AN ABSTRACT OF THE THESIS OF
Joseph Wilfred St.Martin for the degree of Master of Science
June 17, 1983
in the School of Oceanography presented on
Internal Waves: Towed Observations in the Western
Title:
North Atlantic
Redacted for Privacy
Abstract approved:
ayton A. Paulson
Observations of internal waves were made with a towed
thermistor chain between 10 and liOm depth in the Sargasso
Sea and north of the Gulf Stream in a warm core ring.
Spectral
except
levels
that
a
agree
spectral
with
spectrum
Garrett-Munk
the
observed
was
shoulder
in
the
Sargasso Sea observations at a wavenumber of 2-3x103 cpm.
This shoulder coincides with a coherence peak found when
the vertical separation was less than 40m. This coherence
differs
peak
from
the
coherences at low wavenumbers agree.
although
model,
Garrett-Munk
The spectal shoulder
and coherence peak is evidence of dominance by a few low
modes.
The spectral levels from the Sargasso Sea and warm
core ring agree with observations by
and Briscoe
Katz
(1979) from 350 to 750m depth in the Sargasso Sea and with
observations from MILE
1983a)
which were taken
(Spoering,
in
the
1979;
Levine et al.,
upper ocean
Pacific. The observations from Bell
(1976)
in
the NE
taken in the
Sargasso Sea and from JASIN
(Levine et al.,
1983b)
taken
west of Scotland exhibit higher spectral levels than our
observations.
Towed Observations
in the
Western North Atlantic
Internal Waves:
by
Joseph Wilfred St. Martin
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
Completed June 17, 1983
Commencement June 1984
APPROVED:
Redacted for Privacy
Profess r of Oceanography in charge of major
Redacted for Privacy
Dean of the School of
ga phy
Redacted for Privacy
Dean of GraduAtle Schoo
Date thesis is presented
June 17, 1983
Typed by Joseph W. St. Martin for Joseph W. St. Martin
AC KNOWLEDGE MENT
I
wish
to
thank
Dr.
Clayton
Paulson,
my
major
professor, and Dr. Murray Levine for their guidance and
assistance in the developement of my thesis.
I
also would
like
to
thank Rick Baumann
for his
expertise and assistance with the computer and Lynn deWitt
for her advice.
Most
c ,f
all,
I wish to thank my wife,
Debbie, for her support and love.
These last few months
have been hectic and she has helped me make it from day to
day.
This research is supported by the the
U.
S.
Coast
Guard which had enough faith in my abilities to assigned
me to graduate school and the Office of Naval Research,
contract N00014-79-C--0004, project NR 083-102.
TABLE OF CONTENTS
Page
INTRODUCTION .................
1
OBSERVATIONS .................
3
ANALYSIS ...................
11
SPECTRA ...................
15
CONCLUSION ..................
29
REFERENCES ..................
31
APPENDICES
A.
XBT Temperature Profiles and
Isotherms ...............
33
B.
Edited Isotherms ............
39
C.
Ensemble Averaged Spectra .......
52
D.
Desaubies (1976) Towed Vertical
E.
Coherence Equation ..........
62
Ensemble Averaged Vertical
Coherence ...............
66
LIST OF FIGURES
1.
Configuration
of
thermistor
the
chain while
4
and
6
under tow.
2.
showing
Chart
ship's
the
track
cruise
approximate location of the Gulf Stream and a
warm
core
segment
heavy
The
ring.
in
the
Sargasso Sea corresponds to Run 2 and the one
within the warm core ring is Run 3. The light
segment corresponds
which
extends
beyond
an
to
XBT cross-section
tow track
the
of
the
Positions of CTD's are also plotted as
chain.
open circles.
3.
Buoyancy frequency in the Sargasso Sea near Run
9
2 on 13-Sep-81 (Trask et al., 1982).
4.
Buoyancy frequency from a warm core ring (Run
3)
on
17-Sep-81
(heavy
line)
and
from
10
the
Srgasso Sea (Run 2) on 13-Sep-81 (light line)
(Trask et al., 1982).
5.
Spectrum
of
isotherm (0)
the
depth
of
the
23.5
deg
C
from the Sargasso Sea compared to
the ensemble averaged coherence with 5 to lOm
vertical separation (solid line).
13
6.
Ensemble averaged
spectra
of
isotherm depth
16
from the Sargasso Sea at depths of 45-50m (0),
(c), and 100-hOrn (0).
76-80m
scaled
Spectra
multiplying
by
Spectra.
a)
by
the
b)
local
buoyancy frequency.
7.
from
spectrum
average
N-scaled
the
Sargasso
Sea
of
isotherm depth
compared
17
the
to
Garrett-Munk model as formulated by Desaubies
(1976) .
Light
depict
lines
confidence
95%
intervals.
8.
N-scaled ensemble averaged spectra of isotherm
depth from the warm core ring at depths
31-35rn
(0)
(0) ,
35-40m () ,
compared
to
the
41-47m (X) ,
Garrett-Munk
19
of
and 49-54m
spectral
model.
9.
Comparison
N-scaled
of
spectra
of
isotherm
21
depth from the Sargasso Sea (0), the warm core
ring
(a), MILE
(heavy solid line),
Katz and
Briscoe (light dashed line), JASIN (light solid
line) ,
10.
and Bell (heavy dashed line)
Ensemble averaged coherence between isotherms
separated vertically 5 to lOm
the Desaubies
(1976)
(bold line)
and
towed vertical coherence
equation from Appendix E with N
=
12
(light
24
line)
and
N
=
6
(dashed
line) .
Desaubies
equation computed for a vertical separation of
7. Sm.
11.
Ensemble averaged coherence between isotherms
26
separated 5 to lOm in the vertical (bold line)
and the towed vertical coherence of Katz and
Briscoe (1979)
at 350m depth and 8.5m vertical
separation.
12. Dispersion relation for modes
the Sargasso Sea.
1 through
6
in
28
LIST OF TABLES
1.
Location and mean depth
sensors.
chain
temperature
(C)
(T) ,
Each
from
station
pressure
sensor installed.
chain
of
(P) ,
operating towed
either
has
5
a
or conductivity
The distance along the
the depressor
to
the
sensors
denoted by S with units of chain-meters.
is
One
chain-meter equals 1.016m.
2.
Summary
of
isotherms
spectrally
analyzed.
8
internal
22
Isotherms are at 0.5 deg C intervals.
3.
Summary of
waves.
compared observations of
TOWED OBSERVATIONS IN THE
INTERNAL WAVES:
WESTERN NORTH ATLANTIC
INTRODUCTION
Until recently, upper ocean internal waves were not
Roth et
as extensively studied as those at deeper depths.
al.
at
compared data from the upper ocean available
(1979)
that
published
Recent
time.
which
provide
studies
additional
observational
broader
a
been
have
base.
