THE mJIVERSJ.TY OF MIAMI
The Baroclinic Structure of the Florida Current
BY
William 0, Stubbs, Jr.
A THESIS
Submitted to the Faculty
of the University of Miami
in partial fulfillment of the requirements for
the degree of Master of Science
Coral Gables, Florida
June 1971
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THE UNIVERSITY OF MIAMI
The Baroclinic Structure of the Florida Current
BY
William 0, Stubbs, Jr.
A THESIS
Submitted to the Faculty
of the University of Miami
in partial fulfillment of the requirements for
the degree of Master of Science
Coral Gables, Florida
June 1971
HAVAL POSTGl?Jt)TJATE SCHOOD
MOITTEREY, CALIF. 93940
STUBBS, WILLIAM OLAN, JR. (M.S., Physical Oceanography)
The Baroclinlc Structure of the Florida Current. (June 1971).
Abstract of a Master's Thesis at the University of Miami. Thesis
supervised by Professor Christopher N.K. Mcoers .
Nine consecutive days of free-fall, STD data are a'-::'iyzed in a
study of the baroclinic structure of the Florida Current. Mean values
averaged over the nine days are used to reduce tidal aliasing.
A southward flow is confirmed during the nine day period. Based
or', this data and previous works, the southward flow appears to be of
a transient nature,
Com.parison of the directly measured and geostrophica lly computed
current and transport indicates that the Florida Current is essentially
in geos trophic balance.
ACKNOWLEDGEMENTS
My sincerest thanks go to Dr. William So Richardson, NOVA
University, who not only made the data available, but also provided
many helpful suggestions during the preparation of this thesis. I am
deeply grateful to the members of my thesis committee: Dr. Walter
Duing, who suggested the topic, Dr. Claes Rooth and Dr. Harry A .
DeFerrari. In particular, I express my sincere appreciation and
gratitude to Dr. Christopher N.K. Mooers , my thesis committee chairman.
Without his wise guidance, timely suggestions and constant encouragement,
this work might never have been completed. A special thanks to Manuel
Bascuas for his help in computer programming. And to Joyce Stubbs,
the ultimate in gratitude is due.
The financial support for this study was provided by the Office
of Naval Research Contract No. N00014-67-A-0201-0013, Project No.
NR 083-060.
William 0. Stubbs , Jr
Coral Gables, Florida
June 19 71
111
TABLE OF CONTENTS
Page
LIST OF TABLES v
LIST OF FIGURES vi
LIST OF APPENDICES viii
I. INinODUCTION ....,,., 1
II. METHODS 3
A. Data Acquisition 3
B. Data Analysis . 4
C. Analysis of Errors . 24
III. RESULTS 28
A. Comp)arison of Direct Measurements and
Geos trophic Calculations . . . . » 28
B. Features of the Florida Current 36
IV. SUMMARY AND CONCLUSIONS , » 47
A. Summary 47
B. Conclusions 48
LITERATURE CITED . , 51
APPENDIX , , 54
IV
LIST OF TABLES
TABLE
I. Free-fall Instrument Data . , .
Page
6
II. Time of Observation and Depth
of Probe for Free-Fail Transects
LIST OF FIGURES
FIGURE Page
1. Station locations , .«..<,,.. 5
2. Mean temperature (C°) sectrlon ........ o .... . 8
3. Mean salinity (%o ) section 9
4. Mean sigma-t section ........... iQ
5. Observed velocity profile for
stations 5 and 7 12
6. Mean observed axial velocity (cm/sec) . 14
7. Mean dynamic depth difference (AD) . I7
8. Depth of no motion I9
9. Mean axial velocity (cm/sec), observed
and geos trophic (depth of no motion by
Defant's method) .......... . . 20
10. Mean axial velocity (cm/sec), observed
and geos trophic (Vgeos trophic = Vobserved
at surface) 21
11. Mean axial velocity (cm/sec), observed
and geostrophic (Vgeos trophic = 0 at bottom) ...... 22
12. Mean axial velocity (cm/sec), observed
and geostrophic (depth of no motion =
400 meters) .,.,....,... ..... 23
13. Standard deviation for temperature (C°)>
salinity (%q) , and sigma-t (o ^ units) 27
14. Mean surface velocity (cm/sec), observed
and geostrophic (hybrid depth of no motion) . . 29
15. Mean axial velocity (cm/sec), observed and
geostrophic (hybrid depth of no motion) .... 31
16f) . Velocity profile (cm/sec), observed and
geostrophic (hybrid depth of no motion),
stations 2, 3 and 4 ........ 32
vi
FIGURE Page
16b. Velocity profile (cm/sec), observed and
geos trophic (hybrid depth of no motion),
stations 5 and 7 . 33
16c, Velocity profile (cm/sec), observed and
geos trophic (hybrid depth of no motion),
stations 8, 10 and 11 , 34
17, Transport per unit width (m'^/sec), observed
and geostrophic (hybrid depth of no motion),
stations 3, 7 and 10, Dots indicate free-
fall data ..... o 35
18, Thermal wind ratio section 37
19, Baroclinic stability parameter section 39
20, Richardson number section , , . . 40
21, T-S curve, stations 2, 6 and 10 41
22, Mean observed downstream transport (m /sec)
and surface velocity (cm/sec) with standard
errors ......... , 43
23, Mean observed cross-stream transport (m /sec)
with standard errors , 45
vii
LIST OF APPENDICES
APPENDIX Page
A. Tidal aliasing computations 54
Vlll
I. INTRODUCTION
There have been several previous attempts to determine the
validity of the geostrophic approximation in the Florida Current.
