they are
generally far too short a time period to resolve the important low frequency
motions. The first long-term comprehensive set of measurements were
associated with the Woods Hole Oceanographic Institution (WHOI) Site D
•projects (Thompson, 1971; 1977; Schmitz, 1974). Site D is situated on the New
England Continental Rise at longitude 70°W in a similar depth of water (2650
m) to the radioactive waste dumpsite. The topography at Site D has a general
east-west trend. Moorings with subsurface flotation were deployed between
1971 and 1974. Earlier moorings at Site D used surface flotation and current
measurement were contaminated by motions of the surface float. Additionally,
in 1974 an array of 15 moorings with 32 current meters were deployed along
70°W and ^ 69°30'W across the Continental Rise from the slope region to the
Gulf Stream. This was known as the Rise Array (Luyten, 1977; Thompson, 1977)
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2400 m
32OOm
•40OOm
Figure 2.2. Rise Array Mooring Locations
Locations and numbers of moorings in
large array. The isobaths are taken
from Uchupi. The arrows show the mean
flow over 8 months. The thick arrows
are mostly 200 m above the bottom, and
the thinner 1000 m.
(from Thompson, 1977)
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75
^
KELVIN —, J
. ~ r*/ UAL^
Figure 2.3. NESS Array
B a thyme trie map of the Middle Atlantic Bight showing
the location of the moored array. The rectangles
represent areas where detailed bathymetric surveys
were made during the experiment and the dashed arrows
represent the estimated trend of the local topography
at the mooring site. A time series of surface wind
data has been obtained for the location shown by the
triangle.
(from Ou and Beardsley, 1980)
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which was in place for a period of about eight months, and, generally, each
mooring had current meters placed at 1000 m and 200 m off the bottom. Figure
2.2 (from Thompson, 1977) shows the moorings of the Rise Array. Very few deep
water current measurements have been made in this region since the
discontinuation of the Site D moorings. However, more recently measurements
have been made across the Continental Shelf and Slope region. (Ou and
Beardsley, 1980; Ou et al, 1980) from February to August 1976. Figure 2.3
gives the positions of the moorings. One of the purposes of this experiment
was to study the propagation of long period wave motions across the
continental margin. Only the two deep moorings, NE4 and NE5 had meters at a
depth of 2000 m, all the remaining moorings had instruments at depths
shallower than 300 m (Ou and Beardsley, 1980).
The major result from the site D and Rise Array studies is that the low
frequency currents are dominated by topographic Rossby waves (Thompson, 1977).
Topographic Rossby waves are low frequency fluctuations with periods usually
greater than a week, which exist on sloping topography. Their principal
characteristics are that the fluctuations are coherent with depth and bottom
intensified with maximum speeds occurring near the bottom. The waves
propagate westwards at Site D. The original theories of topographic Rossby
waves were given by Rhines (1970) and with respect to site D, Thompson (1971)
and are summarized in the next section. A reanalysis of the Rise Array data
(Hogg, 1981) indicates that long period barotropic Rossby waves (amplitude of
the fluctuations is independent of depth) dominate in water of 4000 m under
the Gulf Stream and as these propagate in a general northward direction
towards the slope, the waves become modified into shorter wavelength bottom
trapped topographic Rossby waves. There is also some indication from Ou and
Beardsley (1980) that these Continental Rise Rossby waves are partially
reflected by the slope and shelf regions with the effect that energy is
intensified close to the Rise-Slope junction.
The current measurements at the 2800 m dumpsite will be compared with the
predictions of the theory of topographic Rossby waves and also the Rise array
measurements. The reader is referred to Thompson (1977), Hogg (1981) and also
Schmitz (1980) for more details on the interpretation of deep ocean current
meter observations in terms of Rossby waves.
10
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2.3 Topographic Rossby Waves
The theory is basically the conservation of potential vorticity assuming
a uniform sloping bottom and a uniformly stratified ocean. The dynamics are
linear so that non-linear advective terms are neglected. Wave solutions are
assumed so that all variables have the form:
P(x,y,z,t) = P(z) ei(kx + ^-^ (2.1)
where (x,y,z) is the right-handed coordinate set with x and y directed
parallel and normal to the direction of the isobaths, respectively and z is
directed vertically upwards, P is the pressure, cu the frequency of the wave,
and k, £, the horizontal wave numbers in the x and y directions, respectively.
The vertical distribution, P(z), is the solution of an eigenvalue equation.
This eigenvalue equation has simple solutions if the stratification is
uniform, namely
P(z) = P cosh (NKz/f) (2.2)
co -k aN/K2 cosh (NHK/f) (2.3)
222
where K = k + £ ; a is the bottom slope defined by h = H + ay, where h is
the depth; f is the Coriolis paramenter; and N is the Brunt-VMisElE frequency
defined by
2
N = -g(9p/8z) /p; where g is the acceleration due to gravity
and p is the density.
Important features of this solution are:
1) The wave motion is bottom intensified. Thus, the current amplitudes
increase in magnitude towards the bottom.
2) There is no phase difference between currents at different depths,
therefore, at any particular wave frequency the motion is columnar.
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3) The maximum frequency or cut-off frequency for topographic Rossby
waves is Net. Wave motions above this frequency are not supported by
these dynamics.
4) From the dispersion relation (2,3), the phase velocity or
equivalently the direction of K is in the fourth quadrant when the
axes are aligned with the bathymetry, i.e. k and H are always
negative. The wave frequency, oos is proportional to the bottom
slope and the cosine of the angle the wave-number vector makes with
the isobaths. At the highest allowed frequency, the phase velocity
is-parallel to the isobaths such that shallow water is on the right
of the direction of wave propagation.
5) The phase relationship between U and V, the x and y components of
the current vector respectively, is either in or out of phase (0° or
180°). The phase relations between the velocity components and
temperature fluctuations are such that they are in quadrature.
6) The flux of momentum is in the downslope direction, but the flux of
energy is given by the group velocity which is in a generally
upslope direction.
These predictions are modified in the presence of changing slopes and
bottom roughness with scales similar to the wavelengths of the wave motions as
described by Hogg and Schinitz (1980) and Hogg (1981).
The implications of Thompson's (1977) and Hogg's (1981) studies are that
the source of energy for the Rossby waves in this part of the Mid-Atlantic
Bight are fluctuations related to the deep Gulf Stream.
2.4 Surface Currents over the Continental Rise
The surface waters above the thermocline between the Gulf Stream and
the shelf break are extremely complex. The majority of the information on
these surface waters comes from the studies of the 106 mile site (Warsh, 1975;
Ingham et al. , 1977; Mizenko and Chamberlin, 1981; Bisagni, 1981). The
12
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physical oceanographic studies emphasize the frequent passage of anticyclonic
eddies westwards and southwestwards along the Continental Slope. The eddies
are formed from the pinching off of Gulf Stream meanders. The eddies often
dissipate in the Slope region, but sometimes maintain their integrity for
100-200 days, eventually being reabsorbed into the Gulf Stream between Cape
May and Cape Hatteras. Mizenko and Chamberlin (1981) discuss the tracks of
twelve eddies, which occurred in 1977, using satellite observations of sea
surface temperature. There appears to be a great deal of variability in the
number of eddies formed each year and the length of time an eddy persists.
Between 1975 and 1977 approximately eight eddies a year were observed and the
106 mile site was partially or completely occupied by eddies about 20 percent
of the year in 1975 and 1976, and 69 percent of the year in 1977 (Mizenko and
Chamberlin, 1981). The mixing of surface Slope water and shallow Continental
Shelf water in the Mid-Atlantic Bight is extremely complex. It is not very
well understood and involves the interaction of Gulf Stream anticyclonic
eddies with primarily wind forced shelf waters. Very complex fronts over the
Shelf break and slope region are observed to result from these interactions
(Bisagni, 1981).
Gulf Stream meanders do not penetrate below about 1000 m from the surface
and there is no evidence from existing observations on the Continental Rise
that' the eddies have any direct effect on deep circulations in this region.
This is confirmed by the analysis below of EPA's current meter observations.
However, if radionuclides reach the surface layer by physical and/or
biological pathways, then the eddy circulations and mixing across the shelf
slope front would be important processes in the transport of radionuclides
into productive shallow shelf waters. Also, if radionuclides become trapped
in a surface layer anticyclonic eddy there is a possibility that the
radioactive waste will enter the Gulf Stream system and thus be transported
across the North Atlantic.
An idea the variability of the surface layer and the large scales
involved in the dispersion of waste by surface currents is given by the
results of experiments using satellite-tracked surface buoys equipped with
near surface drogues (Richardson, 1981; Schmitz et al, 1981; Bisagni, 1980).
13
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Figure 2.4. Surface buoy trajectories (tracked by satellite) smoothed with a
40-day Gaussian filter to show large-scale motion. Large dots
mark the beginning of trajectories, smaller dots are evenly spaced
at 5-day intervals (from Richardson, 1981).
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Figure 2.4 shows smoothed trajectories of 35 buoys released in the Gulf Stream
rings and nearby areas including the Continental Rise of the Mid-Atlantic
Bight. The buoys do not follow water particles exactly because of slippage by
the drogues and drift due to wind drag on the exposed part of the surface
buoys. However, similar to the deep water floats (Figure 2.1), these
observations give a good idea of the dispersion due to surface currents in the
western North-Atlantic over approximately year long periods.
Two satellite-tracked surface buoys were also released at the 106 mile
site in the fall of 1980 (Bisagni, 1980). The drogues moved southwards along
the shelf slope towards Cape Hatteras. The drogues were then entrained into
the Gulf Stream system, traversed the Stream and spun off into the Sargasso
Sea. Eventually, two months after release, one of the buoys was positioned 20
km north of Bermuda. These trajectories from the 106 mile site are of course
only approximate realizations of the true path of surface water parcels and at
releases at different times, completely different tragectories may result, as
Figure 2.4 illustrates.
2.5 Hurricane Belle
Approximately 10 days after the EPA moorings were deployed (see Section
3), on August 10, 1976, Hurricane Belle, a rapidly moving storm, passed over
the Mid-Atlantic Bight and made landfall east of John F. Kennedy International
(JFK) Airport. The storm path is shown in Figure 1.1 (Mayer et al, 1981).
The center of the storm passed closest to the radioactive waste dumpsite at
about 0000 hours GMT on August 10, a distance of about 75 km. Maximum wind
speeds at this time were about 37 m/s (72 knots) . Maximum wind speeds over
the dumpsite, based on models of hurricane wind fields, would be expected to
be about 18-20 m/s. The storm had profound effects in the observed
circulation of the Continental Shelf where direct wind forcing is the major
forcing mechanism for the circulation (Mayer et al, 1981). It is not expected
that the effects of the hurricane would be observable in the low frequency
currents at 2800 m. However, it may be expected that energy from the storm
was transmitted to the sea floor primarily by increasing the amplitude of the
inertial oscillations. This supposition is supported by the 2800 m
15
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radioactive waste dumpsite current measurements and is discussed in some
detail in Section V.
16
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III. DATA COLLECTED
Five Vector Averaging Current Meters (VACM's) were placed on four
moorings laid at the four corners of the dumpsite. Each meter measured water
temperature and east (U) and north (V) components of velocity. Each mooring
had one meter 5.1 m off the bottom and the southwest mooring had an additional
meter at 96 m from the bottom. Table 3.1 gives the meter numbers, mooring
positions, water depths taken from the bathymetric chart, and start and stop
times. The mooring number is the first three digits of the meter number. The
last two digits of the meter number give the position of the meter on the
mooring numbering down from the meter closest to the surface.
The experiment was designed to look at the variability in space and time
of bottom currents over the region of the 2800 m dumpsite. Meters 5.1 m off
the bottom would be expected to be in the bottom boundary layer. Therefore,
in order to measure currents outside the boundary layer, a meter 96 m from the
bottom was placed on the southwest mooring. The flow field outside the
boundary layer is the forcing for boundary layer models (e.g., Weatherly and
Martin, 1978).
The data is of good quality with short gaps (usually about one hour) in
records from meters 06601 and 06901. These were filled by linear
interpolation to produce continuous records. Current meter 06701 had a
failure in the north counter about 20 days from the end of the record,
however, the north component can be reconstructed from the rotor count and the
vane direction. The turbulence levels are so low that the vector components
computed by resolving speed (rotor count) and direction into east and north
components are identical with the vector averaged components for all records.
Similarly, the temperature records were checked for values obviously out
of range, and the few erroneous values found were removed and the gap filled
by linear interpolation.
VACMs record data at 15-minute intervals. The data records were
preliminarily filtered by a three hour Lanzcos low pass filter and sampled at
hourly intervals. This filter removes 8 hours of data at each end of the
17
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EPA CURRENT METER DATA
oo
Meter No. Latitude Longitude Water Depth Height of Meter
m off bottom (m)
06601 38°26'N 72°00'W 2845 5.1
06701 38°36'N 72°00'W 2760 5.1
06801 38°36'N 72°12'W 2720 5.1
06901 96.