Summaries of internal wave observation and theory can be
found in Munk (1979) and Levine (1983)
Internal waves in the deep ocean, where the buoyancy
frequency, N, given by N =
(q/p
p/z)1/2
,
varies little
Garrett
with depth, have been extensively investigated.
and Munk (1972, 1975, 1979) have modeled the distribution
of
internal
wave
energy
this
in
varying buoyancy frequency allowed the
use
approximation in the formulation of the model.
adequately
describes
the
internal
slowly
The
region.
of
WKB
the
This model
spectra
wave
at
frequencies greater than the inertial frequency and less
than
the
local
Garrett-Munk model
buoyancy
However,
frequency.
may not be
applicable
in
the
the
upper
ocean, where the bouyancy frequency changes rapidly and
where there
energy.
may be
sources
or
sinks
of
internal wave
2
In the upper ocean, deviations from the Garrett-Munk
have
model
been
observed.
Pinkel
1981)
(1975,
found
higher levels of spectral energy and a peak in vertical
coherence at frequencies of 3 to 6 cph.
These deviations
were explained as the result of dominance by the lowest
few modes.
Levine et al.
(1983a,
1983b)
found similar
results at high frequency and wavenumber and successfully
modeled the internal wave spectra with a model composed of
only the lowest few modes.
At 350m depth in the Sargasso
Sea, Katz and Briscoe (1979) also observed a peak in the
coherence.
This was again concluded to be the result of
low mode dominance.
The reason for low mode dominance has
not been explained.
The purpose of this paper is to present the results
of observations made with a towed thermistor chain in the
western
North
Atlantic.
Data
were
obtained
between 10 and hOrn at two separate locations.
wavenumber
spectra
and
towed
vertical
various vertical separations are presented.
at
depths
Horizontal
coherences
at
These results
are compared to other observations and to the Garrett-Munk
model.
3
OBSERVATIONS
Observations were made with a towed thermistor chain
in September, 1981. A diagram of the thermistor chain is
shown on Fig.
The chain consisted of
1.
member wound to a drum and connected to
450kg
cylindrical,
attached
to
strain
the
Plastic
depressor.
member
a wire strain
streamlined,
a
were
fairings
throughout
length.
its
Sensors and electronics were incorporated within some of
the
pressure
frequency
and
sensors,
from
signals
of
consisted
These
fairings.
each
system provided
conductivity vs.
recorded
and
4Hz
a
record
sampled
magnetic
on
at
a
The
tape.
pressure,
temperature,
of
3
Analog
sensors.
were
sensors
the
thermistors,
31
conductivity
2
of
of
or
time and distance at the depth of each
Table 1 lists the locations of the sensors on the
sensor.
chain and their mean depth in the water column during the
Spoering (1979) provides a more
two data collection tows.
detailed description of the thermistor chain.
The
thermistor chain was
towed
on
three
separate
occasions during the cruise (hereafter referred to as Runs
2, and 3) .
1,
the
chain was
Data from Run 1 were not analyzed because
deployed
to
a
depth of only 70m
and
3
are shown in Fig.
Sargasso Sea and Run
3
2.
was
Run
a
Tow tracks for Runs
variety of water types were crossed.
2
and
2
was located in the
located north of
the Gulf
Figure
under tow.
Configuration of the thermistor chain while
Table 1. Location and mean depth of operating towed
chain sensors. Each station has either a temperature (T)
The
pressure (P) , or conductivity (C) sensor installed.
distance along the chain from the depressor to the sensors
One chain
is denoted by S with units of chain-meters.
meter equals 1.016 m.
Channel
Station
No.
1
2
3
4
5
7
9
10
11
12
13
16
18
19
21
23
24
25
27
28
29
30
31
32
34
35
36
P0
Ti
T2
CO
T3
T4
T6
T7
T8
T9
S
10
12
16
16.5
17
20
28
32
36
40
44
56
60
64
72
80
84
88
96
T10
T13
T14
T15
T17
T19
T20
T21
T23
T24
T25
P2
T26
T27
100
104
106
108
112
T29
T30
117
120
Cl
Depth of Operating Sensors(m)
(Chain-meters)
116.5
Run 2
Run
116.7
114.7
110.6
110.1
109.6
106.6
98.5
94.5
90.5
86.5
82.5
70.7
66.8
62.8
55.1
47.4
43.6
39.8
32.2
28.5
24.8
22.9
21.1
17.4
13.3
12.8
10.1
107.2
105.2
101.1
100.6
100.1
97.1
89.2
85.2
81.3
77.5
73.6
62.3
58.6
55.0
47.8
40.7
37.3
33.8
27.1
23.8
20.5
18.9
17.3
14.1
10.6
10.2
7.8
3
I
I
I
I
I
I
I
I
42°N
....
1! WARM CORE
RING
40°N
38°N
\
.1
36°N
ç5
'
GULF
STREAM
"
34°N
Ii
76°W
74°W
72°W
70°W
68°W
Figure 2. Chart showing the ship's cruise track and
approximate location of the Gulf Stream and a warm core
The heavy segment in the Sargasso Sea corresponds
ring.
to Run 2 and the one within the warm core ring is Run 3.
The light segment corresponds to an XBT cross-section
the
tow
which extends
beyond
track
of
the
chain.
Positions of CTD's are also plotted as open circles.
7
During each run data were
Stream in a warm core ring.
collected on two separate computer tapes, causing a short
break
in
the record.
Some
the data were not used
of
because of changes in tow speed or the crossing of water
structure not associated with internal waves.
Table
2
summarizes observations which were analyzed.
Observations
temperature
of
depth (Trask et al.,
1982)
N
(g/p
=
vs.
were taken at two sites near
the locations of Runs 2 and 3
frequency,
conductivity
and
(see Fig.
p/Bz)1/2
2) .
computed
,
The buoyancy
these
from
observations is shown in Figs. 3 and 4.
Observations of temperature vs.
near
hourly
(XBT)
expendable bathythermograph
contoured isotherms
and
Runs
with
Appendix A contains vertical temperature
probes.
profiles
during
intervals
depth were taken at
2
and
3
and
from XBT
taken
casts
extending beyond Run
2.
locations of the XBT measurements is shown in Fig. 2.
The
Table 2.
Summary of isotherms spectrally analyzed.
0.5 deg C intervals.
Isotherm
Tape
Begin Time/Date
(Deg C)
(GMT)
Isotherms are at
Duration
(mm)
Tow Speed
(m/s)
Run 2
21 through 25.5
21 through 25.5
20 and 20.5
10
10
0130
0646
0730
14-Sep-81
14-Sep-81
14-Sep-81
314
300
255
2.0
2.0
2.0
12
13
1915
0057
17-Sep-81
18-Sep-81
282
160
2.8
2.5
9
Run 3
18 through 22
20 through 22
9
FRUUENCY (CPH)
9
,.-.
1..
R
A
1
12
14.
16
18
15ø
'-.-, 2ØQ
F
o__ øø
LU
D
25ø
sø
.II'4I
Figure 3. Buoyancy frequency in the Sargasso Sea near
Run 2 on 13-Sep-81 (.Trask et al., 1982).