This thesis is a further examination of the baroclinic structure
of the Florida Current using free-fall, STD instrument data. For
a period of nine consecutive days in May-June 1969 direct measurements
of the transport versus depth of the Florida Current between Miami
and Bimini were made by Dr. William S . Richardson (NOVA University)
using free-fall instruments. At the majority of the stations occupied,
one probe was equipped with the self-contained STD instrument.
A comparison is made of the average velocity structure determined
by differentiating the mean transport versus depth curves and of the
structure determined by geostrophic calculations based on the mean
density field. To first order, geostrophic equilibrium, i.e. a balance
between the Coriolis and pressure gradient forces, holds for most
large-scale oceanic flows.
The first comparison of the observed and computed velocity fields
in the Florida Current was made by Wust (1924) in which he used the
direct measurements of Pillsbury (1890). Considering that the geostrophic
calculations were based on a density field determined from three
independent sources, the agreement between the measured and computed
velocity fields was surprisingly good. The direct measurements of the
current field by free-fall instruments (Richardson and Schmitz, 1965)
have led to more recent comparisons. Broida (1966) used a quasi-
synoptic density field determined from hydrographic stations, and his
computations showed a biaxial structure in the Florida Current while
the direct m.easurements indicated a single axis. The discrepancy was
attributed to aliasing of the hydrographic data by internal tides.
A time averaged comparison of data taken during the summer months of
1965 and 1966 was made by O'Brien (1967). Using a mean T-S correlation,
the density field was determined from the observed temperature only.
O'Brien's analysis confirmed the validity of the geostrophic approx-
imation in the Florida Current,
The free-fall, STD instrument provides for the first time the
simultaneous measurement of the transport of all three of the density
parameters: salinity, temperature, and pressure. By time averaging
this synoptic data, tidal effects are further reduced. Thus, a rare
opportunity exists to compare accurately the directly measured and
the geos trophica lly computed velocity fields.
With an input of geographical station locations, water depths,
and the values of observed velocity and density versus depth, the
output of the CHARSECT computer program (Mooers , 1970) includes the
following baroclinic parameters:
(1) the thermal wind ratio, which described the degree to which
a flow is geostrophic,
(2) the baroclinic stability parameter, which tests the criti-
cality of the isopycnal slopes, and
(3) the Richardson number, which describes the dynamic stability
of the flow.
II, METHODS
A. DATA ACQUISITION
The free-fall technique yields volume transport per unit width
versus depth and surface velocity data. When the free-fall instrument
is equipped with the STD package, a continuous trace of salinity and
temperature versus depth is also available. The free-fall technique
employs weighted instruments that fall (attaining their terminal velocity
of 2 m/sec within a few meters after release) to a pre-selected depth
where the ballast weights are released, and the instrument returns to
the surface under its own buoyancy (attaining their terminal velocity
again within a few meters of ballast release). The precise recording of
time and position of release and recovery provide the information
necessary for measuring the depth-dependent transport and the surface
velocity. At each station one drop is made to the bottom, and one to
three drops are made to pre-selected depths. Since it is necessary to
determine the horizontal deflection of the free-fall instrument, the
navigational system is the controlling factor. The system used is
Hifix (Decca Navigational System), where the master station is located
on the vessel and the two slave stations on the western side of the
Florida Straits. The range of the system is approximately 250 km with
a precision of +1 meter on the western side of the Straits and +2 meters
on the eastern side, A small, high speed vessel is used in conducting
the measurements.