} 38°25'N 72°12'W 2840
06902 5.1
Location relative Start Time Stop Time
to dumpsite center (GMT)
(M/D/Y:HHMM) (M/D/Y:HHMM)
SE 8/01/76:2300
NE 8/02/76:0115
NW 8/02/76:0315
SW 8/02/76:0615
SW 8/02/76:0615
11/10/76:1400
11/09/76:2045
11/11/76:0430
11/11/76:0700
11/11/76:0700
Table 3.1. Mooring Locations.
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record. All records were adjusted to a common start time of 8/03/76:000 hours
GMT (all times are in GMT). This procedure removes high frequency noise and
results in records of manageable length.
The current meter data is analyzed and discussed in two frames of
reference according to the processes being studied. If not explicitly stated,
the U and V components used are in the east and north directions,
respectively. If a rotated frame is specified, then the U and V components
have been rotated clockwise through 45° so that the V component is parallel to
the Continental Slope, and the U component is directed towards the deeper
water perpendicular to the Continental Slope. The isobaths generally trend in
a northeasterly direction. The rotated or isobath frame of reference is the
natural coordinate system for some parts of the analysis. On the figures
'R45' after the meter number denotes a rotated frame of reference (e.g. Figure
4.2).
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IV. LOW-FREQUENCY CURRENTS
4.1 Zero Order Statistics
The dumpsite topography and the mean flows for the five current meters
are shown in Figure 4.1. The topography is fairly smooth for the northern
part of the array, but the SW mooring 069 is on the northern edge of a canyon
(the deep part of the North Toms Canyon) which disappears at 2700 m but
reappears on the slope. The mean velocities are evidently influenced by the
topography and follow the trend of the local isobaths. The mean flows are
probably not very stable estimates given the long periods (10-20 days) of the
fluctuations and the relatively short 3-month time series. However, the mean
flow is substantial (3-4 cm/s) and shows the westward direction seen at site D
and the Rise Array. As Thompson (1977) noted, this is one of the more
substantial mean currents in the deep ocean.
To investigate the low frequencies, the three hour low passed time series
data is filtered with a low pass 40-hour cosine filter to remove inertial and
tidal fluctuations and then resampled at six hour intervals. Two and one-half
days are lost from the ends of the series. Figure 4.1 also shows the
amplitudes of the low frequency fluctuations along the principal axis of the
motion. Principal axes are defined as the orthogonal directions for which the
demeaned components of the current vector are uncorrelated and thus define the
preferred direction of the fluctuations.
The amplitudes of the fluctuations exceed the mean currents. The amplitudes
are also approximately equal along the principal axes for the two eastern
moorings (066 and 067), but the motion is more polarized for the two western
moorings. The fluctuations are weaker in the general direction which is
perpendicular to the topography, also the near bottom current fluctuations at
069 are a little more polarized than at 96 m from the bottom. This may be an
effect of the slightly steeper topography at the two western moorings, also
the relative effect of the bottom slope on near bottom currents as against
currents higher in the water column. The small counter clockwise rotation of
mean flows and the principal axes of the fluctuating flows between 06901 and
20
-------
V
Figure 4.1. Bathymetric map of the 2800 m dumpsite
showing the location of the moorings.
The solid arrows show the mean flow for
each meter and the open arrows are the
principal axes with length proportional
to the standard deviation of the filtered
currents.
21
-------
06902 is probably an effect of Ekman turning in the bottom boundary layer
(Weatherly and Martin, 1978). There is also an increase in kinetic energy
moving from the SE corner to the NW corner as shown by the increase in the sum
of the amplitudes of the fluctuating components.
Table 4.1 shows the statistics in the rotated frame of reference with V
component parallel to the slope. The angle brackets <> denote time averages
and primes denote instantaneous deviations from the mean. The momentum flux
is substantial and directed downslope for all the records as predicted
by the theory. Negative momentum fluxes are also calculated for the Rise
Array (Luyten, 1977; Thompson, 1978) for water depths less than 3000 m. There
are theoretical reasons, reviewed by Hogg (1981), that the distribution of
momentum flux across the upper rise may force the observed westward flowing
mean current. The eddy heat fluxes are very small compared with the
mean heat fluxes, as consequence of U' and T1 being nearly in quadrature. The
eddy heat fluxes are responsible for non-advective long-term diffusion of heat
therefore, they can be regarded as an analogue to the dispersion by the
fluctuating currents of any dissolved constituent or passive sealer quantity.
The fact that eddy heat fluxes are small compared with the heat flux due to
advection by the mean currents indicates that the dispersion by fluctuation
components of velocity is relatively small compared with transport by the mean
2
currents. The temperature variance shows least energy at 066 and most
energy at shallowest mooring 068 similar to the kinetic energy as remarked
2
upon above. There is some decrease of with depth of the records at 069,
but the kinetic energy is almost identical at the two depths.
Comparison of these zero order statistics with the Rise Array and Site D
measurements shows that the means and variances are very similar at comparable
depths (Luyten, 1977: Table I).
4.2 Time Dependent Motions
The low passed filtered currents are shown in the vector plots (or stick
plots) (Figure 4.2) for both East and North and rotated coordinate systems.
The time series plots of the east and north components are shown separately in
Figure 4.3, and both filtered and unfiltered temperature records are shown in
22
-------
EPA CURRENT METER STATISTICS
Start date: August 3, 1976 Length =98.5 days
45 Rotation
Meter
06601
06701
06801
06901
06902
U
-0.28
0.78
-3.26
-2.97
-3.68
V
-4.19
-2.61
-1.58
-1.72
-2.91
-T
2.46
2.49
2.50
2.65
2.46
16.74
22.24
13.16
19.31
17.80
15.09
18.50
45.15
28.70
31.58
5.95
10.20
7.62
8.60
8.92
- .69
1.94
-8.15
-7.85
-9.05
-10.31
- 6.50
- 3.95
- 4.56
- 7.16
.00868
.01328
.01614
.00938
.00773
CU'T'>
.0519
-.0701
.0766
.0101
.0410
.0783
-.0452
-.2282
-.2452
-.1511
Table 4.1.
-------
i
g
i
!
i
grffe
mr*-
UUUXAN DAY* 1070
DAY a IB I« •/ Z/1078
Figure 4.2 (upper panel)
W
2 5 220
JULIAN PAYS 1O7O
DAY etc xs ax 2x1070
310 315 32G
Figure 4.2 (lower panel)
Figure 4.2. Stick plots of the low passed filtered currents in the north
and east frame of reference (lower panel) and in the rotated
frame (upper panel).
-------
vJUUIAN DAYS IB7B
DAY 21 6 Z« »X 2X1 B7O
V-COMPONENT
2 1 C 22
za 225 zse 23
3E 249 2-4C 2G0 2C5 2BQ 2flC
230 265 2QQ 2QC 300 30C 310 31
•JLK-ZAN DAYS 1O7O
DAY SIB IS ex 2XIB70 U-COMPONENT
Figure 4.3. Time series plots of the low passed filtered U (East)
and V (North) components for the five current meters.
-------
215 22O 225
JULIAN DAYS I976
DAY 215 IS 8/ 2X1878
U-COMPONENT
ON
21G 220 22E
JULIAN DAYS IO7B
DAY ZIS IS */ 2X1 070
318 3(6 323 32S
U-COMPONENT
Figure 4.4. Unfiltered and low passed filtered temperature time
series plots for the five meters.
-------
Figure 4.4. Immediately apparent are low frequency fluctuations with periods
of the order 15-20 days. Magnitudes vary from periods of low currents of less
than 5 cm/s to large events where speeds can approach 20 cm/s. The longer
period fluctuations are visually coherent over the array for some events (i.e.
days 245-265, Figure 4.2), but show some striking differences in others.
Thus, between days 260 and 295, the western moorings 068 and 069 show
northeasterly to northerly currents while 067 and 066 show southerly or
southeastern flow. This is rather remarkable considering that the moorings
are only separated by distances on the order of 15-20 km. The moorings of the
Rise Array, separated by distances on the order of 50 km, also show a similar
type of spatial variability (Luyten, 1977). Also in evidence from these time
series plots, particularly the temperature plot (Figure 4.4), is a propagation
of disturbances from the northeast to the southwest. Particularly note the
sharp temperature jump of about 0.2°C as it moves through the array between
days 272 and 276. Comparing Figure 4.4 with 4.2 shows that it is associated
with a current reversal and relatively strong flows towards the southeast.
The most energetic motions are apparently associated with motions with
periods greater than a week. This is clearly illustrated by plotting the
power spectra on an energy preserving plot. Figure 4.5 shows the kinetic
energy spectra of 06901 and 06902 where equal areas under the curve represent
equal amounts of energy. The peak in the spectrum is at about 0.06 cycles per
day (cpd) (^ 16 day period) which is close to that reported at site D by
Thompson (1977), where much longer time series were available for the spectral
estimates. It is noted that the three month time series is just long enough
to satisfactorily resolve this peak. The energy falls by an order of
magnitude from this peak at 16-day period for periods shorter than about eight
days. This is associated with the cut-off frequency for short topographic
Rossby waves, Not. Thus, the steeper the bottom slope the more wave energy can
be supported at higher frequencies. The existence of this cut-off frequency
explains why there is a gap in the energy spectra for periods between eight
days and one day. For periods shorter than one day: tidal and inertial
motions become dominant. An estimate for the bottom slope, a, is a little
difficult to make, given the variable topography, but a reasonable value is
-3 -1
about 0.0057, and a. typical deep water value of N is 1.5 x 10 s gives a
maximum frequency of about an 8.5 day period. If N is estimated from the mean
-------
K)
00
Hi O I—i
i-i ON O
ft) VO £
ja o ft)
d M i-i
ro
3 rt T3
n o fu
• O n>
H-
cr o
3 rt
ft> i-i
> OQ
O 09
N3 p.
ft) rt>
CO CO
OJ rt
Hi (D
§ *
O OJ
rt rt
H- H-
O O
O
O Hi
Hi
w
Hi
O
(D O
CD O^
(I) **D
H O
8.07281669 CPD
TIME SERIES LEN3TH • 69 DAYS
-------
temperatures (Table 4.1) assuming constant salinity, then N ^ 1.33 x 10 s
gives good agreement with the estimate of the cut off frequency given above
and explains the low energy of the currents at frequencies between 0.1 and 0.6
cpd compared with the kinetic energy (K.E.) peak at 0.06 cpd (Figure 4.5).
The theory of topographic Rossby waves also predicts that the energy of
the currents increases with depth. Therefore, the ratio of K.E. at 06901 to
the K.E. at 06902 is predicted to be less than one at frequencies smaller than
the cut off frequency. Thus K.E. ratio is shown in Figure 4.5 and is seen to
be equal or slightly greater than one at the peak of the spectrum (0.06-0.07
cpd). However, this apparent discrepancy with theory may be explained by the
fact that the bottom current meter 06902 is within the bottom boundary layer,
where bottom friction would be expected to decrease the amplitudes of the
current fluctuations from that of currents immediately above the boundary
layer. The fact that the K.E. are equal at the 16-day period indicates that
there is a maximum in wave K.E. between 96 m and 5 m off the bottom. If a
bottom boundary layer depth (Ekman depth) of 10 m is assumed (Weatherly and
Martin, 1978) , then using the estimate for the horizontal wave length of 190
-3 -1
km (given in section 4.4 below) and N = 1.33 x 10 s , then equation (2.2)
predicts a factor 1.076 increase in K.E. at 10 m from the bottom over the K.E.
at 96 m from the bottom, if there is no frictional damping. This predicted
increase is very small, so currents measured by 06901 are probably reasonably
representative of currents outside the boundary layer region. The negligible
difference in K.E. between 06901 and 06902, along with the near coincidence of
principle axes for these measurements, indicates that bottom boundary layer
frictional effects, including Ekman turning, have minor influences at 06902,
when compared with low frequency fluctuations measured above the boundary
layer.