10
FPQUNCY( CPH)
5
,.-
15
'--'
22
251
Ho_ @ø
LU
D
35
4.5
Figure 4.
Buoyancy frequency from a warm core ring
and from the Sargasso
(Trask et al.,
line)
(Run 3) on 17-Sep-81 (heavy line)
on 13-Sep-81
Sea
(Run 2)
(light
1982)
:ii
ANALYSIS
The raw temperature, pressure, and conductivity data
filtered
low-pass
were
by
computing
sequential
30s
This filtering removed fluctuations in chain
averages.
depth caused by surface gravity waves and the roll, pitch,
and heave of the ship.
The temperature data was used to compute the depths
of
isotherms
deg
0.5
(at
intervals)
C
interpolation between the records.
moving
due
out
to
of
internal
the
with
waves
limited depth
linear
These isotherm depths
less than 80%
were edited to remove records which were
complete
by
large
range
of
amplitudes
the
chain.
Records which were more than 80% complete were completed
by
extrapolation
from
adjacent
isotherms.
The
edited
isotherm depths from Runs 2 and 3 are shown in Appendix B.
During Run 3, the chain tended to kite (move to the
side) because of the greater tow speed.
The 30s averages
of pressure provided a record of the vertical movement of
the chain caused by the kiting.
This pressure record was
used to correct the isotherm depths.
performed by
The correction was
linear interpolation between the deep and
shallow pressure record.
Isotherm depths from Run 3 are
less reliable than Run 2 because of uncertainties in the
correction.
Corrections to Run 2 were negligible.
12
Spectra of isotherm depths were computed by use of
standard
taking
techniques.
forward
first
the
were
Data
pre-whitened
first
by
Pre-whitening
difference.
minimizes leakage from band to band (Frankignoul, 1974).
Spectra were then computed by use of conventional Fourier
Transform
dividing
techniques.
by
transfer
the
spectra
The
recolored
were
function of
the
by
differencing
scheme.
were
spectra
The
smoothed
non-overlapping wavenumber
bands,
by
averaging
equally
spaced
in
on
a
Frequency spectra were converted to
logarithmic scale.
wavenumber spectra by using Taylor's hypothesis and taking
the
mean
velocity.
tow
speed
during
each
run
as
the
relevant
A representative spectrum is shown in Fig.
5.
Spectra of individual isotherm depths were also ensemble
averaged with
other
spectra
from similar depths.
The
average spectra for Runs 2 and 3 are shown in Appendix C.
Table 2 lists the isotherms used for spectral analysis and
their lengths.
Towed vertical coherence
coherence)
isotherms
is
a
measure
vertically
(hereafter referred to as
the
of
separated
in
correlation
between
water
column.
the
Coherence was only computed for Run 2 because the kiting
of
the
chain during
coherence values.
Run
3
tended
to
cause
erroneous
13
I
I
llJ
J
I
I
JJ
I
III
6
1
0
5
0
0
0
C-)
LiJ
C-)
0
z
L
0
c
LaJ
C)
0
(J
C)
-J
0
I
5
I
I
1111
III
It.
3
LOG K
(CPM)
&
liii
2
Figure 5. Spectrum of the depth of the 23.5 deg C
isotherm (0) from the Sargasso Sea compared to the
ensemble averaged coherence with 5
to
lOm vertical
separation (solid line)
14
The coherence between isotherm depths
computing
the
cross-spectrum
found by
series.
two
the
of
is
This
results in a real part, the co-spectrum, and an imaginary
The coherence squared is given
part, the quad-spectrum.
by the ratio of the magnitude of the cross-spectrum to the
The coherence is
product of the spectrum of each series.
As with the spectra, the
the square root of this result.
cross-spectra
non-overlapping wavenumber
logarithmic
computed
scale.
for
bands,
Ensemble
isotherm
averaging
by
smoothed
are
equally
coherences
averaged
depths
spaced
various
of
over
on
a
were
vertical
A representative
separations and over all depth levels.
coherence spectrum is shown in Fig. 5.
The coherence estimates were tested for significance
at the 95% level with the null hypothesis test.
values which fall at or below (1-. 05 "-i-
degrees of freedom of
the estimate,
)
,
Coherence
where 2n is the
are considered not
significantly different from zero at the 95% level.
SPECTRA
Sargasso Sea are shown in Fig.
N(z) ,
as
reduced.
of
the
in Fig
6b,
the
in
The spectral
6a.
the
levels
When these spectra are
increase with increasing depth.
scaled by multiplying by the
ranges
depth
three
from
spectra
Averaged
local buoyancy frequency,
scatter among the spectra
is
This suggests that the spectra in the upper hOrn
Sea
Sargasso
scale
with
the
local
buoyancy
frequency in agreement with the model of Garrett and Munk
(1972, 1975)
These three spectra were multiplied by N and averaged
together to create an ensemble averaged spectrum shown in
Fig.
7. This spectrum is compared with the spectral model
of Garrett and Munk as formulated by Desaubies (1976) . The
towed spectrum is given by
'N /
TS(k)=_)
f f
--j
where:
The
Munk
r and t
F
(w 2f2)
3/2
w (p2-k2) -1/2 {t2 (w2-f2)+k2}1 dpdw
f Jk
r
= Eb2N0 = 320 m2cph
t
= j/2bN0 = 3.8x104 cprn/cph
E
=
6.3x103
j
b
=
1.3x103 m
N0 = 3 cph
par ameters are
parameters:
=
3
combinations of the Garrett-
E, the energy
level; j, the
effective
I
-2
a
'-I
-3
Co
0
0
CD
D
-J
0
0
-5
I
I
I
II
b
*
0
L)
-2
Do
U)
('1
_3
z
CD
-5
-It.
-3
LOG K
(CPM)
-2
Figure 6. Ensemble averaged spectra of isotherm depth
from the Sargasso Sea at depths of 45-50m (0)
76-8Gm ()
and 100-11Gm (0).
a)
Spectra. b)
Spectra scaled by
multiplying by the local buoyancy frequency.
,
17
>
0
7
*
S
4-
3
LI)
I
--5
t
iI
-4-
LOS K
iii
-3
liii
-2
(CPM)
Figure 7. N-scaled average spectrum of isotherm depth
from the Sargasso Sea compared to the Garrett-Munk model
as formulated by IJesaubies (1976)
Light lines depict 95%
confidence intervals.
number; b,
mode
vertical scale
the
of N
frequency scale. This equation
buoyancy
numerical
integration.
high
At
;
was evaluated by
wavenumbers,
representation with a
spectra has an analytical
N0, the
and
the towed
k2
slope
(Desaubies, 1976)
Overall, the shape and level of the average spectrum
agree satisfactorily with the Garrett-Munk model (Fig.
cpm the spectrum
However, at wavenumbers lower than lxlO
is
7)
consistently below the Garrett-Munk model
while
at
higher wavenumbers the spectrum is above the model because
of
an
observed
spectral
(flattening
shoulder
the
of
This spectral shoulder is smeared by the
spectral slope) .
because
the
shoulder may not always occur at the same wavelength.