The data for this thesis were obtained from observations made over
a nine-day period from 27 May 1969 through 4 June 1969 by Dr. W. S.
Richardson (NOVA University). A series of thirteen stations were
occupied on a section from Miami to Bimini (Figure 1). Despite the
short crossing time (7 to 8 hours) for a fransect as compared to a
typical hydrographic transect (20 to 24 hours), the distorting
influence of tidal motions remains an important factor. In an effort
to reduce this tidal aliasing, the station times were varied as
practicable by starting transects at Miami and Bimini on alternate
days. Tables I and II describe the free-fall instrument data that
were used. Those observations that included an STD drop are indicated
in Table II.
B, DATA ANALYSIS
The first step in determining the density field was the digitizing
at ten meter intervals of salinity and temperature values from each
free-fall STD trace. At each station the mean values of salinity and
temperature at these intervals were computed for the nine day period.
These mean values were used as the input to the standard hydrographic
computer program. •*■ The output of this program included sigma-t,
specific volume anomaly, and dynamic depth. The cross stream sections
of mean temperature, salinity, and cr^ (Figures 2, 3 and 4) are plotted
with the observed current axis superimposed.
Mean values of observed transport versus depth, rather than
daily values, were used to compute observed velocity.'^ With the volume
Mean value is defined as the nine day average.
^An observed quantity is either a directly measured quantity (such
as surface velocity) or a quantity (such as sub-surface velocity)
directly computed from the free-fall measurement of volume transport.
30
79°00'
ro LITTLE
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BANK
30
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I 3 5 '7 8 9 10 l2(tA
i ■? 4 & 11 'liJ^BlMINI
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?6°00'
30'
25°00'
82°00
30
8I°00'
60°00'
79°00
_^ 24°00'
30'
Figure 1. Station locations
TABLE I
Station Number
1
2
3
4
5
6
7
8
9
10
11
12
13
Distance from
reference point
(km)
10
15
20
25
30
35
45
55
65
70
75
80
83
Maximum depth
(m)
135
285
345
350
340
665
765
795
830
790
735
580
395
Average number
of drops per
station occupation
1
3
4
4
4
4
4
4
4
4
4
3
3
Total number of
station occupations
8
9
9
8
9
9
9
9
8
8
9
6
5
Total number of
observations with
STD
5
6
6
6
7
7
7
6
5
5
4
3
4
Free-fall Instrument Data: Miami-Bimini
Da tes : 27 May 1969 through 4 June 1969
Reference Point: Lat. 25°44.5'N
Long. 80°08.8'W
S I'Al'lON NtI>n,ER
1
2
3
1
5
6
7
8
9
10
11
12
13
UA XE OF
THANSECr
Time 01 occupation
STD
STD
STD
STD
STD
STD
STD
STD
STD 1
0745
0812
0500
0930
1020
1115
1215
1255
1^40
1530
27 May
Depth oi probes
122
84
103
10^
102
173
173
171
340
170
176
163
175
224
361
360
387
608
332
283
288
325
323
3-s5
269
330
448
645
588
755
795
780
532
Time oi occupation
STD
STD
STD
STD
STD
STD
STD
STu
STD
STD
1428
1355
1320
1240
1120
1045
0940
Oi'05
0810
0750
0655
2S May
Depth oi probes
97
86
135
239
180
177
169
110
176
84
86
154
94
166
349
341
346
338
357
354
320
181
i
270
329
335
4 37
650
423
753
563
785
4 14
818
644
782
512
721
578
395
29 May
Time of occupation
STD
STD
STD
STU
STD
STD
STD
STD
STD
STD
0806
0850
0900
0942
1018
1048
1150
1245
1340
1442
1512
1600
1630
Depth oi probes
120
88
82
88
91
173
176
173
172
165
191
99
94
1
183
167
173
164
393
364
373
329
385
380
315
172
280
337
340
344
328
335
463
657
605
747
539
773
515
563
780
705
570
388
'
Time oi occupation
STD
STD
STD
STD
STD
STD
STD
STD
STD
STD
STD
STD
STD
1348
1324
1248
1218
1148
1112
1018
0918
0830
0748
0712
06 36
0612
i
30 May
Depth Oi probes
118
88
92
95
95
181
177
231
233
177
170
96
98
183
171
225
175
372
351
357
344
354
385
327
177
270
265
330
326
494
598
520
525
523
695
570
320
350
340
636
748
780
806
776
Time Ol occupation
0710
0730
0810
0930
1000
1030
1115
1200
1300
1330
1350
1415
1430
1
31 May
Depth of probes
133
95
99
93