4.3 Spectra
The power spectra are plotted in Figures 4.6-4.10 for velocity spectra,
and 4.11-4.13 for temperature spectra. The former group was plotted using
rotary components where the velocity vector is decomposed into clockwise (-)
and anticlockwise (+) components rotating at constant angular velocity equal
to the frequency. This form of presentation has the advantage that the rotary
29
-------
LO
O
htj
i-i
m
o
rt
X)
o
s!
ft)
O
rf
O
i-!
rt
tD
O
ON
ON
O
PHASE
COHERENCE
!
ec
o
VARIANCE/CPD
o
o
m
(0
06601
DATE • 76/ 8/ 3: 008
SOLID -)• COMPONENT
DASHED - COMPONENT
DEGREES OF FREEDOM = !8
BANDWIDTH . 8.09375083 CPD
TIME SERIES LENGTH 96 DAYS
-------
H-
OQ
C
ro
-P-
-j
03
•5
i-t
cn
fD
n
o
l-i
a
fD
rr
fD
i-i
PHASE
COHERENCE
VARIANCE/CPD
o
n
r~
m
-<
0870)
DATE 787 8/ 3-. 088
SOLID + COMPONENT
DASHED - COMPONENT
DEGREES OF FREEDOM : 18
BANDWIDTH . 0.09375003 CPD
TIME SERIES LENGTH 98 DAYS
-------
OJ
H-
OP
l-t
CD
do
rt
PJ
•O
CD
n
rt
i-i
Mi
o
I-J
CD
I-i
o
ON
00
O
PHASE
COHERENCE
VARIANCE/CPD
O
o
m
VI
06801
DATE 76/ 8/ 3: 000
SOLID + COMPONENT
DASHED - COMPONENT
DEGREES OF FREEDOM : 18
BANDWIDTH . 0.09375803 CPD
TIME SERIES LENGTH = 96 DAYS
-------
PHASE
COHERENCE
VARIANCE/CPD
OJ
H-
era
c
(D
•P-
VD
rt
•d
1
o
rt
H
Ml
o
l-i
rt
fl>
J-l
O
oo
s>
CD
5)
ro
o
rn
I
86001
DATE • 78/ 8/ 3: 000
SOLID + COMPONENT
DASHED - COMPONENT
DEGREES OF FREEDOM : 13
BANDWIDTH • 8.09375003 CPD
TIME SERIES LENGTH . 98 DAYS
-------
H-
OQ
ft
(D
§•
ft
0)
l-i
tl
I
H
cn
13
(D
n
(U
M)
o
ro
n
o
o
K)
PHASE
COHERENCE
VARIANCE/CPD
m
§
06902
DATE . 76/ 8/ 3= 000
SOLID + COMPONENT
DASHED - COMPONENT
DEGREES OF FREEDOM 18
BANDWIDTH . 0.09375003 CPD
TIME SERIES LENGTH : 96 DAYS
-------
OJ
Ln
H-
OQ
PHASE
COHERENCE
,Q (D
e a
P3 t3
i-i ro
ro H
cu pa
» rt
d
T3 O
o1 s:
v ro
cn i-i
ro
cn
hh T3
O rt>
H O
(T
O i-i
O\ CD
CO »
O
M n
o
d, l-(
ro
o 0
O"> O
o~i ro
o
n
P
m
N
>
6)
00
6>
VARIANCE/CPD
6>
G>
ro
m
06801
06601
DATE • 76/08/03:
SOLID
DASHED
TEMPERATURE
TEMPERATURE
DEGREES OF FREEDOM . 18
BANDWIDTH -. 0.09375003 CPD
TIME SERIES LENGTH • 96 DAYS
-------
LO
H-
OP
C
(t>
-P-
1-1 (D
(ti i-i
a. fD
T3 -O
P* O
hh CO
O T3
i-! ro
n
O rt
ON )-(
a. n,
VO
O
B
o
ro
PHASE
COHERENCE
VARIANCE/CPD -
O (9
O
P
m
05
w
•
m
o
50
06701
0690)
DATE • 76/ 8/ 3: 000
SOLID TEMPERATURE
DASHED TEMPERATURE
DEGREES OF FREEDOM : 18
BANDWIDTH . 0.09375003 CPD
TIME SERIES LENGTH : 96 DAYS
-------
u>
H-
CW
c
l-i
PHASE
COHERENCE
VARIANCE/CPD
ro
B
(B c
0 H
o- ro
13 T)
P4 O
BJ s;
CD (I)
ro i-!
HI en
O t)
i-i ro
o
O rt
ON l-i
cu ex
0
0- O
ON ro
o ro
o
ro
o
o
m
>
-<
06001
06902
DATE : 76/ 8/ 3: 000
CD
ro
w
•0
m
o
71
SOLID TEMPERATURE
DASHED TEMPERATURE
DEGREES OF FREEDOM : 18
BANDWIDTH - 8.09375003 CPD
TIME SERIES LENGTH : 96 DAYS
-------
components are not dependent on the frame of reference. For example, the
inertial and semidiurnal tidal peaks have an order of magnitude more energy in
the clockwise rotating component were the V component leads the U component by
90°. Inertial and tidal motions will be discussed in later sections.
It is immediately apparent that only the currents from the meters on
mooring 069 have one rotary component that dominates at frequencies less than
0.13 cpd. This is again the clockwise component (Figures 4.9 and 4.10). The
other three records,, the anticlockwise and clockwise motions have
approximately equal energy and moderately high coherence (or stability in this
context), indicating that the velocity fluctuations along the principal axes
at low frequencies have phase lags of 0° or 180° approximately. The lowest
panel of these plots, marked phase on Figures 4.6-4.10, is the angle of
orientation from the x (or east) axis of the principal axes of the motion at
frequencies where the coherence or stability is significant. (Purely rotary
motion has no definable principal axes.) It can be seen that the orientation
calculated for frequencies less than 0.] cpd in Figures 4.6-4.10 is very
similar to the orientation of the principal axes shown in Figure 4.1.
All the spectra are red and show lack of energy in the 1-day to 1-week
band. Most of the minor peaks in this band are not significant at the 99%
level.
4.4 Spatial Structure
The coherences at low frequencies in the topographic Rossby wave band,
and thus the spatial structure of the current and temperature records, are
investigated using Empirical Chrthogonal .Function (EOF) analysis in the
frequency domain. This method has been described by Wallace and Dickinson
(1972) and applied in a similar context to deep ocean currents by Hogg and
Schmitz (1980) and Hogg (1981).
EOF analysis has a number of advantages over conventional coherence and
phase analysis. The technique involves constructing the cross spectral matrix
for a given frequency band, then using standard numerical methods to construct
the eigenvalues and complex eigenvectors of the matrix. The eigenvectors are
38
-------
called modes, and usually there are as many modes as sets of spectra used to
construct the cross-spectral matrix. Each eigenvector mode is orthogonal to
all the other modes (i.e. there is no coherence between modes) and represents
the spatial structure of the records. The associated eigenvalue gives the
variance of the mode, and since the eigenvalues are ordered by variance, only
a few low numbered modes account for a large fraction of the total variance of
all the records for the given frequency band. It is noted that EOF analysis
is a statistical technique, and shape of the eigenvectors or modes is purely a
reflection of the statistics of the data and may not necessarily have any
physical significance. However, physical significance can usually be attached
to a mode if it explains a large percentage of the total variance (50-70% for
the first mode for this data), and the coherence squared of each data record
with the mode is significant for a large majority of the data records. The
eigenvectors are complex, so that they give the spatial structure in the form
of amplitude and phase differences. The significance levels and confidence
limits on these amplitudes and phases are given by the number of degrees of
freedom used to calculate the cross-spectral matrix.
The similarity of the low frequency motions at 5.1 and 96 m from the
bottom at mooring 069 has been discussed above and indicates that bottom
boundary layer frictional effects only have a minor influence on the near
bottom flows compared with flows above the boundary layer. Therefore, the
spatial structure of the wave motions can be investigated using measuremeuts
from the four bottom current meters assuming that frictional effects can be
neglected and currents are almost identical to currents above 100 m from the
bottom. This extrapolation to water movements above the boundary layer
assumes that the depth and shear structure of the bottom boundary layer are
similar at all four moorings. Boundary layer effects on the Rossby wave
motions are discussed further below.
The normalized cross-spectral matrix was constructed for all the
variables (U,V and T) of the four bottom current meters (i.e. excluding 06901)
and the eigenvalues and eigenvectors calculated for the low frequency band, w
< 0.146 cpd. This first mode accounts for 48.5% of total variance. Only this
mode was considered to be important, since the second mode had generally low
coherence with individual records and accounted for only 26.2% of the total
39
-------
MODE I COMPLEX EIGENVECTORS
FREQUENCY-.0417CPD BANDWIDTH-.0729CPD DE6REES OF FREEDOM-!4
PERCENT VARIANCE - 50.3X
200
Id
Q
-200
TEMP
S
a
in
u
o
kl
a
ui
V COMP
U COMP
TEMP
12345
06982 06601 06701 06801 METER NUMBER
Figure 4.14.
Amplitude, phase and coherence
squared of the record with the
mode for the first mode EOF of
the low frequency band.
40
-------
variance. There are 28 degrees of freedom, and the 95% significance level for
coherence squared is 0.206. The analysis was also performed considering only
the U and V components, also dividing the low frequency band into two, each
with 14 degrees of freedom. The results for the lowest frequency band for U,
V and T using 14 degrees of freedom are shown in Figure 4.14. Using U and V
only, the first mode represents 73.4% of the total variance. However, the
results from these latter calculations show only minor changes in structure
when compared to Figure 4.14.
Examination of Figure 4.14 shows that U and T have similar spatial
structure and reasonably consistent phase difference of ^ 180°. The V
component magnitude and phases at moorings 066 and 067 have wide error margins
due to the low coherence squared of the data with the mode, but even so, the
phase differences are reasonably close to 180°. However, the V component
leads the U component by about 90° for mooring 069, indicating predominantly
clockwise rotary currents, whereas the U and V component are clearly in phase
at 068. The theory of topographic Rossby waves outlined above requires phase
differences between U and V of 0° or 180°; therefore, pure topographic wave
motion is evidently being modified in the SW corner of the array. Phase
differences between U and V, which differed from 0 or 180°, were also found by
Thompson (1977) and Hogg (1981) for the Rise Array data.
The phases of U and T in Figure 4.14 indicate southward phase
propagation. From these phase differences between the variables, the wave
numbers can be calculated from
A is the phase difference of a variable (U, V or T) between moorings,
i and j, (Ax.., Ay..) is the spacing between the moorings in east and north
J *J
coordinates, and (k, £) are the horizontal wave numbers which are the
reciprocals of the east and north components of the wave length. Estimates
for k and Si were found by using the phase differences from the first mode for
all four stations and using the variables separately and in combination and
calculating the best fit by a least squares technique. The results are shown
-------
EPA CURRENT METER DATA
Wave Number Estimates
(north and east coordinates)
Variables Frequency Degrees of Wave Number
(CPD) Freedom k 1
(cycles/km) = (k2+
U 1 .000196
V -.022007
T ? .0781 28 -.002148
U.V.T -.007985
U,T ' .000974
U,T -0417 14 -.000552
U,T .1146 14 -.005298
-.005732
-.000943
-.004530
-.003735
-.005131
-.004846
-.009326
Wave Length
i. K (km)
^
.005735
.022027
.005013
.008815
.005223
.004877
.010711
174
45
199
113
191
205
93
Angle
(Degrees
from North
178°
268°
205°
245°
191°
186°
210°
Table 4.2.
EPA CURRENT METER DATA
Vertical Phase Differences at Mooring 069
Frequency - 0.0781 cpd., Degrees of Freedom 28
Variable
Phase Difference
6901-6902
95% Sig. Level
U
V
12.7'
14.7C
11°
9°
Table 4.3.
42
-------
in Table 4.2. Except for taking the phases from the first eigenmode, the
estimates are made using essentially the same method as Thompson (1977).
Not unexpectedly, the most consistent results came from the least square
solution using U and T together. The calculated wave vector points into the
SW quadrant and the wavelength is approximately 200 km. Therefore, the
topographic Rossby waves show a component of phase velocity directed towards
the southwest or along the isobaths and there is good agreement with
Thompson's similar calculations for Site D and the Rise Array (Thompson,
1977). If we divide the low frequency band into two, then the higher
frequency has a shorter wavelength (93 km), and the wave vector is rotated
towards the isobath direction when compared with the lower frequency. This is
precisely the kind of behavior to be expected as the frequency increases
towards the cut-off frequency. Net.
The final comparisons with topographic Rossby wave theory to be made by
using the dumpsite data are the vertical phase differences at mooring 069.
Topographic Rossby waves should show essentially columnar motion with an
increase in energy towards the bottom. The dumpsite data shows negligible
increase in energy between 96 m and 5.1 m off the bottom, and it is therefore
of interest to investigate whether the phase differences are significantly
different from zero. Again, the EOF method is used to calculate the phase
differences. The results are presented in Table 4.3 and show phase
differences slightly greater that the 95% significance level for zero phase
difference. Meter 06902 is within the bottom boundary layer; therefore,
bottom frictional effects will affect the phase of the currents (Weatherly and
Martin, 1978). The fluctuating currents within the boundary layer are
predicted to lag the currents outside the boundary layer and this is confirmed
in Table 4.3. The small phase lag, the small angle of Ekman veering seen in
the mean and fluctuating low frequency currents (Figure 4.1), and the
negligible reduction of kinetic energy at 06902 compared with 06901 indicates
that current meter 06902 is close to the top of the boundary layer, thus the
average boundary layer thickness may be similar to the 6-12 m indicated by
Weatherly and Martin (1978) for their data in a stratified boundary layer
above a sloping bottom, rather than the theoretical neutral boundary layer
thickness of order 30 m.
43
-------
4.5 Dispersion by Low Frequency Currents
The low frequency motions can be summarized as being dominated by
topographic Rossby waves at frequencies lower than the cut-off frequency (^
9-day period) which is determined by the stratification and the slope of the
bottom. The peak in the low frequency spectrum falls at about the 16-day
period. The wavelength of the topographic waves is on the order of 200 km and
phase propagation is directed into the southwest quadrant with the propagation
of energy being in the upslope direction. The motions seem to be bottom
trapped with amplitudes of about 7 cm/s. The currents are evidently
influenced -by topography, particularly in the orientation of the principal
axes and direction of the mean currents. The latter are substantial,
averaging about 3-4 cm/s in a generally westward direction. As expected,
there is very little energy in the 1-day to 1-week period of the spectrum.
Figure 4.1 and Table 4.1 provide a good summary of the low frequency motions.