The
process
of
averaging
spectra
individual
spectral shoulder is more pronounced in some individual
spectra as shown in Fig. 5.
Averaged spectra from the warm core ring are shown
scaled by the local buoyancy frequency in Fig.
8.
These
spectra are from depths of 31-35, 35-40, 41-47, and 49-54m
with local buoyancy frequencies of 15,
17, 20, and 15 cph
The scaling of these spectra only slightly
respectively.
scatter of
reduces
the
little
variation
of
the
points.
buoyancy
However,
frequency
there
is
that
a
so
conclusive statement about N-scaling cannot be made.
8
also
shows
the
same
Garrett-Munk
spectral
Fig.
model
19
0
7
(-)
N
*
5
4-
3
U)
-5
1,.
LOG K
-3
-2
(CPM)
Figure 8. N-scaled ensemble averaged spectra of
isotherm depth from the warm core ring at depths of 31-35m
(0), 35-40m (0), 41-47rn (X), and 49-54m (0) compared to
the Garrett-Munk spectral model.
20
Spectra from the warm core ring agree
described above.
with
model
the
level
in
and
The
slope.
increase
in
observed spectral level at high wavenumbers is fictitious,
caused by errors associated with the kiting of the chain.
There is no spectral shoulder evident in the spectra.
The averaged spectrum from the Sargasso Sea and the
spectrum averaged over 34 to 40m depth from the warm core
ring
with
compared
are
spectra
towed
other
from
experiments and the Garrett-Munk model in Fig. 9. Table 3
summarizes
observations
the
observations from MILE
results.
average
around
The
agree with our
1979)
The deep ocean spectrum of
1x103 cpm.
Katz and Briscoe
in
(Spoering,
comparison.
A spectral shoulder was observed during MILE at
a wavenumber of
also
and
(1979)
from a depth of 350 to 750m is
spectrum
This
agreement.
spectra which scatter by
of
average.
the
and
Katz
the
is
a
approximate
factor
Briscoe
of
±1.5
Spoering
and
concluded that their spectra adequately agreed with the
Garrett-Munk model.
In the wavenumber range from 1x104 to 2x103 cpm the
results from JASIN (Levine et al., 1983b) and Bell
(1976)
are higher than the others by factors of 2 to 6. The JASIN
observations
slightly
also
lower
wavenumbers,
exhibit
a
wavenumber,
the spectral
spectral
shoulder
6x104 cpm.
At
at
a
lower
levels of the JASIN and Bell
21
liii
I
I
liii
I
III
I
7
0
C)
0
(N
*
5
\
0
3
0
0
LI)
2
LD
D
-J
I
-5
i
iii
-4-
LOG K
I
I
III
-3
I
I
III
-2
(CPM)
Figure 9. Comparison of N-scaled spectra of isotherm
depth from the Sargasso Sea (0), the warm core ring ()
NILE (heavy solid line) , Katz and Briscoe (light dashed
line), JASIN (light solid line), and Bell (heavy dashed
line)
Table 3.
Summary of compared observations of internal waves.
Levine
et al.
Run 2
Location
Ocean Depth
Run 3
Sargasso
Sea
Warm core
5000m
2000m
ring
(1983a)
(MILE)
Levine
et al.
(1983b)
(JASIN)
Katz
Bell
(1976)
&
Briscoe
(1979)
NE
West of
Sargasso
Pacific Scotland Sea
Sargasso
500Dm
500Dm
1500m
1500-
Sea
500 Om
Observation
Depth
Percent Diff.
from GM model
45-lOOm
+20
30-50m
20-40m
+5
+20
Sept
Sept
20-70m
80-120m
350-750m
+450
+160
+5
Aug
Sept
Oct
at 1x103 cpm
Time of Year
Sept
t)
23
observations are more in agreement with the other results
and
the
Garrett-Munk
This
model.
may
be
low
due
to
for
various
statistical significance at low wavenumber.
The
coherences
from the
Sargasso
Sea
vertical separations are compared with the Garrett-Munk
(see Appendix D)
model as formulated by Desaubies (1976)
The values were calculated by numerical integration.
A
comparison of the observed coherence at 5 to 10m vertical
separation
with
equation
Desaubies'
buoyancy
using
frequencies of 6 and 12 cph is shown in Fig. 10. Over the
depth range of the data, the mean buoyancy frequency is 9
cph.
Therefore the low wavenumber results are consistent
Ensemble average coherences
with the Garrett-Munk model.
for
various
Garrett-Munk
vertical
model,
separations,
are
shown
in
compared
Appendix
to
E.
As
the
the
vertical separation increases the number of significant
coherence estimates decreases.
the model more uncertain.
confirms
This makes a comparison to
However, an overall comparison
that the Sargasso Sea results
agree with
the
Garrett-Munk model at low wavenumber.
At
high
wavenumber,
coherence occurs
a
significant
peak
for vertical separations of
in
less
the
than
40m. This peak does not agree with the Garrett-Munk model
which predicts a fall-off to low coherence with increasing
24
L!iaJ
LU
ø.6
LU
LU
D
ci
-5
1,
-3
LOG K
(CPM)
-2
Ensenble
averaged
Figure
10.
coherence
between
isotherms separated vertically 5 to lOrn (bold line) and
towed vertical coherence equation
the Desaubies
(1976)
from Appendix D with N = 12 (light line) and N = 6 (dashed
equation
for
line)
Desaubies
computed
a
vertical
separation of 7.5 m.
.
25
wavenumber.
This peak is coincident with the shoulders in
many of the spectra of individual isotherms (Fig. 5)
Katz and Briscoe (1979) noticed a peak in coherence,
at
350m
depth,
occurring
also
2-3x103 cpm.
at
Their
observations were made in September in the Sargasso sea
approximately 600nm to the east of the site of Run 2.
comparison between the coherence for
from
separation
Run
coherence
the
and
2
Briscoe at 8.5m vertical separation (Fig.
their peak,
though not
similar
wavenumber.
buoyancy
frequency
high
as
profiles
a
and
shows that
11)
occurs
the
of
shows
Katz
of
or broad,
comparison
A
lOm vertical
to
5
A
similar
at
a
respective
vertical
structure with both having a local minimum in the buoyancy
frequency at 350rn depth.
Katz and Briscoe hypothesized
that the peak in coherence was due the inabilty of higher
modes
to
"tunnel"
into
the
region
of
the
buoyancy
However, our observations occur in a
frequency minimum.
region of maximum buoyancy frequency.
Therefore Katz and
Briscoe's explanation does not apply to our data taken at
shallow depths.
The coherence peak and spectral shoulder is evidence
of dominance of the internal wave spectrum by the lowest
few modes at high wavenumber.
frequencies from
dominate.