102
91
96
95
93
92
90
90
91
179
235
' 185
134
172
166
160
160
208
167
372
133
277
277
316
310
607
600
613
673
610
474
573
395
I
326
350
336
662
754
782
814
765
733
Time of occupation
1 June
1150
1130
1120
1040
1020
0945
0900
0830
0730
0710
0630
Depth of probes
94
278
97
90
94
98
95
103
95
86
93
160
158
177
170
173
152
176
721
290
331
337
650
763
783
812
777
Time of occupation
STD
STD
STD
STD
STD
STD
STD
STD
1
1730
0800
0850
0920
1000
1045
1140
1345
1520
1730
1805
1
2 June
Depth of probes
125
87
89
84
89
91
89
115
86
87
158
169
176
176
228
165
165
242
172
171
310
275
250
328
278
443
480
483
509
465
679
340
340
340
658
548
750
780
800
737
Time of occupation
STD
STD
STD
STD
STD
STD
STD
STD
STD
STD
1712
1700
1625
1555
1530
1450
1400
1312
1215
0840
0700
0615
0530
3 June
Depth of probes
128
92
89
99
84
93
145
96
93
96
81
240
34
181
182
171
178
243
167
161
187
144
169
288
183
282
255
282
291
428
510
488
236
182
367
580
395
340
330
645
750
788
466
810
470
780
610
'^ June
Time of occupation
STD
STD
STD
STD
STD
STD
STD
STD
STD
0842
0906
0930
1012
1042
1118
1236
1324
1430
epth of probes
123
96
96
92
85
154
166
230
228
170
172
187
175
390
378
401
363
268
265
342
303
342
330
644
755
780
803
STATION NUMBER I 2 3 4 5 6
DISTANCE (km) 10
100
200-
^ 300-
LiJ
I-
UJ
^ 400
I-
Q.
UJ
Q
500-
600
700-
800
OBSERVED CURRENT
AXIS
Figure 2. Mean temperature (C°) section,
STATION NUMBER 12 3 4 5 6 7 8 9 10 II 12 13
DISTANCE (km) lO 20 30 40 50 60 70 80
100
200
^ 300
LlJ
Q.
UJ
Q
400-
500-
600
700-
800-1
OBSERVED CURRENT
AXIS
Figure 3. Mean salinity (%q) section
10
STATION NUMBER 12 3 4 5 6 7 8 9 10 II 12 13
DISTANCE (km) 10 20 30 40 50 60 70 80
100
200
^ 300
UJ
I-
UJ
400-
UJ
Q
500
600
700-
800-1
-OBSERVED CURRENT
AXIS
Figure 4. Mean sigma-t section.
11
transport available at several depths, a transport versus depth curve
was drawn for each occupation of each station. Values were read from
each curve at 50 meter intervals; these values were then averaged to
obtain the mean volume transport curves . By differentiation of these
curves, the mean velocity versus depth profiles were obtained.
Using the method of least squares, second, third and fourth order
polynomials were fitted to these transport curves. Two constraints
were placed on the polynomials :
1. The transport was forced to equal zero at zero depth (sea
surface .
2. At zero depth, the derivative of the polynomials was forced
to equal the observed mean surface velocity.
An examination of the various orders of polynomials showed that the
third order generally had the best fit and resulted in the most realistic
profile. The third order polynomial was also used as the best fit in a
similar treatment of free-fall data (Richardson, Schmitz and Niiler,
1969), Comparing the velocity versus depth profiles at stations 5 and
7 for second, third and fourth order polynomials (Figure 5), it appears
that the third order polynomial yields the most realistic profile.
The methods described above for determining a mean transport curve,
and, subsequently, the velocity versus depth profiles, were not the
only ones attempted. After several tries, it was found that 50 meters
was the minimum increment that could be used for fitting a polynomial
to a mean transport curve.
Another method tried was a least squares polynomial fit (with the
same two constraints) to the raw transport data, i.e. the actual values
12
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III. RESULTS
A. COMPARISON OF DIRECT MEASUREMENTS
WITH GEOSTROPHIC MEASUREMENTS
Other than on the anticyclonic side, where the Delanc method is
in doubt, there is a good agreement between the directly and indirectly
determined depths on no motion (Figure 6)„ From this figure, a "best"
depth of no motion, called a hybrid depth of no motion, is chosen and
used for the final comparisons of observed and computed fields. On
the cyclonic side, the hybrid depth of no motion is the level determined
by the Defant method. On the anticyclonic side, it is the bottom.