Dispersion by the low frequency motions is a stochastic problem for large
space and time scales. An important measure of the time scales, or
persistence of the currents are the auto correlations, R (T) , R (T) and R (T)
for velocity and temperature,
where < U* (t) U* (t + T)>
= ' etc>
The autocorrelations plotted against lag, T, for the U and V components and
temperature are shown in Figures 4.15-4.19. The velocity correlations fall to
zero at lags of 3-7 days with the majority around 5-6 days and the temperature
correlations at lags of 15-18 days. These times represent the memory of the
velocity and temperature fields. Therefore, time scales on the order of 5-15
days are important for long time (order years) dispersion of radioactivity
from the bottom. These correlation functions would play a fundamental role in
any stochastic theory that may be developed to model long-term dispersion in
the boundary layer (Csanady, 1973). (For an example of a stochastic model
applied to climate variability, see Hasselmann, 1976).
44
-------
AUTOCORRELATIONS
I .0-
0.5-
0.0-
N.
•0.5-
i i I r
5
i i i i i i i i i
10 15 20
06601 R45
LAGCDAYS)
Figure 4.15.
Autocorrelations as a function of lag,
T, for low passed data for meter 06601
)RU(T), ( ----- )
45
-------
AUTOCORRELATIONS
1 .0
0.5
0.0
-0.5
-1 .0
06701 R45
LAG
Figure 4.16.
Autocorrelations as a function of lag,
T, fcr low passed data for meter 06701
' ( )Rt(T)
46
-------
AUTOCORRELATIONS
I .0-
0.5-
0.0-
-0.5-
-1 .0-
\ i i i i i i r r i i i i i i i i
5 10 15 20
06801 R45
LAGCDAYS5
Figure 4.17.
Autocorrelations as a function of lag,
T, for low passed data for meter 06801
c
( ----- )R(T)' (
47
-------
AUTOCORRELATIONS
1 .0-
0.5-
0.0-
-0.5-
-1 .0-
I I I I
0 5
15
20
06901 R45
LAGCDAYS)
Figure 4.18. Autocorrelations as a function of lag,
T, for low passed data for meter 06901
48
-------
AUTOCORRELATIONS
I .0
0.5
0.0
-8.5
0
06902 R45
LAGCDAYS)
Figure 4.19.
Autocorrelations as a function of lag,
T, for low passed data for meter 06902
' ( )Rt(T)
49
-------
PROGRESS VE VECTOR DIAGRAI
o
in"
O o-
Ld
ct:
O
o
o
(N '
C
in
Of
I ~1 T
-300 -250
6601
-200 -150 -100 -50 0 50
-WEST KILOMETRES +EAST
100
150
8/ 5/76 TO 11/ 7/76 40HR LP FILTER
Figure 4.20. Progressive Vector Diagram for 06601. Low passed
filtered data. The date is indicated every 10
days.
50
-------
o
m
CM
Ld
I—
UJ o
O
o
'
X
on
o
UT
PROGRESS VE VECTOR D AGRAM
-300 -250 -200 -150
-WEST
6801
-100 -50
KILOMETRES
0 50
+ EAST
100
150
8/ 5/76 TO 11/ 7/76 40HR LP FILTER
Figure 4.22. Progressive Vector Diagram for 06801. Low passed
filtered data. The date is indicated every 10
days .
51
-------
PROGRESS VE VECTOR DIAGRAM
I
t—
o
z
-f
LJ
(—
UJ
2
o
o
o .
- o
lr
0
in
CN
^2A_>
4^
1 1 1 1 1 1 l 1
-150 -100 -50 0 50 100 150 200
-WEST KILOMETRES +EAST
i i
250 300
6701
8/ 5/76 TO 11/ 7/76 40HR LP FILTER
Figure 4.21. Progressive Vector Diagram for 06701. Low passed
filtered data. The date is indicated every 10
days.
52
-------
PROGRESS VE VECTOR D AGRA
o
LJ
cr
i—
LJ o
^ 2
O
in
I
-350 -300 -250 -200 -150 -100 -50 0
-WEST KILOMETRES +EAST
50
100
6901
8/ 5/76 TO 11/ 7/76 40HR LP FILTER
Figure 4.23. Progressive Vector Diagram for 06901. Low passed
filtered data. The date is indicated every 10
days.
53
-------
PROGRESS VE VECTOR D AGRAM
o
in -i
(fi
UJ
UJ o
2 e-
o
n:
o
en
o-
-450 -400
6902
-350 -300 -250 -200 -150 -100
-WEST K LOMETRES +EAST
-50
8/ 5/76 TO 11/ 7/76 40HR LP FILTER
Figure 4.24. Progressive Vector Diagram for 06902. Low passed
filtered data. The date is indicated every 10
days.
54
-------
To show an estimate of Lagrangian motion, the progressive vector diagrams
of the five current meters are shown in Figure 4.20-4.24. These diagrams are
not to be interpreted as the path that a particular particle of radioactivity
would follow in this time period, as the true Lagrangian path is influenced by
the local topography. Rather, they should be viewed as estimates of the
distances and directions such a particle may follow in a three month period.
Evidently, even though the current meters are only 17-20 km apart, the
directions are quite different, reflecting the influence of the local
topography on the mean currents. The effects of very steep topographic
features, such as canyons, on the mean flow over the Continental Rise is not
understood at this time. The progressive vector diagrams also illustrate the
excursions from the mean path of a water particle caused by the low frequency
wave motions. The largest apparent excursion occurs between 4-29 of October
1976 (e.g. Figure 4.22) which indicates deviations of ± 40-50 km from the mean
path. An excursion of this magnitude would bring a water particle to the
region of the slope-rise junction, thus possibly being influenced by the more
complex dynamics (Ou and Beardsley, 1980). The effect of the low frequency
wave motions may be to disperse radionuclides over much of the Continental
Rise to the southwest of the dumpsite. If the total distance traveled along
the 2800 m isobath is taken to be approximately 300 km from the progressive
vector diagram over the period of the measurements, then the particle will be
just north of Cape Hatteras. From Cape Hatteras, we may speculate that the
water particle may be transported by the Western Boundary Undercurrent under
the Gulf Stream and enter the South Atlantic Bight. Such a particle may also
become part of the deep Gulf Stream system and be dispersed into the
northwestern Atlantic as indicated by the quasi-lagrangian float tracks shown
in Figure 2.2 as discussed in Section 2.
It is of also interest to use the temperature fluxes to estimate
horizontal eddy dif fusivities due to low frequency wave motions, i.e.
, = -K
x Y
where K K are eddy diffusion coefficients and the horizontal gradients are
x' y
given by 3T/3x and 8T/3y (rotated frame of reference). Using the results from
Table 4.1 if and for the four lower meters are averaged, and
55
-------
estimating 8T/3x, 8T/8y across the corners of the array, then the values
/• fy s~ r\
calculated for K and K are 7 x 10 cm /s and 7.3 x 10 cm /s, respectively.
x y
These diffusion coefficients are reasonable values for the deep ocean and
indicate a reasonable amount of dispersion is occurring from the low frequency
fluctuating currents. Note that due to the depths of the four lower current
meters, the cross slope and long slope gradients and diffusion coefficients
are calculated parallel to the bottom rather than in the horizontal plane in
which eddy fluxes are normally defined.
This section may be summarized by asking the question, "how do the
relatively -well understood dynamics of these energetic low frequency motions
contribute to the dispersion of radioactivity leaking slowly from a source on
the bottom?" The problem is essentially that of motions of water and sediment
in the bottom boundary layer. Dispersion of dissolved constituents is
discussed above, and the horizontal eddy diffusion coefficients estimated.
Sediment transport is also important because radionuclides attach readily to
sediment particles. The current measurements at 5.1 m off the bottom show
evidence of Ekman veering and are similar in magnitude to currents measured at
96 m from the bottom, and for reasons cited above, can be considered to be
within the boundary layer but probably near the top of the boundary layer (see
Section 4.4). A typical example of the statistics of these boundary layer
currents is given in the form of a bivariate frequency distribution in Table
4.4 (for data from 06902), which includes high frequency inertial and tidal
motions. The currents exceed 10 cm/s 30% of the time, and exceed 15 cm/s
about 6% of the time. The most persistent current direction is approximately
southwards (27% of the time), which also shows the highest speeds. Only the
highest speeds above 18 cm/s, which occur less than 1% of the time, would be
capable of suspending fine grain sediment. Sediment suspension by currents
depends upon the detailed shear structure in the boundary layer which is
influenced by stratification and small scale topographic variations (Weatherly
and Martin, 1978). This detailed vertical structure is not given by this
data, thus deductions made on the transport of sediments sediments are not
precise. It appears that transport of very fine grain sediments from the
dumpsite by the currents is not an important process in the dispersal of
radionuclides in the bottom boundary layer. This conclusion ignores possible
catastrophic events such as turbidity currents flowing down from the Slope
56
-------
FREOUENCV DISTRIBUTION
1.00 HOURLY DATA
STATION! 06902
3HRLP
SPANNING 8/ 3/74 TO 11/11/76
DIRECTION
DEGREES
0- 30
30- 60
60- 90
90-120
120-150
150-180
180-210
210-240
240-270
270-300
300-330
330-360
SPEED
CM/S
,B 1,7
.8 3,0
1,2 3.0
,9 1.9
.6 1.3
.5 1.1
.3 1,5
,8 1.6
,7 2.5
,4 2,7
,5 2.2
,7 1.9
0 3
i i
1,0
1,7
1,6
1,3
,8
,9
1,7
2.9
4,8
4,6
1,5
1,1
6
i
,7
1,0
,5
,2
.3
.5
,9
2,1
6,7
5,0
1.4
,9
9
j
1,2
.4
,0
,0
,2
,0
,1
,8
6,6
4,2
.8
.8
12
,
,5
,0
.0
.0
,1
,1
,1
,3
2.7
1,9
.3
.2
15
j
,1
.0
,0
,0
,0
,0
.0
,0
,6
,9
.0
,2
18
,
3 6 9 12 15 18 21
PERCENT 8.3 24,4 24.0 20,3 15.1 6,1 1,8
MEAN OIR 160 179 209 236 243 247 26?
STD DEV 106 107 92 79 82 69 65
PERCENT
6,0
7,0
6,3
4,3
3,3
3,1
4,7
8,7
24.5
19,6
6,7
5,8
HEAN
SPEED
8,33
6.17
5,28
4,97
5,91
6.41
7,13
7,84
10,76
10,45
7.80
7,93
HIM
SPEED
1,42
,26
1,13
1,06
.80
.74
1.42
.41
1.46
1,24
2,02
.52
MAX
SPEED
19,82
14,35
11,64
14.46
16,97
17,63
16,56
16,29
20,55
20.47
16.18
20.14
STD. DP
4,90
3,2V
2.48
2,86
3.66
3,36
2.94
3,63
3,96
4.21
3,84
4.65
100,00
SUMMARY STATISTICS
MEAN SPEED = B.56 CM/S MAXIMUM = 20.55 CH/S
STANDARD DEVIATION = 4,25 CM/S
MINIMUM
SKEWNESS
,26 CM/S
.39
RANGE = 20.30 CM/S
IN A COORDINATE SYSTEM WHOSE Y AXIS IS POSITIONED ,00 DEGREES CLOCKWISE FROM TRUE NORTH
MEAN X COMPONENT = -4, -18 PM/S STANDARD DEVIATION = 4,82 CM/S SKEWNFSS =
MEAN Y COMPONENT = .41 CM/G ^TAM'iARD DEVIATION - 4.95 i.'M/H SKEWNESS -
.02
Table 4.4. Bivariate Frequency Distribution for speed and direction for meter
06902 (east and north frame of reference).
-------
FREQUENCV DISTRIBUTION
1,00 HOURLY DATA
STATION! 06601
3HRLP
SPANNING 8/ 3/76 TO 11/10/76
DIRECTION
DEGREES
0- 30
30- 60
40- 90
90-120
120-150
150-180
180-210
210-240
240-270
270-300
300-330
330-360
SPEED
on CM/S
oo
.5 1,6
,4 1.0
.9 1.1
1.0 1.7
,8 1.9
.7 2,0
1,8 4.0
1.3 5.5
1.5 4.4
.9 3,4
.8 1,7
.9 1.3
0 3
3 6
,7
.8
.6
.8
1.6
3,8
3,5
5.2
6.4
3,0
1.0
.6
6
9
,1
, 2
i
,3
2,0
2.1
3,0
2.9
6,2
2.3
,4
,3
9
I
12
,0
,0
,0
,2
,3
.6
1,1
1,2
3,1
,9
.1
.0
12
15
.0
.0
,0
,0
,0
.0
.1
,7
1,5
,3
.0
,0
15
i
18
.0
.0
,0
,0
,0
,0
,0
,1
,1
,2
,0
,0
IB
i
21
PERCENT
PERCENT 11,6 29,9 28,2 19.9 7,5 2,6 .4
HEAN DIR 197 204 210 219 230 249 258
STD DEV 92 84 71 60 42 32 31
SUMMARY STATISTICS
HEAN SPEED = 7,23 CM/S MAXIMUM = 19,B8 CM/S
STANDARD DEVIATION - 3.59 CM/S
100,00
MINIMUM
SKEUNESS
.20 CM/S
,59
HIN
MAX
STD. DEV.