3
to
6
cph
Pinkel (1975) found that at
the
lowest few modes did
This result is similar to the JASIN (Levine et
26
1
ri
L'I
.0
SI
6
D 0.4-
-5
-4-
-3
LOG K
(CPM)
-2
coherence
between
averaged
Ensemble
Figure
11.
isotherms separated 5 to lOrn in the vertical (bold line)
and the towed vertical coherence of Katz and Briscoe
(1979) at 350rn depth and 3.5m vertical separation.
27
In frequency space, the
al, 1983b) data previously cited.
JASIN coherence peaked at a frequency of 2 to 4 cph.
corresponded
2x103 cpm.
Sargasso
2x103
to
a
dispersion relation
The
Sea
site
shows
that,
(Fig.
at
8x10
of
a
frequencies for the
for
12)
wavenumber
the
of
of
our
Therefore the internal wave
lowest few modes in the wavenumber
coherence
peak
and
(Levine
coherence
peak
et
al.,
found
This
1983b).
in
the
(1975)
and
that
the
suggests
Sargasso
dominance by the lowest few modes.
shoulder
spectral
correspond to the high frequencies of Pinkel
JASIN
to
cpm, the frequency for mode 1 is at least 6 cph and
for mode 2 is at least 3 cph.
range
range
wavenumber
This
Sea
is
due
to
2
(-)
0
CD
-J
-2
-s
-/t-
LOG K
-2
-3
(CPM)
Fi;ur 12. Disersjon relation for
in thn Sar;asso Sna.
o
1 throuoh 6
29
CONCLUSIONS
Observations of upper ocean internal gravity waves
were made with a towed thermistor chain in September, 1981
at two sites in the western North Atlantic. One site was
in the Sargasso Sea and the other was within a warm core
ring located north of the Gulf Stream. Spectra of isotherm
depths were computed and compared to the predictions of
the Garrett-Munk model
and
to other
experiments.
The
following conclusions can be drawn.
1.
The spectral slopes and levels from the Sargasso Sea
and the warm core ring agree with the Garrett-Munk
Averaged spectral levels from the Sargasso
model.
proportional
are
Sea
the
to
local
buoyancy
frequency.
2.
There
is
spectral shoulder in the Sargasso Sea
a
results at
this
a wavenurnber of
there
wavenumber,
.between
isotherms
whose
1-2x103 cpm.
is
a
peak
vertical
in
Also at
coherence
separations
are
less than 40m. This feature does not agree with the
Garrett-Munk model.
The dispersion relation shows
that these wavenumbers correspond to frequencies of
at
least
3
to
6
cph.
The
coherence
peak
and
spectral shoulder observed in the Sargasso Sea are
evidence of dominance of a few low modes.
30
3.
A comparison of the Sargasso Sea and warm core ring
observations was made with other observations in the
Sargasso
(1979) ,
The
Sea.
results
Katz
of
Briscoe
and
taken from 350-75Gm depth, agree with our
results.
A peak in coherence was found by Katz and
Briscoe at 35Gm depth whose wavenumber corresponded
to our coherence peak.
However, the observations of
Bell (1976) taken in the upper ocean were generally
higher in
level
by
factor
a
of
2.
Bell
did not
observe a coherence peak or shoulder.
4.
A comparison of the Sargasso Sea and warm core ring
results was made with experiments conducted in other
oceans.
(Spoering,
MILE
data
from
1979; Levine et al.,
our results.
the
MILE
The
the
NE
Pacific
1983a) agreed with
A spectral shoulder was observed in
towed
spectra
at
1x103 cpm.
The
JASIN
observations (Levine et al., 1983b) west of Scotland
exhibited
spectral
levels higher than ours
by
a
factor of about 6. A spectral shoulder and coherence
peak were observed at 6x10
cpm.
31
REFERENCES
Baumann, R. J., L. M. deWitt, M. D. Levine, C. A. Paulson,
Towed Thermistor Chain
1982:
Wagner,
and J.
D.
Report,
Stream.
Gulf
the
Across
Observations
Reference 82-3, School of Oceanography, Corvallis, OR
97331, 98 pp.
Bell,
The Structure of Internal Wave
Chain
Thermistor
from
Determined
Measurements. J. Geophys. Res., 81, 3709-3714.
T.H.,
Jr.,
as
Spectra
Desaubies, Y.
Internal
976-981.
1976:
F.,
J.
Wave
1976:
Analytical Representation of
Spectra.
J.
Phys.
Oceanogr.,
6,
Frankignoul, C., 1974: A Cautionary Note on the Spectral
Analysis of Short Internal Wave Records. J. Geophys.
Res., 79, 3459-3462.
Space-Time Scales of
Garrett, C. and W. Munk, 1972:
Internal Waves. Geophys. Fluid Dynamics, 2, 225-264.
Space-Time Scales of
1975:
and W. Munk,
C.
Internal Waves: A Progress Report. J. Geophys. Res.,
Garrett,
80,291-297.
Garrett, C. and W. Munk, 1979: Internal Waves
Ocean. Ann. Rev. Fluid Mech., 11, 339-369.
Gradshteyn,
I.
S.
and
I.
M.
Ryshik,
1965:
in
Tables
Integrals Series and Products. Academic Press,
the
of
1086
pp.
Katz, E. J. and M. G. Briscoe, 1979: Vertical Coherence of
the Internal Wavefield from Towed Sensors. J. Phys.
Oceanogr., 9, 518-530.
M.D., R.A. de Szoeke, and P.P. Niiler, 1983a:
Internal Waves in the Upper Ocean During MILE. J.
Phys. Oceanogr., 13, 240-257.
Levine,
Levine, M.D., C.A. Paulson, M.G. Briscoe, R.A. Weller, and
Internal Waves in JASIN. Phil.
Peters, 1983b:
H.
Trans. R. Soc. Lond., 308, 389-405.
Levine, M.D., in press: Internal Waves in the Ocean:
Review. Revs Geophys Space Phys.
A
32
Munk, W., 1981: Internal Waves and Small Scale Processes,
In:
Evolution of Physical Oceanography. Warren &
Wunsch, editors, Mit Press, 623 pp.
Pinkel, R., 1975: Upper Ocean Internal Wave Observations
from FLIP. J. Geophys. Res., 80, 3892-3910.
Pinkel,
1981:
Observations
of
R.,
Internal
Wavefield.
Phys.
J.
1248-1257.
Roth,
M.W., M.G. Briscoe, and
Internal
Waves
in
the
Oceanogr., 11, 1234-1247.
C.H.
Upper
Near-Surface
the
Oceanogr.,
11,
McComas
Ocean.
III,
J.
1981:
Phys.
1979:
Towed Observations of Internal
T.
J.,
Waves in the Upper Ocean. Report, Reference 79-10,
Spoering,
School of Oceanography, Corvallis, OR 97331, l2lpp.