Since the hybrid depth of no motion nearly coincided with the depth
where the observed velocity equals zero, the latter could have been
used as the best depth of no motion. The hybrid depth was chosen for
the following reasons:
(1) it does closely approximate the depth of no motion determined
by the observed velocity field, and
(2) its use sets a precedence for determining a depth of no
motion in the Florida Straits when no observed velocity data
are available.
The computed surface velocity distribution using both the Defant
and hybrid reference depths is compared to the observed surface velocity
distribution in Figure 14. On the anticyclonic side the agreement
between computed and observed surface velocities is poorer than on the
cyclonic side. East of station 9, the surface velocities computed with
29
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the hybrid depth shows less agreement with the observed surface
velocities than those computed using the seemingly less reliable
depth found by Defant's method.
Using the hybrid depth of no motion, a comparison of the computed
and observed velocity sections is made (Figure 15). As with the
surface velocities, the best agreement is on the cyclonic side of the
stream. Compared to the geostrophic velocity, the observed isotachs
are deeper, except near the surface, and the observed current axis is
skewed to the east. The agreement between the position of the observed
current axis and the position of the geostrophic current axis improves
as depth increases.
The geostrophic, using the hybrid depth of no motion, and observed
velocity profiles are compared in Figure 16 for each station where
both computed and observed values were available. The geostrophic
subsurface maximum at station 11 is similar to the observed subsurface
maximum by Diiing and Johnson (1971). The closest fit of the absolute
values of the curves occurs on the cyclonic side. However, comparison
of the vertical shear shows the best agreement on the anticyc Ionic side.
Because of the uncertainties in determining the observed velocity
fields by differentiation of the mean transport curves, an informative,
if not more accurate, test of the validity of the geostrophic approx-
imation is the comparison of transport curves. Figure 17 shows
transport per unit width curves, observed and computed. A representative
station from the cyclonic side, the middle and the anticyclonic side is
used for the comparison. The previously established pattern of close
agreement of absolute values on the cyclonic side and poorer agreement
31
STATION . NUMBER 12 3 4 5 6 7
DISTANCE (Km) 10 20 30 40
100
10 11 12 13
200
(O
300
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u
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400
I
1-
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o
500
600
700
800-'
■--_^-- OBSERVED
n GEOSTROPHIC
Figure 15. Mean axial velocity (cm/sec), observed and geostrophic
(hybrid depth of no motion) .
32
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THE UNIVERSITY OF MIAMI
The Baroclinic Structure of the Florida Current
BY
William 0. Stubbs, Jr.
A THESIS
Submitted to the Faculty
of the University of Miami
in partial fulfillment of the requirements for
the degree of Master of Science
Coral Gables, Florida
June 1971
33
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36 :
on the anticyclonic side is clearly illustrated.
The thermal wind relation derived from the assumption of geo-
s trophic and hydros ta.tic equilibrium is
t~^ = -£211
Po
where
V"2 is the derivative with respect to depth of the mean axial
velocity,
Px is the derivative with respect to horizontal distance of the
mean density,
pQ is the reference density,
and, g is the gravitational acceleration.
Using the observed velocity and density data, the ratio of left
hand side to the right hand side describes whether or not the thermal
wind relation is satisfied. If the ratio is unity, the thermal wind
relation is satisfied. If the ratio is greater (less) than one, the
observed shear is greater (less) than the geostrophic shear.
From Figure 18, the areas of observed southward flow and the area
east of station 9 are where this ratio differs the greatest from unity.
B. FEATURES OF THE FLORIDA CURRENT
To extract additional information about the baroclinic structure
of the Florida Current, the free-fall data were analyzed by studying
the following:
(1) Baroclinic stability parameter
(2) Richardson number
(3) Mean T-S curves
37
STATION NUMBER 123456 7 8 9 10
DISTANCE (km) 10 20 30 40 50 60 70
100
II 12 13
80
200-
^ 300
UJ
I-
UJ
400-
Q.
UJ
Q
5C0
600
700-
800 J
Figure 18. Thermal wind ratio section.
i
38
(4) Net transport between selected isopycna Is
(5) Total downstream transport
(6) Cross-stream f low
The results of these studies are discussed below.
(1) The baroclinic stability parameter is the ratio of the
slopes of an isopycnal, S, to its critical value, Sc (Mooers , 1971),
When S > Sc , baroclinic instability, or hydrodynamic disequilibrium,
can occur. The baroclinic stability is relatively low in the pycnocline
on the cyclonic side (Figure 19),
(2) The gradient Richardson number is expressed as
Ri = _
(^z)^
where
9 0
N = t-^g is the Vaisa la "Brunt frequency.