SPEED
3.
2.
2.
4.
6,
9,
13,
16,
23,
11.
4.
0
3
B
0
6
2
5
9
4
0
1
3,1
4,
5.
4,
5,
7.
7.
7.
7.
a.
7.
5,
92
48
59
37
16
45
01
39
72
62
,58
4.85
SPEED
1,79
1,65
1,48
1,08
1,67
1.14
1.28
,75
.77
1,20
.20
1,58
SPEED
10.
10,
9.
13,
14.
13.
16.
IB.
19,
19.
16,
11,
23
48
75
98
12
97
00
32
04
88
84
i42
2-
2.
2,
2,
3,
3,
3.
3.
3,
3,
30
72
51
95
17
14
55
86
96
84
2,98
2,45
RANGE - 19.68 CM/S
IN A COORDINATE SYSTEM WHOSE Y AXIS IS POSITIONED ,00 DEGREES CLOCKWISE FROM TRUE NORTH
HEAN X COMPONENT = -3.17 CM/S STANDARD DEVIATION « 5.41 CM/S SKEWNESS = -.0?
MEAN Y COMPONENT - -2.68 CM/S STANDARD DEVIATION = 4.32 CM/S SKEUNESS = .02
Table 4.5. Bivariate Frequency Distribution for speed and direction for meter
06601 (east and north frame of reference).
-------
SPANNING BX 3/76 TO ll/ 9/76
FREQUENCY DISTRIBUTION
1.00 HOURLY DATA STATION! 06701 3HRLP
DIRECTION
DEGREES
0- 30 ,6 1,1 ,8 ,1 .0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 .0
30- 40 ,8 1,3 1,5 ,2 ,0 .0 .0 .0 ,0 ,0 ,0 ,0 ,0 .0
60- 90 1,1 2.1 1,8 .4 ,1 .0 .0 .0 .0 ,0 ,0 ,0 .0 .0
90-120 1,4 4.4 2,5 ,6 ,3 ,0 ,2 .1 .0 .2 .1 .0 .0 ,1
120-150 1,5 3,9 3,6 1.5 ,3 ,2 ,3 .1 ,1 .0 .0 ,0 .0 ,0
150-180 1.7 3.3 3.0 1,5 ,2 .1 ,1 .1 ,0 ,0 ,0 ,0 .0 .0
180-210 1,2 4,3 3,7 1,4 ,2 ,2 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0
210-240 1,4 4,5 3,9 2,8 1,4 .5 ,2 ,0 ,0 .0 .0 ,0 .0 .0
240-270 .9 3,4 4.2 4.1 2,8 ,6 .1 ,0 ,0 ,0 ,0 ,0 ,0 .0
270-300 ,9 1,5 1,7 1,8 ,8 ,3 .1 .0 ,0 ,0 .0 ,0 ,0 ,0
300-330 ,9 1,9 1,3 ,3 ,0 ,0 .0 .0 ,0 ,0 ,0 .0 .0 ,0
330-360 ,6 1,5 ,5 .3 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 ,0 .0
PERCENT MEAN HIM MAX
SPEED SPEED SPEED
STD. DEV.
2,6
3,7
5,5
9,6
11,5
10,0
11,1
15,0
16.2
7.1
4,4
3,0
4,
5.
5,
7.
7,
6,
6.
7,
8,
7.
5.
4,
95
37
65
22
07
58
47
75
74
99
17
93
1,06
.94
1.09
.94
,83
,67
.42
,45
,94
.26
.47
1,15
9
11
38
40
28
27
31
39
21
18
13
10
,B6
,66
,43
,04
,96
.26
.32
,30
.01
,33
.37
,84
^
2
4
6
4
4
3
4
4
4
2
2
,33
.50
.20
,44
.48
,38
,74
.54
.06
.25
.82
.56
i-Q
SPEED 0
CM/S '
12 15 18 21
12
24 27 30 33 36 39
i j i | I | f j I |
15 18 21 24 27 30 33 36 39 42
PERCENT 13.1 33,1 28.5 14,8 6.4 1,9 ,9 .4 ,2 ,3 ,1 ,0 ,0 .1
MEAN DIR 177 182 183 214 229 231 183 150 154 122 138 96 79 142
STD HEV 90 83 79 66 52 32 62 57 47 22 36 0 0 77
SUMMARY STATISTICS
MEAM SPEED = 7.06 CM/S MAXIMUM - 40,04 CM/S
STANDARD DEVIATION = 4,32 CM/S
100.00
MINIMUM
SKEWNESS
,26 CM/S
2.11
RANGE = 39.77 CM/S
IN A COORDINATE SYSTEM WHOSE Y AXIS IS POSITIONED ,00 DEGREES CLOCKWISE FROM TRUE NORTH
MEAN X COMPONENT = -1.24 CM/S STANDARD DEVIAIION = 4.40 CM/S SKEWNESS = .52
MEAN Y COMPONENT - -2.50 CM/S STAt/flARI"' DEVIATION - 4.45 CM'S SKEUNE3S = -.54
Table 4.6. Bivariate Frequency Distribution for speed and direction for meter
06701 (east and north frame of reference).
-------
FREQUENCY DISTRIBUTION
1.00 HOURLY BflTA
STATION: 06801
3HRLP
DIRECTION
DEGREES
0- 30
30- 40
60- 90
90-120
120-150
150-180
180-210
210-240
240-270
270-300
300-330
330-360
SPEED
CTl CH/S
0
1,7
1.0
1.1
1.0
1.4
.6
,9
!,">
,7
1.0
1,5
1,3
0
i
3
3
1
1
1
1
1
1
1
3
4
4
4
.0
.5
.2
.0
.7
.1
,9
,1
.5
,5
T
3
i
6
1.7 ,8
1,3 1.0
1.0 ,8
.5 ,1
.5 ,0
1,0 .1
1.1 .3
4.5 4.3
4.4 1,6
4.1 1.3
2.2 1,4
6 9
[ ;
9 12
,7
,8
,1
,0
,0
.0
.0
3.1
1,0
,0
1.7
12
i
15
,3 ,0
.9 ,3
,1 .0
.0 ,0
.0 .0
,0 .0
.0 .0
.7 .4
2.5 2.3
.7 ,3
.0 .0
1.4 .0
15 18
i t
18 21
.0
,0
.0
.0
,0
.0
,0
( j
.6
,1
.0
.0
21
I
24
.0
.0
,0
.0
.0
,0
,0
. 0
,1
.0
.0
,0
24
t
27
SPANNING 8/ 3/76 TO 11/10/74
PERCENT
MEftN
MIH
MAX
STD. DEV,
SPEED
8,
7.
4.
2.
3l,
2.
4.
7,
21,
13.
11.
12,
1
9
3
7
7
B
1
8
4
6
4
2
6,
8.
5,
4.
4.
5.
5,
8,
11.
7.
5,
6,
28
17
94
28
13
10
11
06
26
63
95
01
SPEED
.42
,56
,64
1.08
,87
,87
.39
.96
1.55
.08
,47
,98
SPEED
IB.
19.
15,
9,
9.
12.
10.
23.
26,
44
90
55
38
29
47
90
90
00
23,39
12,
73
17,96
3
5
3
2
1
2
2
5
5
4
2
4
.96
.23
,74
,54
.67
,87
,38
.49
.26
.18
,65
,69
PERCENT 13.6 31.2 24.0 12.4 8.1 6.5 3.3 .8 .1
tefiH DIR 178 212 229 227 233 234 231 251 249
STD DEV 112 112 100 99 101 98 70 38 76
SUMMARY STATISTICS
H£AN SPEEIi = 7.75 CM/S MAXIMUM = 26.00 CM/S
STANDARD DEVIATION = 4.82 CM/S
100.00
MINIMUM
SKEWNESS
,08 CM/S
.96
RANGE
25.92 CM/S
IN A COORDINATE SYSTEM WHOSE Y AXIS IS POSITIONED ,00 DEGREES CLOCKUISE FROM TRUE NORTH
MEAN X COMPONENT = -3.-I5 CM/S STANDARD DEVIATION = 6,53 CM/S SKEWNESS = -,29
MEAN Y COMPONENT = 1.12 CM/S STANDARD DEVIATION = 5.25 CM/S SKEUNESS = ,42
Table 4.7. Bivariate Frequency Distribution for speed and direction for meter
06801 (east and north frame of reference).
-------
FREC1UENCY DISTRIBUTION
1.00 HOURLY DATA
STATIONI 04901 3HRLP
SPANNING 8/ 3/74 TO 11/11/74
DIRECTION
DEGREES
0- 30
30- 40
60- 90
90-120
120-150
150-180
180-210
210-240
240-270
270-300
300-330
330-360
.4 1,2 1,5 ,6 1,1 .5 .1 ,1
1.0 1.7 ,9 .9 ,9 1,0 .3 ,0
1,0 2,8 1,8 .7 ,5 .2 ,0 .0
1,1 3,4 1,0 .7 ,0 ,0 .0 ,0
1,5 1,4 1.3 .6 ,3 ,0 ,0 .0
.9 1,4 1,5 .6 ,2 .1 ,0 .0
,8 1.3 1.4 .t ,4 ,0 ,0 ,0
,8 2,2 3,4 2,0 .7 .2 ,0 ,0
.7 2,6 4,8 5.0 2.? 1,0 .5 .0
.5 2,8 4,0 5,6 4.0 1.4 ,9 .0
.4 1.9 2.6 2,3 1,7 ,4 ,2 .0
,4 1,3 2,0 .5 .4 ,1 .0 ,0
PERCENT
5.
6.
7,
6,
5.
4,
4,
9.
17,
19.
9.
4,
5
9
0
3
0
6
5
5
2
5
5
7
MEAN
SF'EED
9
9
6
5
5
6
6
7
9
10
9
7
,26
.10
.42
.25
,47
,21
,54
,49
.44
.34
,09
.30
HIM
SPEED
2,05
.99
1,85
1,44
.76
,93
1,49
,92
,65
,78
1.14
1.84
MAX
SPEED
22
21
14
13
14
17
18
17
19
20
21
17
.17
.OS
.95
.86
,60
,03
.48
.13
,64
.77
.16
.96
STD.
4
5
3
2
3
3
3
3
4
4
4
3
DEI
,82
,52
,54
.49
,33
,43
,47
,49
.01
.10
.18
.20
CT)
SPEED 0
CM/S l
12 15 18 21
12 15 18 21
24
PERCENT 9,524.024.519,912.8 5,1 2.0 ,2
MEAN DIK 160 180 215 234 225 195 228 100
STD PEM B9 100 95 83 101 116 102 144
SUMMARY STATIC!IIS
MEAN SPEED = 8.33 CM/S MAXIMUM = 22.17 CM/3
STANDARD DEVIATION -- 4.21 CH/S
100,00
MINIMUM
SKEUNESS
.65 CM/S
.52
RANGE = 21.52 CM/S
IN A COORDINATE SYSTEM WHOSE. Y AXIS IS POSITIONED .00 DEGREES CLOCKWISE FROM TRUE NORTH
MEAN X COMPONENT - -3.27 CM/S STANDARD DEVIATION - & .
-------
region and is based on only three months of data. Statistics of the data from
the other bottom current meters are shown in Tables 4.5-4.8. The maximum
speeds measured vary considerably for the five meters with the highest speed
of 40 cm/s measured at meter 06701. However, distribution of speeds below 18
cm/s is similar for all five current meters and speeds above 18 cm/s generally
occur less than 3% of the total length of each record.
In this section on dispersion by low frequency currents, a few parameters
such as eddy diffusivities, correlation times, and particle excursions have
been estimated from the data, which will be of use for any dispersion
calculations made at this site. A qualitative discussion of sediment
transport at the 2800 m dumpsite indicates that suspension of sediments due to
high currents will occur less than 1% of the time and thus transport of
contaminated sediments away from the site is likely to be minimal.
62
-------
V. INERTIAL CURRENTS
The next most energetic part of the spectrum after the low frequency
topographic wave motions is the inertial motions. Inertial currents are
internal wave motions which occur with periods near 2II/f, where f is the
Coriolis parameter. The inertial period is closely related to a half pendulum
day and is a natural resonance period of the ocean which varies with latitude.
The inertial wave motions are caused by rapid changes in wind forcing and
possibly also by the interaction of low frequency currents with rough bottom
topography. Inertial currents can be characterized as a nearly horizontal
current vector rotating clockwise at frequency, to, which is close to the
inertial frequency, f. The energy of the inertial oscillations propagates
downwards from the generation zone at the surface, thus any instant the
velocity vector turns 360° over the depth of the vertical wave length of the
inertial oscillation. This turning of the velocity vector is equivalent to a
vertical phase difference, and this phase change with depth results in
instantaneous vertical shears due to the inertial wave. These shears, along
with vertical mixing, are a very effective mechanism for the horizontal
dispersion of radionuclides in deep water by analogy with the horizontal
dispersion of pollutants by oscillating tidal currents (Bowden, 1965).