Trask, R. P., M. G. Briscoe and N. J. Pennington, 1982:
Long Term Upper Ocean Study (LOTUS) , A Summary of the
Historical Data and Engineering Test Data. Technical
WHOI-82-53,
Woods
Hole
Oceanographic
Report,
Institute, Woods Hole MA, 02534, 107 pp.
APPENDICES
33
APPENDIX A
XET Temperature Profiles and Isotherms
section
This
contains
the
temperature
vertical
profiles of XET data simultaneous to Runs
2
and
3
and
extending beyond Run 2. Also shown are contoured isotherms
computed
temperature
profiles
casts.
linear
by
data.
are
The
interpolation
offset
proportional
to
of
the
between
the
time
XBT
the
XBT
temperature
elapsed
between
A table listing the position and time of each XBT
cast is first.
34
XBT Drop Sites/Times
Sargasso Sea
33
33
33
33
33
34
34
34
34
34
34
34
34
34
34
35
35
35
35
35
45.5N
47.7N
51.3N
55.0N
58.6N
02.3N
06.1N
10.1N
14.1N
18.1N
22.ON
25.7N
28.1N
38.5N
51.6N
00.ON
03.7N
16.ON
26.ON
37.9N
Warm Core Ring
69
69
69
69
70
70
70
70
70
70
70
70
70
70
69
70
69
69
70
70
59.7W
59.9W
59.8W
59.9W
00.3W
00.8W
01.1W
00.9W
00.9W
00.9W
00.7W
00.8W
00.1W
00.0W
59.9W
00.1W
57.6W
59.4W
00.0W
01.8W
38
38
38
38
38
38
39
39
39
39
39
39
39
39
39.ON
42.5N
46.1N
49.8N
53.5N
57.5N
01.4N
05.3N
08.9N
12.5N
16.1N
17.9N
20.5N
21.9N
0100
0200
0259
0400
0459
0559
0659
0800
0901
0959
1058
1158
1610
1700
1800
1843
2200
2300
2357
0057
17,18-Seo-81
Time (GMT)
Position
XET
103
104
105
106
107
108
109
110
111
112
113
114
115
116
Time (GNT
Position
XBT
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
14,15-Sep-81
71
71
71
71
71
71
71
71
71
71
71
71
71
71
29.5W
28.8W
26.9W
25.1W
23.2W
21.5W
19.5W
17.4W
15.3W
13.7W
12.2W
11.5W
10.6W
10.0W
1230
1945
2030
2115
2159
2245
2330
0015
0059
0145
0230
0255
0330
0352
14-SEP-81
sargasso sea
3øø
F-
aLiJ
D500
[J1I'
VAf!I
[;Ji&
8
12
16
20
24
28
TEMPERATURE (DEG C)
LJ
01
warm core ring
1 7 18-SEP-81
[!AI
3øø
0
L
D500
'4,4
[;T'4J
8
12
16
20
24
28
TEMPERATURE (DEG C)
0
)
34
69
103
137
0320
0540
0800
1020
172
(KM)
100
200
_300
100
0
L.iJ
500
600
700
r.
800 0100
i ---T
XBT IGOTI-IERMS VG TIME/DISTANCE
1240
1',.-SEP-81
(GMT)
64.5
21.5
0
(KM)
100
200
Ip00
0
Lii
1=
H.....
Tf1
[T'E1
I
1830
I
2050
......
I
I
2310
0130
XBT ISOTHERMS VS TIME/DISTANCE
1718-SEP-81
(GMTI
39
APPENDIX B
Edited Isotherms
This appendix contains edited isotherm depths from
Runs
2
and
3
which
were
spectrally
analyzed.
The
isotherms and the times at which they were observed are
listed first.
on each figure.
of 0.5 deg C.
The highest and lowest isotherm are given
Intermediate isotherms are at increments
40
Isotherms Used for Spectral Analysis
Run 2
Time
Isotherm
(Deg C)
(GMT)
Tape
9
21.0
21 5
22 0
22 5
23 0
23 5
24 0
24 5
25 0
25.5
It
U
Tape 10
0730-1145
17-Sep-81
1915-2357
II
Tape 13
21 5
22.0
Average Depth
(M)
104.87
93 78
84 31
76 62
70 03
64 25
58 95
54 08
49 43
45.60
90.80
83 12
76 15
70 10
65 37
61 53
57 95
54 69
51
18.0
18 5
19 0
19 5
20 0
20 5
21 0
21 5
22.0
0
14-Sep-81
0646-1145
1
Tape 12
21
14-Sep-81
0130-0644
U
21.0
21 5
22 0
22 5
23 0
23 5
21 0
24 5
25 0
25.5
20.0
20.5
20.0
20 5
14-Sep-81
18-Sep-81
0057-0337
II
II
II
It
'6
48.00
110.57
99.72
53.27
49 51
46 88
44 77
43 00
41 36
39 73
37 97
36.17
35.76
34 96
34 09
33 07
31.82
(KM
5
0
20
30
50
60
H-
0
LU
70
80
90
100
110
120
130
v1j
LOJL1
k1210
0230
0250
EDITED IOTk[RM DEPTH V9 TIME/DISTANCE
IOTHERM 25.5 TO 21 .0 DEG C
0310
(GMT)
111---5EP-81
H
(KM)
5
0
10
20
30
110
50
60
F-
70
D
80
0
LiJ
90
100
110
120
130
0330
0350
04..10
04-30
EIDTED IGOTI-IERM DEPTH V
OTHEPM
04.50
TIME/DIGTANCEI
25.5 TO 21.0 DEG C
0510
14--EP-81
(GMT)
(KM)
'4
'4
FcL
Ld
Q
.,,4
-
-I-" P
-
100
110
120
130
0530
0550
0610
0630
0650
EDITED IGOTRERM DEPTH V TIME/DITRNCE
IOTHERM9 25.5 TO 21 .0 DEG C
0710
1--5EP-81
(GMT)
(KM)
5
'4
'4
'4
'4
.'
F-
0
U
D
.-----'
-'-
\/
'_'
V
'-'
V V
V
-
''4
'4
'4
rwaJ'i
'iYAI'i
i;ii
i;!T'i
EDITED ISOTRERM OEPTR V TIME/DISTANCE
ISOTHERMS 25.5 TO 20.0 DEG C
41II4
(e1I
1L---SEP-81
.