Po
Ril implies
stability. From Figure 20, the area where the dynamic stability is
the lowest is near the bottom on the cyclonic side. The dynamic
stability is the greatest near the surface on the anticyclonic side.
(3) The mean T-S diagrams for stations 2, 6 and 10 (Figure 21) are
in agreement with the T-S diagrams presented by Wennekens (1959) for
the Florida Current, The cross channel distribution of water mass
properties described by Wennekens is illustrated in the T-S curves.
Station 2 is representative of the Continental Edge Water, station 6
is representative of the Transition Zone Water, and station 10 is
representative of the Yucatan Water. The Yucatan, or Caribbean, Water
is identified by its well defined salinity maximum. The great reduction
in the intensity of this salinity maximum is the conspicuous feature of
39
STATION NUMBER 12 3 4 5 6 7 8 9 10 II 12 !3
DISTANCE (km) 10 20 30 40 50 60 70 80
Figure 19. Baroclinic stability parameter section.
40
STATION NUMBER 12 3 4 5 6 7 8 9 10 II 12 13
DISTANCE (km) 10 20 30 40 50 60 70 80
100
200
^ 300
UJ
UJ
400
h-
Q.
UJ
Q
500-
60C-
700-
8C0-I
Figure 20. Richardson number section (isolines have non-uniform
spacing) .
41
35.00
SALINITY (%o)
36.00,
3700
Figure 21. T-S curve, stations 2, 6 and 10.
42
the Edge Water.
The water that flows through the Florida Straits originally comes,
in large part, from the southern half of the North Equatorial Current
and from a branch of the South Equatorial Current. This water flows
through the Caribbean, and then, without mixing with the waters
endemic to the Gulf of Mexico, passes through the Florida Straits in
very nearly its original state. Because this water has acquired a
large admixture of Antarctic Intermediate Water at mid-depths from
the South Atlantic, there is a salinity minimum (between 600 and 800 m
depth) in the water exiting out of the Florida Straits (Stommel, 1966).
This salinity minimum is present in stations 6 and 10.
(4) The net axial transport across the Straits and between
isopycnals was determined in the vicinity of the southward flow. A
net transport southward would favor the existence of a southward
undercurrent rather than a large scale eddy. In all combinations of
isopycnals, the net transport was always greater to the north. This
result admits the possibility of a large scale eddy being the cause
of the southward flow. An example of the results are shown below.
Isopycnal Interval Inclusive Stations Net Transport
27.2 - 27.3 2 ^- 9 7.5 x 10^ m^/sec North
27.4 - 27.5 6-9 3 x 10^ m-^/sec North
(5) The net downstream transport value at each station was
integrated across the channel (Figure 22). The total mean volume
transport of 33.4 x 10° m /sec compares favorably with the value
obtained by Richardson and Schmitz (1968) of 32.2 x 10" m-^/sec for data
averaged over the period of May-June 1965.
J
43
MEAN SURFACE VELOCITY (cm /sec)
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The volume transport for each of the nine days was computed
separately and is shown in the table below. The average of these
ft o
nine values is 33.4 x 10 m /sec.
Date Volume transport
(x 10^ m^/sec)
27 May 30.3
28 May 33.3
29 May 34.7
30 May 33.2
31 May 36.8
1 June 31.2
2 June 36.5
3 June 31.3
4 June 32,9
Continuous electrode potential measurements of transport based on
two electrodes located at stations 2 and 3 showed good agreement with
the free-fall measurements during the nine day period. The directly
measured and electrode measured transport differed by less than 10%,
but tidal aliasing of the free-fall measurements precludes any firm
conclusion (DeFerrari, 1970).
(6) The cross-stream data is not of sufficient quality for a
detailed analysis of the mean cross-stream velocity structure. A
general pattern can be ascertained by the differentiation of the mean
transport curves. On the cyclonic side, the velocity is westward except
for a mid-depth layer (50-70 meters thick) of eastward flow. On the
anticyclonic side, the velocity is eastward in the upper 400-500 meters
and westward below this depth.
45
The mean cross-stream transport is shown in Figure 23, where
positive values indicate eastward transport and negative values,
westward transport. There is westward transport in the westward side
of the Straits, eastward flow in the eastern side of the Straits, and,
hence, an area of divergence near the center. The mean patterns are
statistically significant at the 95% level.