Apart from horizontal dispersion, inertial currents also contribute to
the turbulent fluxes in the bottom boundary layer. The downward inertial
energy flux into the boundary layer for an inertial current magnitude of 10
cm/s is of the same order of magnitude as the rate of turbulence production n
the bottom boundary layer by a steady current of 10 cm/s just above the
boundary layer (Kundu, 1976). Since 10 cm/s is a representative magnitude for
the low frequency currents and maximum inertial currents at the 2800 dumpsite
then inertial events originating from the surface layer can significantly stir
the boundary layer.
Inertial oscillations can be summarized as clockwise rotating currents (V
leads U by 90°) generated by storms in the surface layer. The vector speed is
almost constant with the rotation over one inertial period, but the
oscillations are highly intermittent. Figure 5.1 shows inertial currents
63
-------
RAW DATA - U COMPONENT
20 r—
10
.
O
H
O
O
_J
UJ
0
-! 0 I—
-20
iiTiiTTnninTir
0 10 20 30 40 50 60 70 80 90 100
06901
DAYS
DOF36
DATE 767 8/3: 0
Figure 5.1. Band passed (frequency = 1.2428 cpd, band
width 0.1875 cpd) inertial currents for
meter 06901.
64
-------
260 265 278 27S 288
JULIAN DAYS 1976
DAY 2IS IS B/ 2/1976
U-COMPONENT
Figure 5.2. U component time series plots for 3 hour low passed data.
65
-------
generated by bandpass filtering about the inertial period. The currents
achieve maximum magnitudes of about 10 cm/s. The intermittent growth and
decay of the envelope is a striking feature of these oscillations, which have
also been observed in other studies of inertial currents (Kundu, 1976;
Perkins, 1976). The first 60 days of the U component of all five currents
meters are presented in Figure 5.2 to show the inertial and tidal oscillations
superimposed on the low-frequency currents. The maximum inertial currents
occur at approximately 17 and 31 days from the beginning of the record (Figure
5.1) (Julian days 233 and 247, respectively, Figure 5.2). These peaks in
inertial energy are possibly related to the passage of Hurricane Belle (see
Figure 1.1). The spacing of the current meter array at the 2800 m dumpsite
makes possible some estimates of the horizontal and vertical wavelengths and
vertical phase and group velocities for deep inertial wave motions. This
analysis follows Kundu (1976), who studied inertial motion in shallow water
using current meter records from the Oregon Continental Shelf.
Previous studies of inertial currents in the Mid-Atlantic Bight include
Wunsch and Hendry (1972), who used a small triangular array with approximately
1 km horizontal spacing placed on the Continental Slope (39°50'N, 70°56'W)
south of Cape Cod at a depth of about 1000 m. The experiment was designed to
study bottom intensification of internal waves due to reflection from the
bottom slope. Tidal and inertial currents were examined, but emphasis was
placed on the former. Perkins (1976) studied inertial currents from the site
D observations and correlated shifts in the observed inertial frequency from
2II/f with the relative vorticity of the low frequency currents. Mayer et al.
(1981) studied inertial oscillations generated on the Continental Shelf by the
passage of Hurricane Belle (Figure 1.1).
Measurements of inertial oscillations usually show upward propagation of
phase and hence downward propagation of energy. The observed frequency is
also between 5-10% above f- the local inertial frequency, and the spectral
peaks (see Figures 4.6-4.10) are broad and not sharply defined. This is
partly due to the intermittent nature of the oscillations.
The relevant formulae are the dispersion relation (Kundu, 1976)
66
-------
'2 29 ?
in = (k^ + O (NZ -
2 ,2 -
to - f
where m is the local vertical wave number; k and H the horizontal wave
numbers, N the Brunt Vaisala frequency, f the Coriolis parameter and also the
local inertial frequency, and u> the observed frequency. The vertical
components of the phase and group velocities, c and c , respectively, are
8
related by
- * c((f/W)2 - 1) (5.2)
3m
where c = u)/m.
Figure 5.3 shows an EOF analysis for U and V components of the five
current meters for a frequency band of width of 0.188 cpd centered on the
inertial frequency 1.245 cpd (corresponding to 38°30'N). The computations are
made using 36 degrees of freedom and 95% significance level for coherence
squared is 0.162. The first EOF mode accounts for 73.3% of the total variance
in this frequency band, and the coherence squared of the individual records
with the mode is high for all the meters except 06701. Thus, excluding 06701,
the horizontal and vertical wave numbers can be estimated from the remaining
four meters using the phase differences similar to the method employed for the
topographic Rossby wave numbers. The three bottom meters, 06902, 06801, and
06601 were used to estimate horizontal wave numbers, using a least square fit
to the phase differences. The results were displayed in Table 5.1, where the
inertial frequency has been estimated from a detailed plot of the spectral
peak (Figures 5.4-5.8). The vertical wave number, m, is calculated directly
from the phase differences between the measurements at 06901 and 06902 and
-3 -1
through the dispersion relation (5.1) where N is assumed to be 1.33 x 10 s
and 0) = 1.3362 cpd. It can be seen that they agree fairly well, which gives
confidence in the vertical phase and group speed estimates. The phase and
group speeds are higher by an order of magnitude than Kundu's estimate for the
shelf, and their vertical wavelength is on the order of half the water depth
as against 110 m estimated by Kundu for a water depth of 100 m. The results
depend upon the local value of the Brunt-Vaisala frequency, N, which is a
67
-------
Ill
Q
I-
H
_l
Q.
Q
UJ
W
H
tt.
a
150
100
CO
Id
Q
Q.
MODE 1 COMPLEX EIGENVECTORS
FREQUENCY*1.2448 CPD BANDUIDTH*.1875 CPD DEGREES OF FREEDOM=36
PERCENT VARIANCE = 73.3X
U COMP
a
ui
u
z
UJ
cc
UJ
X
a
a
i 2 3 4 5 6
66S02 B690I B660I 86301 0670! METER NUMBER
Figure 5.3. Amplitude, phase and coherence
squared of the record with the
mode for the first mode EOF for
the inertial frequency band.
68
-------
EPA CURRENT METER DATA
VERTICAL WAVENUMBER
en
UD
Meter Wavenumber Wavelength Inertial Frequency
m (cycles/m) (m) w (cpd)
6901 9.405 x 10~4 1063 1.3103
6902 -1.35 x 10~4 -743 1.3362
HORIZONTAL WAVENUMBER
Variable Wavenumbers (cycles/km) Wavelength
k I K = (k2+£2)'S (km)
U .000215 -.00517 .00517 193
V .000745 -.00276 .00286 350
U,V .000480 -.00397 .00400 250
Phase speed
c (cm/s)
1.61
1.64
Angle from North
(Degrees)
178°
164°
173°
Group Velocity
c (cm/s)
8
- 0.
- 0.
16
22
Calculated Vertical
wavenumber (cycles/m)
12.539
6.936
9.701
x 10 4
x 10~4
x 10~4
Table 5.1. Inertial Oscillation Parameters.
-------
H-
OQ
PHASE
COHERENCE
VARIANCE/CPD
O Tl
O O
3 ST
TJ ro
a *
(T> CD
3 -a
rt ft)
CO O
rt
i-ti t-(
O (U
3 M
(0 O
rt rt
n> CO
H
Hi
O O
CJS l"f
06681 R45
06601 R45
DATE : 76/ 8/ 3= 000
SOLID U COMPONENT
DASHED V COMPONENT
DEGREES OF FREEDOM : 18
BANDWIDTH = 0.09375003 CPD
TIME SERIES LENGTH 96 DAYS
-------
PHASE
COHERENCE
VARIANCE/CPD
OQ
On
O ^
O O
3 S3
•a ro
o *-t
3
fD W
a x)
rt- (D
CD O
rt
i-h i-j
O CD
3 M
(D O
rt rt
(D CD
i-t
i-h
O O
ON t-i
3
CL
06731 R45
06701 R45
DATE 76/ 8/ 3= 000
SOLID U COMPONENT
DASHED V COMPONENT
DEGREES OF FREEDOM : 18
BANDWIDTH . 0.09375003 CPD
TIME SERIES LENGTH : 96 DAYS
-------
H-
OP
c
I-i
(I)
o IT)
O o
a z
-d CD
o i-i
ft> (n
3
rt
fD
en o
rt
HI >-t
o m
i-i
T3
a M
n> o
rt- rt
0) 03
O O
01 i-i
CD
3
<
PHASE
I
oo
S
C9
(/I
n
o
05
X
ro
s
06801 R45
06801 R45
DATE 76/ 8/ 3: 000
COHERENCE
•VARIANCE/CPD
eg
o
to
i 1 1
m
n
SOLID U COMPONENT
DASHED V COMPONENT
DEGREES OF FREEDOM : 18
BANDWIDTH • 0.09375803 CPD
TIME SERIES LENGTH 96 DAYS
-------
00
H-
OQ
C
Ln
-~J
n >-ti
O O
a s
T> CD
O H
fD CO
3 T3
rt fD
CO o
rt
•o
3 i-1
(D O
rt rt
fD CO
t-i
Hi
O O
(^ l-i
-------
H-
CK)
ci
fD
01
00
o >-ci
§ i
T3 (D
O l-i
0
(D CO
3 T3
rt (D
CD n
rf
Hi i-!
O pi
i-t
T3
B M
CD O
n- n-
HI
o o
o d
N3
. (B
CU
PHASE
COHERENCE
VARIANCE/CPD
0)
1 I I ! Mill I I I I Mil I i I I I
06902 R45
96902 R45
DATE 76/ 8/ 3: 000
SOLID U COMPONENT
DASHED V COMPONENT
DEGREES OF FREEDOM • 18
BANDWIDTH : 0.09375003 CPD
TIME SERIES LENGTH 96 DAYS
-------
factor 10 smaller at the 2800 m dumpsite than off the Oregon coast, and so
these estimates of wave number, vertical phase, and group speeds are
reasonable when compared with Kundu's estimates. The results of the analysis
are also consistent with the inertial wave dispersion relation, in that the
rotation is clockwise (V leads U by approximately 90°) at all meters, and the
U and V amplitudes are almost equal for the first EOF mode (Figure 5.3), with
the phase velocity being upwards and the vertical component of the group
velocity downwards. The latter represents the vertical propagation speed of
the inertial energy down from the surface. The group velocity estimates
represent a travel time for inertial energy between 15 and 20 days for 2800 m
of water. These travel times for inertial energy to reach the bottom are
under estimates because the group velocities will be much smaller in the upper
half of the water column due to higher stratification. It is noted that there
is a decrease in amplitude between 96 m and 5.1 m off the bottom at the SW
mooring 069 of about 35%. This indicates that the inertial oscillations are
being damped within the boundary layer. Mooring 069 also has the highest
inertial energy of the four moorings. There is also a possibility that
inertial energy is being reflected from the bottom, as well as being
frictionally dissipated. In a reflected inertial wave, the velocity vector
rotates anticlockwise. The energy in the anticlockwise component is two
orders of magnitude smaller than the clockwise component at both 06901 and
06902 (Figures 4.9-4.10). There is, however, a small increase in the height
of the anticlockwise inertial peak at 06902 compared with 06901, indicating
there may be a very small amount of reflected inertial energy which decays
with height above the bottom.
The horizontal wave number estimates in Table 5.1 indicate that
horizontal phase propagation is towards the south, which indicates that the
energy source, in the surface layers, is situated to the north of the site.
The horizontal wavelength (^ 250 km) is similar to that of topographic Rossby
waves and the wave vector direction is also similar for both types of waves.
A possible speculation is that there is resonance between the two types of
waves, which would imply a non-linear transfer of energy between inertial and
topographic Rossby waves.
75
-------
The inclination of the group velocity vector with the horizontal is given
by tan" (K/m) = 0.24, which is very similar to the slope of the bottom
=0.3°, According to Wunsch and Hendry (1972), when K/m > a (the bottom slope)
the waves are refracted so that the waves are turned parallel to the slope,
rather than being reflected, which may account for the lack of a reflected
wave in the records.
The estimates of the travel time for inertial energy to reach the bottom
from the generation zone at the surface, given above, are relevant to the
passage of Hurricane Belle. If we assume that maximum wind stress on the
surface layers above 2800 m dumpsite occurred on the August 9-10, 1976, then
the minimum time that a peak in the inertial energy would occur at the bottom
is 15-20 days after this date, but may be as long as 30-40 days. The maximum
inertial currents (Figures 5.1 and 5.2) measured at meter 06902 occurred 24
days after August 10, though another maximum only slightly less intense
occurred 10 days after August 10. Therefore, either of these peaks could have
been caused by Hurricane Belle, but given that the travel times estimated are
minimum estimates, that peak on Julian day 247, 24 days after August 10 is
more likely to be the direct result of Hurricane Belle winds.
The final part of this section on inertial oscillations draws attention
to the spectra plots (Figures 5.4-5.8), where the frequency axis is linear so
that details of the inertial and tidal motions between 1 and 2 cpd may be
examined. The power spectra exhibit prominent peaks between the inertial
(^1.3 cpd) and M2 tidal peaks (^1.99 cpd) which are difficult to explain.