(KM)
5
'4
'4
'4
'4
'4
0
LJ
D
'4
r4
'4
0930
0950
1010
1030
1050
EDITED I5OTHERM DEPTH VG TIME/DIGTANCE
IOTHERM 25.5 TO 20.0 DEG C
1110
(GIlT)
1L-SEP_B1
U'
(KM)
5
U
U
50
'60
70
LJ
90
100
110
120
130
1130
1150
1210
1230
1250
EDITED ISOTHERM DEPTH VS TIME/DISTANCE
ISOTRERMS 25.5 TO 200 DEG C
1310
1L,-SEP-81
(GMT)
15
10
5
0
(KM)
1!J
II
20
30
Ito
50
LI
0
LU
D
E
.4
'4,4
'4
'4
'4
1915
1935
1955
2015
2035
2055
ISOTHERM DEPTH VS TIME/DISTANCE 17-SEP-81
iSOTHERMS 22.0 TO 18.0 DEG C
(GMT)
10
5
0
(KM)
15
U
LII
,50
'60
-70
90
100
110
120
130
2115
2135
2155
2215
2235
2255
ISUTkERM DEPTH VG TIME/DISTANCE 17-EP-81
ISOTHERMS 22.0 TO 10.0 DEG C
<GMT)
5
(KM)
15
0
10
20
30
1t-0
50
60
0
LU
D
70
80
90
100
110
120
130
2315
2335
2355
IOTHEIPM DEIPT1-I V
ISOTHERM
0015
0035
0055
TIME/OITANC
17118-EIP-81
200 TO 18.0 DEG C
(GMT)
15
5
(KM)
U
n
Li
I-.
D
E
'.4
P4
120
130
0115
0135
0155
0215
0235
0255
ISOTHERM DEPTH VS TIME/OiSTPNCE 18-SEP-81
SOTHERMS 22.0 20.0 OEG C
(G1T)
Ui
0
15
5
(1(M)
U
0
I 70
ci
90
100
110
120
130
0315
0335
0355
015
0435
0455
18-SEP-81
ISOTHERM DEPTH VS TIME/OIGTIRNCE
ISOTHERMS 22.0 TO 20.0 DEG C
(GMT)
u-I
52
APPENDIX C
Ensemble Averaged Spectra
This appendix contains the ensemble averaged spectra
of Runs 2 and 3 for various depth bands.
The spectra were
computed by the use of standard techniques.
The results
of Run 2 are shown before those from Run 3. The run number
and depth band of each ensemble average is listed at the
top
of
each
figure.
A
table
listing
isotherms and their average depths is first.
the
analyzed
53
Ensemble Averaged Isotherms
Run 2
Depth Band
14-Sep-81
Isotherm
(Deg C)
Average Depth
(m)
45-50m
25.5 Tape 9
25.0
"
25.5 Tape 10
45.60
49.40
48.00
51-55m
24.5 Tape 9
25.0 Tape 10
24.5
"
54.10
51.50
54.70
56-62m
24.0 Tape 9
24.0 Tape 10
23.5
"
58.95
57.95
61.50
64-66m
23.5 Tape 9
23.0 Tape 10
64.25
65.37
70-71m
23.0 Tape 9
22.5 Tape 10
70.00
70.10
76-77m
22.5 Tape 9
22.0 Tape 10
76.60
76.15
83-85m
22.0 Tape 9
21.5 Tape 10
84.30
83.10
90-94m
21.5 Tape 9
21.0 Tape 10
93.80
90.80
99-105m
21.0 Tape 9
20.5 Tape 10
104.90
99.70
54
Run 3
Depth Band
17,18-Sep-81
Isotherm
(Deg C)
Average Depth
(m)
31-35m
20.5 Tape 13
21.0
"
21 5
"
22.0
34.96
34 09
33 07
31.32
35-40m
21.0 Tape 12
21 5
22.0
"
20.0 Tape 13
39.73
37 97
36.17
35.76
41-47m
19.0 Tape 12
19 5
"
20 0
20.5
46.88
44 77
43 00
41.36
49-54m
18.0 Tape 12
"
18.5
53.27
49.51
'
-j
Cl)
*
c-i
cL4
5
0
(CPM)
0
LOG K
0
-3
0
-4
0
0
-2
0
0
45-50M 01P1H
0°
RUN 2
Li
-J
U
1)
'-I
E
*
a4
5
5
0
LOG K
0
0
0
(CPt-1)
-3
00
0
0
-2
0
51-55M D[PT1
00
-4
0
RUN 2
Ui
-J
U)
*
Ci
Q4
5
[;I
-s
0
0
0
00
(CPM)
0
LOG K
0
-3
0
0
-2
0
0
56-62M DEPTH
-4
0o
RUN 2
C-)
U)
*
cL4
6-
-5
00
00
(CPM)
0
LOG K
0
-3
00
0
-2
0
0
64-66M DEPTH
-4
0
RUN 2
tJI
-J
U)
0
1
u2
-S
*
Q-4
5
[;I
-5
0
0
00
(CPM)
0
LOG K
0
-3
0
0
-2
0
0
70-71M DEPTH
-4
RUN 2
E*
cD
-J
U)
1'
Ii
'-'3
cL4
Ci
S
-5
0
0
0
(CPM)
0
LOG K
0
-3
0
0
-2
0
0
76-77M DEPTH
-4
00
RUN 2
01
-1
-5
00
0
0
0
0
0
c-i
cL4
Q
-J
-I
-3
(CPM)
-4
LOG K
-2
-J
-I
'-.3
000
'-'3
0
5
*
0
*
c-i
5
0
-5
0
0
00
(CPM)
0
LOG K
00
-3
0
0
0
0
-2
0
90-94M DEPTI-I
-4
0
RUN 2
-J
(I)
0
u2
*
cL4
ci
4
6-
5
0
0
0
0
0
(CPM)
0
LOG K
0
3
0
0
0
2
0
99-1ØSM DEPTH
4
RUN 2
Ui
-5
00
0
0
0
-j
(I)
1I
'-3
Oc?
-3
(CPM)
-4
LOG K
-2
r;i
cD2
cD
(f)
*
C-)
*
C)
Q-4
00
S
c4
5
6
RUN 3 31-35M DEPTH
-5
0
0
0
0
00
0
(CPM)
0
LOG K
0
-3
0
-4
L.A
RUN 3 35-40M DEPTH
-2
J
II
CD2
*
C)
5
[;I
-s
0
0
(CPM)
0
LOG K
0
-3
0
-4
0
0
RUN 3 41-47M DEPTH
-2
1
*
C-)
a.
1
-S
0-
4-
5-
6-
I
.
0
(CPM)
0
I
LOG K
..I
0
IIJ
0
I
-3
&
I
-4
...1
,-0
'
I
III
a
-2
III
00
I
RUN 3 49-54M DEPTH
62
APPENDIX D
Towed Vertical Coherence
The towed vertical coherence as given by Desaubies
(1976) is:
(27raV) 2
TVC(2iraV)=
1s2[s2_(2V)2]
N/f
i
2N2/f2
[
1
i
1}I(s)ds
2V
where
I(S)=(N2/f2_l)2[0tcos(st)[(l+t2)(N2/f2+t2)2]_ldt
= wavenumber
V = vertical separation
N = buoyancy frequency
f = coriolis parameter.
c.
I(s) can be expressed in terms of exponential
integral functions as follows.