46
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47
IV. SUMMARY AND CONCLUSIONS
A. SUMMARY
Nine consecutive days of free-fall, STD data, taken by Richardson
during late May and early June of 1969, were analyzed in a study of the
baroclinic structure of the Florida Current. The directly measured
transport was used to obtain the mean velocity field, and the directly
measured temperature and salinity profiles were used to obtain the mean
density field. Mean (i^e. averaged over the nine day period) vice
daily values were used to reduce the tidal aliasing problem.
The mean axial velocity was southward beneath the Florida Current
during the nine day period. This indication of southward flow was
consistent with Hurley (1963), Neumann (1970), Diiing and Johnson (1971).
and Duing (1971). Richardson, Schmitz and Niiler (1969) did not find
this southward flow as permanent feature when more extensive data were
analyzed .
For the geos trophic calculations, three methods were used to
determine the depth of no motion: the depth where the observed
velocity equals zero, equating the geostrophic and observed velocities
at the surface, and Defant's method. On the cyclonic side, there was
good agreement between the depths of no motion determined by the three
methods, and on the anticyclonic side the agreement was not so good.
Likewise, on the cyclonic side Defant's method showed a definite depth
of no motion, but on the anticyclonic side the results were less
48
conclusive.
Using the hybrid depth of no motion, the geos trophic velocity
field was computed. The comparison of the observed and computed
velocity fields showed good agreement on the cyclonic side and much
less agreement on the anticyc Ionic side. The same pattern of agreement
between absolute values existed in the comparison of surface velocities
and of velocity and transport profiles at several stations. The thermal
wind equation was shown to be a good approximation, i.e. the flow was
essentially geostrophic throughout the Straits. The greatest dis-
crepancies occurred in the area of the southward flow and in the
easternmost part of the anticyclonic zone of the Straits. The dis-
crepancy may be related to the limitations of the observational and
data analysis techniques.
Also, the study of the standard deviation of temperature, salinity
and a^ showed a zone of high variability on the cyclonic side.
The study of stability parameters showed an area of low dynamic
and baroclinic stability on the cyclonic side,
B. CONCLUSIONS
(1) The validity of the free-fall, STD measurements was established
by comparison with previous total transport values,
(2) The Defant method was a valid method for determination of a
depth of no motion on the cyclonic side. The bottom was a reasonable
depth of no motion on the anticyclonic side. Thus, absolute geostrophic
velocities can be computed independent of a direct method for depth
of no motion determination.
(3) The Florida Current was essentially in geostrophic balance.
49
(4) A southerly flow beneath the Florida Current was confirmed
during the nine day period. The T-S curve of the mid-channel southward
flow has shown the salinity minimum that is characteristic of the
Antarctic Intermediate Water, If a steady countercurrent existed,
different T-S curves would be likely. In the vicinity of this
countercurrent, the net transport between isopycnals was substantially
to the north. The lack of net southward transport, and of a distinction
in the T-S correlations, precluded resolving whether a large eddy or
a steady countercurrent exists on the basis of the present data,
Richardson, Schmitz and Niiler (1968) showed that, over a longer time
span, the north component of velocity fills the whole channel, which
implies a transient nature for the southerly flow. The velocity
profile analysis by Duing and Johnson (1971) and Duing (1971) gave
definite indications of a transient southerly flow with reversals on
a time scale as short as a day.
Based on the present data and the previous works cited, the
southward flow appeared to be of a transient nature and southerly
origin.
(5) The free-fall, STD method provided the synoptic measurement
of the velocity and density fields necessary for a study of the
baroclinic structure of the Florida Current, Due to the tidal aliasing
problem, time averaged mean values must be used.
There are numerous other techniques that could have been used to
process and analyze the free-fall, STD data. Some examples are: use
of some other order of polynomial besides cubic; use of the spline
technique for curve fitting rather than least squares technique;
50
fitting a polynomial to the raw (i.e. the actual values of transport
measured) data to obtain a mean transport curve; and direct differen-
tiation of the mean, or individual, transport curves rather than of
the polynomial representative of the curves. Additionally, the same
curve fitting technique used with the observed transport curve could
be applied to the geos trophic transport curve. This would make the
comparisons between the computed and observed quantities more uniform.
Because of the uncertainties in determining the "best" technique,
more emphasis in the future should be given to statistical and error
analyses. Despite the lack of these analyses, the results of this
thesis gave a realistic nine day mean description of the baroclinic
structure of the Florida Current.
51
LITERATURE CITED
52
BROIDA , S,, 1969. Geos trophy and direct measurements in the Straits
of Florida. J, Mar. Res., 27 (3) : 278-292.