Particularly note the prominent peak at '^1.5 cpd, just above the inertial peak
at ^1.3 cpd on record 06801, which also may be present for 06701 (Figures 5.5,
5.6). A little less prominent are the peaks at ^1.75 cpd, seen in the spectra
of 06601 and 06701 (Figures 5.4, 5.5). A common feature is the high coherence
between U and V, and the 90° phase lag between U and V, which indicates that
the velocity vector is rotating in a clockwise sense. The origin of these
motions is uncertain, but could be due to dispersive effects of internal waves
and/or the interaction of the inertial wave with the complex bottom
topography.
76
-------
VI. TIDAL CURRENTS
Tidal Currents in deep water over the Continental Rise are primarily the
result of the interaction of the barotropic deep sea tide, which is generated
by astronomical tidal forces and produces a tidal current which does not vary
with the depth coordinate, and the steep topography of the Continental Slope.
This interaction generates internal waves at tidal frequencies which are
larger than the inertial frequency. These internal waves propagate along
characteristic ray paths from the generation zones on the Continental Slope
towards the deeper water of the Continental Rise. These internal wave rays
intersect the bottom where they are reflected or dissipate in the bottom
boundary layer. Thus there may be regions of the Continental Rise boundary
layer where enhanced mixing occurs due to the reflection and dissipation of
the internal tidal energy. One of the major features of internal tides in
deep water is the localization of tidal energy in the water column, which may
only be 20-50 m thick and positioned according to the path of the
characteristics. The kinematics of the internal tidal waves can be described
by the dispersion relation (5.1), and the path of the characteristics refract
due to changing horizontal and vertical density gradients. Present
information indicates that baroclinic tidal energy may not be present more
than 50-100 km seaward of the generation zones on the Continental Slope, which
would include the dumpsite in the region where internal tides may be expected
to influence the high frequency currents. Theories of the generation and
propagation of baroclinic tides have been developed by Rattray et al. (1969)
and Baines (1974), among others. Baines (1974) applied this theory to the New
England Continental shelf and slope and Torgrimson and Hickey (1979) have
investigated the internal tide from current meter data for the Oregon shelf.
The only energtic tidal motions observed in the current meter data are
the semi-diurnal or M2 tides with a period of 12.42 hours. The astronomical
M2 tide is generated by the gravitational force of the moon as it orbits the
earth. A classical harmonic tidal analysis was performed on the current meter
records, where the observations are least square fitted to a time series
generated from astronomical considerations. The method used follows the
treatise of Godin (1972) as implemented by Foreman (1979). The rotary spectra
77
-------
M2
06801
M2
I 2
06701
CO
-2 -I
M2
I 2
06901
-2 -I
M2
I 2 -2
06902
M2
I 2
0660
Figure 6.1. Hodographs of M2 tidal motion at all five meters. Ax±s units : cm/s.
-------
(Figures 4,6-4.10) show relatively broad peaks compared with the sharp tidal
lines seen in shallow water current spectra, and are thus some indications of
the dispersive internal wave nature of the tidal signal. The results from the
tidal harmonic analysis are shown in the form of current ellipses in Figure
6.1. Note the small amplitudes of the currents (0.5-1.6 cm/s), the uneven
distribution of energy, and the variability in the direction of the axes of
the elipses. Tidal currents are stronger at the two northern than at the two
southern moorings, with most energy at the shallowest NW mooring closest to
the Continental Slope (068). The two current meters on the SW mooring 069
have similar energy at the M2 frequency, with bottom tidal currents being
slightly more energetic. However, unlike the other three moorings, the tidal
currents at 069 are also energetic at another semi-diurnal frequency; the N2
with a period of 12.66 hours. The N2 tidal elipses have similar amplitudes
and phases to the M2 elipses for mooring 069. The ratio of current energy at
the N2 and M2 frequencies is 3.42 for 06901, and 1.50 for 06902. The reason
for the dominance of the N2 tide over the closely related M2 tide at 069,
which is unlike the results from the other three current measurements, is
difficult to determine with the present data.
An EOF analysis centered at the M2 tidal frequency; 1.93227 cpd, with 36
degrees of freedom for all five current meters was performed. The relatively
wide bandwidth covers all semi-diurnal motions, including the N2 tidal
frequency. The first mode accounts for 54% of the total variance and all
records are significantly coherent with the mode. Figure 6.2 shows the
results for the first mode. The vertical phase differences indicate slight
upward propagation of phase, but the 5.2° and 3.5° phase difference between
06902 and 06901 U and V components, respectively, are not significant at the
95% level. The slope of the characteristics, K/m, has the value 0.1, which is
equivalent to a bottom slope of 6.9°, is much greater than the local bottom
slope and implies reflection off the bottom rather than dissipation in the
bottom boundary layer. Horizontal wave number estimates are given in Table
6.1, and the vertical wave number, m, was estimated using the mean of the
phase differences for the U and V components, given above, assuming 91 m
separation between 06901 and 06902. Again, clockwise rotary motion dominates
and has characteristic horizontal scales of about 62 km. The direction of the
horizontal phase propagation is clearly offshore and away from the generation
79
-------
LJ
Q
H
Q.
^r
<
kl
W
H
A
CD
Id
8
I
Q.
-100
-200
MODE ! COMPLEX EIGENVECTORS
FREQUENCY=I.S323 CPD BANDWIDTH**. 1875 CPD
DEGREES OF FREEDOM = 36 PERCENT VARIANCE = 54.
U COMP
V COMP
3
7
0
100 £
i 1- j-i
123456
H 1-
U CCMP
Q
kl
U.
<.
a
u
a
UJ
a
UJ
Q
a
U COMP
V COMP
123
06902 0690, 0660,
Figure 6.2.
Amplitude, phase and coherence
squared of the record with the
mode for the first mode EOF
for the M2 tide.
80
-------
EPA CURRENT METER DATA
Variable
Wavenumbers
k £
(cycles/km) Wavelength Angle from North
_ ,,22,^ km (Degree)
U 0.01429 -.00584
V 0.01512 -.00723
U,V 0.01470 -.00653
.01543
.01676
.01609
65
60
62
112"
Table 6.1. M2 Tide: Horizontal Wavenumber Estimates.
81
-------
zones on the Continental Slope. This fact along with short horizontal
wavelengths, confirms the hypothesis that measurements are of the baroclinic
tide rather than the long wavelength (several 1000 km) barotropic tide.
Evidently, where the tidal beams reflect off the bottom, additional energy
will be input into the bottom boundary layer with possible increases in mixing
and turbulent levels over ambient.
82
-------
VII. HIGH FREQUENCY INTERNAL WAVES
Between the M2 tide and the Brunt Vaisala frequency, the energy seen in
the spectra is due to internal wave motions. Examination of the temperature
spectra at these frequencies for the four moorings (Figures 4.11-4.13) shows
that the energy levels increase towards the slope and decrease towards the
bottom. The records are not coherent for the horizontal and vertical spacing
of this dumpsite array as given in Table 2.1. The increase in high frequency
energy towards major topographic features, such as the slope and canyons, has
been commented upon by Wunsch and Webb (1979) and is probably related to the
reflection of energy by the steep slopes of these features (Wunsch and Hendry,
1972) and consequently increases in mixing in the boundary layers. The
velocity spectra (Figures 4.6-4.10) show isotropy at the highest frequencies,
but increasing anisotropy with the clockwise component dominating, as the
frequency decreases towards the M2 tide. This may be due to focusing effects
of the internal waves by the steep bottom of the Continental Slope (Wunsch and
Webb, 1979).
83
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VIII. THE NORTHWEST ATLANTIC 3800 m RADIOACTIVE WASTE DUMPSITE
The deeper radioactive waste dumpsite centered at 37°50'N and 70°35'W is
situated close to the deepest part of the lower Hudson Canyon. The data
analyzed in the present report is not directly relevant to this site.
However, this data and the Rise Array Data (Thompson, 1977; Luyten, 1977;
Hogg, 1981; c.f. Section 2.2) allow some inferences to be made on the general
statistics of the motion which might be expected at this site. Only motions
above the bottom boundary layer in the lower part of the water column are
considered. No current measurements have been made exactly within this 3800 m
dumpsite.
The closest moorings to this dumpsite are WHOI moorings 530 and 533, with
meters at nominally 1000 m and 200 m (533 only) off the bottom. One thing
that is immediately apparent is the higher energy levels at these WHOI mooring
sites compared with the upper Continental Rise and the 2800 m dumpsite
measurements (Luyten, 1977) , with total low-frequency variance being from 2-5
times the energy levels on the upper Continental Rise (e.g., Site D). The
analyses by Thompson (1977) and Hogg (1981) also show that Rossby wave
dynamics dominate at periods longer than eight days. However, rather than
being short wavelength, bottom trapped topographic Rossby Waves, the
low-frequency wave motions are barotropic, long Rossby Waves, with horizontal
wavelengths of order 300 km (Hogg 1981). Currents have been known to exceed
60 cm/s in deepwater of 4000 m depth.
How the topography of the deep Hudson Canyon interacts and modifies these
energetic low-frequency motions is not known at the present time, though some
clues as to the variability over short distances when rough topography is
present can be found in Hogg and Schmitz (1980). The surface waters of the
dumpsite are likely to be frequently under the direct influence of the Gulf
Stream, which may explain the high energy levels found below 1000 m in this
vicinity.
There is again a gap in the spectra between one and eight days, and since
the bottom slope is less in this region than on the upper continental rise,
84
-------
the cut-off frequency shifts to a lower frequency. Hogg (1981) shows that in
the southern part of the Rise Array the peak in the low frequency energy
occurs in the 22-108 day period rather than the 12-20 day period of the
shallower northern measurements. Hogg (1981) shows that the deep currents
over the whole of the Continental Rise can be considered as part of the same
system of Rossby waves. This system of deep wave motions is modified by the
bottom slope as the waves propagate towards the Continental Slope.
The inertial and tidal motions of the Rise Array measurements have been
investigated by Perkins (1976) and Baines (1974), and it is concluded that in
the deeper water and at greater distance from the slope, the baroclinic M2
tide is expected to be much less prominent at the 3800 m site, though inertial
motions could still be important at these depths and may be expected to again
dominate the high frequency part of the spectrum.
85
-------
IX SUMMARY
The current and temperature measurements from the 2800 m dumpsite have
been analyzed with a view to identifying the dominant space and time scales in
the records and identify, where possible, the dynamics responsible for the
motions and how these dynamics relate to potential transfer of materials from
the dumpsite.
The records can be divided into three energetic frequency bands: low
frequencies, with periods greater than about 8-days; the inertial frequency
band; and the M2 tidal band.
Mean currents over the 3-month period from August to November 1976 were
substantial (3-4 cm/s), directed westwards or southwestwards, and influenced
by the relatively variable topography of the site.
Low-frequency energy dominates the measurements and agrees fairly well
with short wavelength, topographic bottom trapped Rossby wave theory (Rhines,
1970). The 10-20 day period motions dominate the spectra, with the peak at
about 16-days. The low-frequency -variability exceeds the mean flows.
Analysis of the length scales, using phase differences estimated from the
first mode of an empirical orthogonal function (EOF) analysis, showed phase
propagation towards the south and wavelengths estimated to be about 200 km.
The phase relations between U, V, and T generally agreed with the theory, even
though the near bottom current meters are within the bottom boundary layer.
Comparing currents at 96 m and 5 m off the bottom at the SW mooring (069)
showed evidence of a minor amount of Ekman turning and frictional dissipation
in the boundary layer. Otherwise, the results generally agree with
measurements taken on the upper Rise at Site D (Thompson, 1977) and along 70°W
(Luyten, 1977; Hogg, 1981).
The analysis of the low frequency currents indicates that the long term
transport of radionuclides is dominated by the mean currents with the
transport being approximately pa rallel to the isobaths and directed towards
the southwest. In the boundary layer, Ekman turning of this mean current will
86
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produce a small component of the mean current normal to the Isobaths and
directed shorewards. The low frequency wave motions serve to disperse the
radionuclides by causing excursions of water parcels from a particular
(~\ 9
isobaths. Horizontal diffusion coefficants of approximately 7x10 cm Is were
calculated from the fluctuating components of temperature and current. The
estimated displacement over three months of a water particle at the site is of
the order of 300-400 km and is comparable with the displacements of Lagrangian
float measurements made by Schmitz et al. (1981) over the Mid-Atlantic Bight
Continental Rise (Figures 2.1, and 4.20-4.24). Thus the major processes
responsible for transport and dispersion of radionuclides at the 2800 m
dumpsite are the mean currents and the low frequency Rossby waves, which can
be considered as continuous processes. There is no evidence of near bottom
jets or periods of exceptionally strong currents which might be mechanisms for
accelerated transport of material. The 3800 m dumpsite, however, is situated
in the Hudson Canyon, and it is unknown whether flows within the canyon would
enhance the transport. Above the lip of the canyon, low frequency currents
would be expected to be similar in nature to those at the 2800 m dumpsite, but
2-5 times more energetic.