The integrand of I is
expressed in terms of partial fractions.
tcos (st)
(1+t2) (N2/f2 + t2)2
(Dt + Ft3 )cos(st)
Btcos (st)
+
1 +
(
where
B = (y - 1)_2
D = (1 - 2y) (y - l)_2
F = -(y
y = N2/f2
12and
+ t2)2
63
Hence
IBtcos(st) dt
I(s)= (_1)2
(1+t2)
iJ
((Dt + Ft3)cos(st) dt
+
J0
[o
The first integral
B5tcos(st) (1+t2)1 dt = B[_1/2(e_SE1(s)+eSE1(_s))]
(from Gradshyteyn and Ryzhik, 1965)
where
'
t
E.(s)
=)0e /t dt
1
E.(_s)=J'et/t dt
1
The second integral can be divided into two integrable
parts by adding and subtracting yt(y+t2Y2 to the integrand
(co
(Dt + Ft3)cos(st) (y + t2)2 dt =
J
0
(cx,
tcos(st) (y + t2)2 dt +
(D/F_'r)J
0
/
Jo
tcos(st) (y + t2)' dt
The first part can be integrated by parts to equal
(D/F-y) [l/(2y)-s/2 Jsin(st) (y + t2)1dt]
which, from Gradshteyn and Ryzhik (1965) becomes
-sV
(D/F-1) {1/(2y)-s/2{1/t2/) (e
E1(S/y) - e
The second part can be evaluated
Gradshetyn and Ryshik (1965)
Jtcos(st) (i+t2Y1dt =
e5 1E1() + e5
S1
directly from
64
Therefore, I(s) becomes
I(s) = -l/2[e -s E.1 (s) + eSE. (-s)} -
(1 -y)y1 +
[(1-y)s(2Y' - 1]eE, (s) +
1
{(l-'y)s(2[yY1 +
lie
E.(-S/).
1
The function TVC(2rrcV) is plotted in Fig. 01 for
various
values of N/f.
65
I
1
Ill
I
liii
1
U
III
I
1
Iii
n/f = 21.5
LU
z
LU
(-)
n/f =257
LU
D
n/f
iii
I
-3
-'
I
liii
-2
I
I
III
-1
I
128.5
1111
0
LOG 27ra<V
Figure
Dl.
Towed
vertical
coherence
model
of
Desauhies (1976) at N/f = 21.5, 123.5, and 257. Plotted as
coherence vs 2lTa V
where
is the wavenumber (cpm) and V
is the vertical separation (m)
,
APPENDIX E
Ensemble Averaged Vertical Coherence
This section contains the ensemble averaged vertical
at various vertical separations from Run
coherences
2.
Vertical coherences from Run 3 were not computed due to
the vertical movement of the chain.
heavy
line
is
the
ensemble
On each figure, the
average
coherence
for
all
isotherm pairs whose vertical separation fit within the
the
band
listed.
The
table
at
the beginning of
this
section contains a list of the isotherm pairs used.
The light line on each figure is the Null Hypothesis
test level for each ensemble average.
which
fall
below
this
line
cannot
Coherence points
be
considered
significantly different from zero at the 95% level.
The
dashed line is the model of towed vertical coherence at
N = 12 cph as formulated by Desaubies (1976)
(see Appendix
67
Vertical Coherence Isotherm Pairs
Separation
Depth Difference
I sotherms
(Deg C)
(m)
5-1 Urn
23.5-23.0 Tape 9
22.0-21.5
25.5-24.0 Tape 10
21.0-20.5
"
5.78
9.47
9.95
8.92
10-15rn
25.5-24.0 Tape 9
24.5-23.5
23 0-22 0
"
21.5-21.0
24.5-23.0 Tape 10
23.0-22.0
"
22.0-21 0
20.5-20.0
13.35
10.17
14.23
11.09
10.68
10.78
14.65
10.85
16 -2 Urn
24.5-23.0 Tape 9
25.5-23.0 Tape 10
21.0-20.0
15.95
17.37
19.77
20-25rn
25.5-23.0 Tape 9
23.5-22 0
23.0-21.5
"
22.0-21.0
24.5-22.0 Tape 10
22.0-20.5
U
24.42
20.06
23.70
20.56
21.46
22.57
25-3 Urn
23.5-21.5 Tape 9
25.5-22.0 Tape 10
23.0-21.0
29.53
28.15
25.43
30-35m
24.5-22.0 Tape 9
23.0-21.0
23.0-20.5 Tape 10
22.0-20.0
"
30.23
34.79
34.35
34.42
36-40m
25.5-22.0 Tape 9
24.5-21.5
24.5-21.0 Tape 10
38.71
23.5-21.0 Tape 9
25.5-21.0 Tape 10
24.0-20.5
40.62
42.80
41.71
II
4 0-4 3m
I,
39 .70
36.11
45-5 3m
25.5-21.5 Tape 9
24.5-21.0
"
25.5-20.5 Tape 10
24 0-20 0
"
H
23.0-20.0
48.18
50.79
51.72
52 62
45.20
5 9-6 3m
25.5-21.0 Tape 9
25.5-20.0 Tape 10
59.27
62.57
RUN 2
LiJ
5-1ØM
[PRRRTJON
RUN 2
LU
ø.6
LU
10-1SM
EPARflT ION
øj
LU
a:
LU
LU
DØ.
C-)
C-)
'4
WI
-5
_1,_
-3
LOG K
(CPM)
-2
-o
LOG K
(CPM)
RUN 2
1
J
LNI
16-21f1 SEPARATION
T 1iJ
I
I
1I
1
I
RUN 2
20-25M SEPARATION
-5
_Lt_
-3
LOG K
(CPu)
I-E'
\
-
cØ1
Li
\
-
DØ.4Li
w1
'4
\
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-S
(III
I_
I
ill
I
-'
-3
LOG K
(CPM)
liii
-2
-2
-J
0
RUN 2
1
25-80M SEPARPUON
III
I
1
I
liii
I
I
RUN 2
30-35M SEPARATION
IIJ
\
\
Lii
Ø.6
\
-
LU
\
LU
Lii
\
LU
LU
DØ.4-
DØ.
()
(-)
\
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-5
iiil
i
iii
I
-It.
-3
LOG K
(CPM)
I
III
-2
'-I
-r
LOG K
(CPM)
H
RUN 2
4-5-53M
RUN 2
EIPAR1RT ION
LU
LU
LU
LU
LU
Lii
DØH
Li
59-63M
EIPRRRTION
DØ.
Li
-.3
-
-u
LOG K
(CPM)
_._)
--I-
LOG K
(CPM)
-J
IRUN 2
1
36-'-øM SEPARATION
'''I
1
liii
1
1
RUN 2
't-ø-'..3M SEPARATION
lJ,
N
Lii
LU
ø.6
Ui
Lii
\
Ui
Ui
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DØ.lt
DØH
C-)
C-)
\
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\
'4,4
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-5
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i
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-3
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(CPM)
iii
-2
_'t-
LOG K
(CPM)
-1
U)