DEFANT, A,, 1941. Die absolute Topographie des physika lischen
Meeresniveaus und der Druck flachen, sowie die Wasserbewegungen
im Atlantischen Ozean. Meteor-Werk, 6 (2) ; 191-260.
DEFERRARI, H.A„, 1970. Dynamically induced fluctuations in acoustic
transmissions. Rosenstiel School of Marine and Atmospheric
Science, University of Miami, Technical Report No. ML 70116,
88 pp.
DUING, W. , 1971. Unpublished data from Project SYNOPS ('Synoptic
observation of current profiles in the Straits). June 1971.
(personal communication).
DiilNG, W., AND D, JOHNSON, 1971. Southward flow under the Florida
Currents Science (in press).
FORMIN, L.M. , 1964. The Dynamic Method in Oceanography. Elsevier
Pub. Co., New York., 212 pp.
HURLEY, R.J. , AND L.K. FINK, 1963. Ripple marks show that counter-
current exist in Florida Straits. Science, 139 (3555) : 603-605,
MOOERS, C.N.K, , 1970. CHARSECT computer program. (personal
communica tion) .
1971. Several effects of baroclinic currents on the
cross -stream propagation of inertia 1-internal waves. Submitted
to Geophys . Fluid Djmamics ,
NEUMANN, A„C., AND M.M. BALL, 1970., Submersible observations in the
Straits of Florida: geology and bottom currents. Geol. Sec.
Amer., 81 : 2861-2874.
NEUMANN, G., AND W.J. PIERSON, JR., 1966. Principles of Physical
Oceanography. Prentice-Hall, Inc., London, 545 pp.
O'BRIEN, F.J., III, 1967. On the validity of the geos trophic approx-
imation for the Florida Current. Masters Thesis, University of
Miami, 46 pp.
PILLSBURY, J.E., 1890. The Gulfstream - A description of the methods
employed in the investigation and the results of the research.
U.S. Coast and Geodetic Survey Publ. Report 1890, Appendix No. 10,
pp. 44-620.
RICHARDSON, W.S. , AND W.J. SCHMITZ, JR., 1965. A technique for the
direct measurement of transport with application to the Straits
of Florida. J. Mar. Res., 23 : 172-185.
53
RICHARDSON, W.S., ANDW.J. SCHMITZ, JR, , 1968. On the transport of
the Florida Current. Deep-Sea Res., 15 (6) : 679-693.
RICHARDSON, W.S,, W.J. SCHMITZ, JR., AND P.P. NIILER, 1969. The velocity
structure of the Florida Current from the Straits of Florida to
Cape Fear. Deep-Sea Res., Suppl. 16 : 225-231.
SANDSTROM, J.W., AND B. HELLAND-HANSEN, 1903. IJber die Berechnung von
Meerestromungen. Rapt, on Norwegian Fishery and Marine Inves-
tigations, 2 (4) : 1-43.
SCHUREMAN, P., 1938. Manual of Harmonic Analysis and Prediction of
Tides. U.S^ Government Printing Office, Washingtoi., D.C., 317 pp.
SMITH, J.A., B.D. ZETLER AND S. BROIDA, 1969. Tidal modulation of the
Florida Current surface flow. Mar. Tech. See. J., 3 (3) : 41-46.
STOMMEL, H. , 1958. The Gulf Stream, a physical and dynamical
descriptio'". University of California Press, Berkeley, 202 pp.
WENNEKENS, M.P. , 1969, Water iriass properties of the Straits of
Florida and related waters. Bull. Mar. Sci. Gulf Caribbean,
9 (1) : 1-52.
WUST, G., 1924. Florida - und Antil lenstrom. Veroff. Inst. f.
Meereskunde. Univ. Berlin Reihe A , 12 : 1-70.
]
54
APPENDIX A
Tidal Aliasing Computations
55
The average crossing time for a transect was about 8 hours.
Because of the distorting influence of the periodic tidal forces, it
was necessary to work with mean values averaged over the nine days
rather than daily values. As shown in Table II, the station times
were varied as practicable by starting a transect at Miami and Bimini
on alternate days in an effort to reduce the tidal aliasing.
Because of the short record length, a tidal analysis was not
possible. The following method was used to determine the tidal aliasing
effect.
For the diurnal tide, consider
1 N r
cv = - e [sin(26tj)] sin (atj+G) ,
N j=i
and for the semidiurnal tide
3 = i e [cos^(6t)] sin 2(atj+0),
Nj=i
where