At periods less than one day, the spectra are dominated by a broad
inertial peak at frequencies about 5-10% above the local inertial frequency,
f, (about 19.3 hours). Clockwise rotary currents dominate, with nearly
vertically upwards propagation of phase. The group velocity vector has a
small downwards component and a horizontal component directed towards the
south. The horizontal and vertical wavelengths are 250 km and 1 km,
respectively, and the wave parameter relationships agree fairly well with the
linear internal wave dispersion relation. The passage of Hurricane Belle
close to the dumpsite on August 10, 1976, seems to increase the inertial
currents at the bottom about 24 days later. The large amplitude inertial
events input about as much energy into the boundary layer as do the maximum
low frequency currents, and thus may be responsible for enhanced vertical
mixing and resuspension of fine sediment particles. Sediment particles would
be transported by the low frequency currents while suspended in the boundary
layer until they sink to the bottom by the action of gravity. Thus transport
of radionuclides attached to fine sediment particles would be very
intermittent, but generally in the direction of the mean currents.
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The next important process is the baroclinic M2 tide, which is generated
in regions of steep bathymetry O6°) on the Continental Slope. Amplitudes are
about 1-2 cm/s, and again clockwise rotary currents predominate. Horizontal
wavelengths of about 60 km with offshore horizontal phase propagation were
calculated from phase difference analysis, using the first EOF mode.
There is also energy between the M2 tide and the inertial frequency,
which, at least at one mooring (068), exceeds the inertial peak. The origin
of these motions, which are again predominantly clockwise rotating currents,
is not known, as the frequencies (1.5 and 1.75 cpd for example) do not
correspond to any known dynamics or forcings as far as is known to the author.
They would thus appear to be non-linear phenomena.
Therefore, apart from these latter currents occurring at frequencies
between the inertial and the M2 tide, the origin and dynamics of the energetic
parts of the spectra can be accounted for by similar general observations at
corresponding depths in the surrounding area.
The data described in this report could be used as the basis for a model
of the dynamics of the benthic boundary layer over sloping topography forced
by a mean current and linear topographic Rossby waves. This type of model
would be similar to that of Weatherly and Martin (1978), except for the
inclusion of Rossby wave motions. A quantitative simulation or hindcast of
the boundary layer currents at the 2800 m dumpsite, using a fully three
dimensional boundary layer model, is not possible because the data does not
adequately define the boundary conditions in terms of currents and density on
the open boundaries. Information on the detailed structure of the density
field is lacking, so that initialization of such a simulation model could only
be achieved by making some assumption on the distribution of salinity and
temperature.
88
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X. RECOMMENDATIONS
The low-frequency motions between 100 m and 1000 m off the bottom are
fairly well understood. The basis for this knowledge are the WHOI
measurements from Site D and the Rise Array, and the theories of topographic
Rossby waves (Rhines, 1970). The bottom current measurements made by EPA at
the 2800 m dumpsite are within the boundary layer; however only one mooring
had measurements outside the boundary layer at 96 m from the bottom.
Therefore, detailed analysis of the space and phase relationships of boundary
layer currents to the currents above 100 m from the bottom over variable
topography is unavailable from this data. It was pointed out in Section 4.5
that boundary layer shears and mixing processes are vital to the understanding
of dispersion from the bottom. Detailed shear measurements are not available
from the limited number of current meters used in this dumpsite survey. Since
the large scale dispersion may be regarded as a stochastic or random walk
process, the details of how the waste is dispersed within the bottom boundary
layer should be the focus of further experiments. The complex topography of
both dumpsites might be expected to impose small space scale variability on
the boundary layer flows, which will need to be investigated because of impact
on local dispersion. Therefore, future studies should concentrate on boundary
layer measurements, including investigations of the mixing processes and the
time and space dependence of the depth of the boundary layer over the site.
However, the flow above the boundary layer should also be measured so that the
forcing for the boundary layer is well defined.
Since topographic waves and internal wave dynamics are functions of the
stratification and the bottom topography, both these parameters should be
carefully measured in future studies. A detailed bottom topography map of the
3800 m site is crucial, because the only generally available topographic maps
of this region are from Uchupi (1965) which lack the fine detail required in a
deep canyon.
The 3800 m dumpsite in the lower Hudson Canyon needs measurements both
within and upstream and downstream of the canyon in order to determine the
effects of the canyon the large scale mean flow and wave motions. At the
89
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present time, the effects of canyons on deep abyssal flows on the lower
Continental Rise is unknown.
The final point to be made is that.future measurements should be made for
a period of at least 9-12 months so as to resolve the dominant low-frequency
motions; also to give more stable estimates of the substantial mean flows on
the Continental Rise.
A detailed simulation model of the time and space dependant flows in a
boundary layer over a dumpsite requires a large measurement program to
adequately define the boundary conditions of the horizontal and vertical
boundaries delineating the dumpsite. However the data requirement for models
is determined by the type of model employed and the purpose to which the model
is being put. Thus a model of large scale transport and dispersion may
require the modeling of the whole ocean basin in all four dimensions, whereas
a model of mixing processes within the abyssal boundary layer may use a
quasi-theoretical model of boundary layer dynamics which is compared with data
in only a general qualitative sense, so that some determination of whether
this type model includes all the most important dynamical processes can be
made. Thus assessing the data needs for models cannot be performed until the
types of models to be employed to investigate the fate of radionuclides have
been chosen. The recommendations above, therefore, concentrate on a
measurement program which will improve knowledge of boundary layer flows and
dispersion, particularly for the unexplored flows in the lower Hudson Canyon,
which in turn may give a better basis on which modeling of the fates of
radionuclides may be made in the future.
90
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ACKNOWLEDGEMENTS
Thanks are due to Nelson Hogg, Robert Beardsley
and G. T. Csanady for useful contribution on
this work during a visit to Woods Hole Oceano-
graphic Institution in January 1981.
91
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REFERENCES
Baines, P. G. , 1974. The generation of internal tides over steep continental
slopes. Phil. Trans. Roy. Soc. London, A277, pp 27-58.
Bisagni, J. J. , 1981. Physical oceanographic studies at 106-mile site, July
1977. In Assessment report on the effects of waste dumping in 106-mile
Ocean Waste Disposal Site. NOAA Dumpsite Evaluation Report 81-1,
Rockville, MD, pp 233-242.
Bisagni, J. J., 1980. Circulation study at 106 mile dumpsite uses satellite
to track drogued buoys. Coastal oceanography and Climatology News, _3_(1) :
6-7-
Bowden, K. F., 1965. Horizontal mixing in the sea due to a shearing current.
J. Fluid Mech. 21:83-95.
Csanady, G. T., 1973. Turbulent diffusion in the environment. Reidel, 248
pp.
Devine, M., E. R. Meyer, and T. O'Connor, 1981. Assessment Report on the
Effects of Waste dumping in 106-Mile Ocean Waste Disposal Site. Part I:
NOS Assessment. NOAA Dumpsite Evaluation Report 81-1, Rockville, MD, pp
3-30.
Dyer, R. S., 1976. Environmental surveys of two deep-sea radioactive waste
disposal sites using submersibles. International Symposium on the
Management of Radioactive Wastes from the Nuclear Fuel Cycle,
International Atomic Energy Agency, Vienna, 22-26 March 1976,
IAEA-SM-207/65.
Foreman, M. G. G., 1979. Manual for tidal currents analysis and prediction.
Institute of Ocean Sciences, Patricia Bay, Victoria, B.C. Pacific Marine
Science Report 78-6.
Godin, G., 1972. The Analysis of Tides. University of Toronto Press,
Toronto, 264 pp.
Hasselmann, K., 1976. Stochastic climate models. Part I. Theory. Tellus
2^:473-485.
Hogg, N. G., 1981. Topographic waves along 70°W on the continental rise. J.
Mar. Res. 39_: 627-649.
Hogg, N. G. and W. J. Schmitz, Jr., 1980. A dynamical interpretation of low
frequency motions near very rough topography - the Charlie Gibbs Fracture
Zone. J. Mar. Res., 38_:215-248.
Ingham, M. C., J. J. Bisagni and D. Mizenko, 1977. The general physical
oceanography of deepwater dumpsite 106 In Baseline Report of
Environmental Conditions in Deepwater Dumpsite 106 (Volume 1), NOAA
Dumpsite Evaluation Report 77-1, Rockville, MD, pp 29-86.
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Kundu, P. J., 1976. An analysis of inertial oscillations observed near the
Oregon coast. J. Phys. Oceanogr. ^_:879-893.
Luedecke, A. R. , 1959. Disposal of radioactive wastes into the Atlantic
Ocean and the Gulf of Mexico. Industrial Radioactive Waste Disposal
Hearings Before the Joint Committee on Atomic Energy 5_ Washington, D. C.
Luyten, J. R., 1977. Scales of motion in the deep Gulf Stream and across the
Continental Rise. J. Mar. Res., 35:49-74.
Mayer, D. A., H. 0. Mofjeld and K. D. Leaman, 1981. Near-inertial waves
observed on the outer shelf in the Middle Atlantic Bight in the wake of
Hurricane Belle. J. Phys. Oceanogr., 11, 87-106.
Mizenko, D. and J. L. Chamberlin, 1981. Gulf Stream anticyclonic eddies and
shelf water at 106-mile site during 1977. J_n Assessment report on the
effects of waste sumping in 106-mile Ocean Waste Disposal Site. NOAA
Dumpsite Evaluation Report 81-1, Rockville, MD, pp 207-232.
Ou, H. W. and R. C. Beardsley, 1980. On the propogation of free topographic
Rossby waves near continental margins. Part II: Numerical model. J.
Phys. Oceanogr. 10:1323-1339.
Ou, H. W., J. A. Vermersch, W. S. Brown and R. C. Beardsley, 1980. New
England Shelf/Slope Experiment (February-August, 1976). Data Report:
The moored array WHOI. Tech. Rep. 59pp.
Perkins, H., 1976. Observed effect of an eddy on inertial oscillations.
Deep-Sea Res., 23_, 1037-1042.
Rattray, Jr., M., J. G. Dworski and P- E. Kovala, 1969. Generation of long
internal waves at the continental slope. Deep-Sea Res. 16 (Supplement),
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Rhines, P. B., 1970. Edge-, bottom-, and Rossby waves in a rotating
stratified fluid. Geophysical Fluid Dynamics. _1_:273-302.
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buoys. J. Phys. Oceanogr., 11, 999-1010.
Schmitz, Jr., W. J., J. F. Price, P. L. Richardson, W. B. Owens, D. C. Webb,
R.E. Cheney and H. T. Rossby, 1981. A preliminary exploration of the
Gulf Stream system with SOFAR floats. J. Phys. Oceanogr. 11, 1194-1204.
Schmitz, Jr., W. J., 1980, Weakly depth-dependent segments of the North
Atlantic circulation. J. Mar. Res. 38, 111-113.
Schmitz, Jr., W. J., 1974. Observations of low-frequency current fluctuations
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Thompson, R.O.R.Y., 1971. Topographic Rossby waves at a site north of the
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Thompson, R.O.R.Y., 1977. Observations of Rossby waves near site D. Prog.
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oceanic bottom boundary layer. J. Phys. Oceanogr. ^:557-570.
Wunsch, C. and R. Hendry, 1972. Array measurements of the bottom boundary
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U.S. GOVERNMENT PRINTING OFFICE: 1982 0 — 361-085/4467
94
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA 520/1-82-002
3. RECIPIENT'S ACCESSION NO.
4. TITLE AND SUBTITLE
Analysis of Current Meter Records at the Northwest
Atlantic 2800 Metre Radioactive Waste Dumpsite
5. REPORT DATE
June, 1982
Date of
Preparation
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Peter Hamilton
8. PERFORMING ORGANIZATION REPORT NO,
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Science Applications, Inc.
4900 Water's Edge Drive, Suite 255
Raleigh, North Carolina 27606
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
68-01-6235
12. SPONSORING AGENCY NAME AND ADDRESS
Office of Radiation Programs
U.S. Environmental Protection Agency
401 M Street, S.W.
Washington, B.C. 20460
13. TYPE OF REPORT AND PERIOD COVERED
Final
14. SPONSORING AGENCY CODE
ANR-461
15. SUPPLEMENTARY NOTES
16. ABSTRACT ~ ' —~
In August, 1976, four current meter arrays were deployed for a period of three
months at the Atlantic 2800 meter radioactive waste disposal site as part of a
scientific survey by the U.S. Environmental Protection Agency to assess the environment
al conditions at this formerly used site. The disposal site is located on the Conti-
nental Rise and is centered at 38°30'N, 72°06'W. The four arrays were placed in a
rectangle near the periphery of the site, each with a current meter 5.1 meters off the
bottom, with an additional meter located 96 meters from the bottom at the southwest
mooring. The principal findings included a 3-4 cm/s southwesterly mean current
observed near the bottom. The low frequency part of the spectrum is explained as botto i
trapped topographic Rossby waves. The high frequency motions are dominated by inertial
oscillations with a maximum amplitude of about 10 cm/s. The potential for sediment
transport during the measurement period is considered very small based on the observed
current speeds.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
c. cos AT I Field/Group
Ocean Dumping/Sea Disposal
Radioactive Waste Disposal/Nuclear Waste
Disposal
Deepsea Currents
Ocean Currents
8. DISTRIBUTION STATEMENT
Unlimited Release
19. SECURITY CLASS (This Report)
Unclassified
21. NO. OF PAGES
101
20. SECURITY CLASS (This page)
Unclassified
22. PRICE
EPA Form 2220-1 (Rev. 4-77) PREVIOUS EDITION is OBSOLETE
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