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 i ''U. LIBRARY NAVAL P( MONTEB^:^^ CALIF. yj^^U^.- | NAVAL POSTGEJSJUAT/, b ^^ ' ; t(1390B0 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 % BAHAMA BANK 30 -^ 27°00' I 'f • I I / !/^' I 3 5 '7 8 9 10 l2(tA i ■? 4 & 11 'liJ^BlMINI .^ >k. iiiCAT GRAND ! y. CAYS 1 \V,-. ; 8»\ o lo

" / \ ?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 CJ o o _i UJ > ■ r- ^-;. '- >- V _l o s d a. a. a. a: (£ a: iij UJ bJ a a o a: q: oc o o o -a c to m 0] C o •H 4J CO o •i-l IW O U a. >^ ■u •i-i o o r-l 0) > •a > QJ XS u CO c TO i-i CO S-i (SW3i3W) Hid3a 28 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 [O J CVJO. — 00 2g cn - o 00 o lO h- - o, i£> ^^ ro O. CVJ OJ _o. N COASTLINE "■•:/•■•'•.. / / V / ./ / y *•''''' 1 * ,^ '^' / ^ a / / ; ^ '/ E e ' , «*- -'/ 1 r ■o o ">— * \- (r 7i CO < >- U. o X UJ UJ 1 o 1- o (^ < Q X X _l llI Q- a. o > o o Q. ir I- co < CO o o 1— GO UJ UJ X O O O UJ I I BNiniSVOO — r- o o — r- O lO o o o in — r- O o in I (09S/UJ0) AIIOOIBA 30VddnS NV3IAI c o •l-l ■u o o c (U ■rl 4= O •i-l o u 4J 1/1 o (U W) -o c ro > u (U (0 o >^ •U •H O O 1—1 <]} > 0) o CO >-l :3 W C ro (U 30 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 iX. Hi 1- u z ^^ 400 I 1- 0. UJ o 500 600 700 800-' ■--_^-- OBSERVED n GEOSTROPHIC Figure 15. Mean axial velocity (cm/sec), observed and geostrophic (hybrid depth of no motion) . 32 G O t\ ■U O s o a o :S (U TJ •H i-l u 0) CO o •n( 4-1 O H a >. 4-> • •H CO • *v CO CNJ ^ I— 1 CO C (U O J-l •H 13 4J 00 CO •M 4-) ClH cn o o ro (sa3i3iM) Hid3a 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 E (J >- H O O _l UJ > (Sd313W) HidBQ C o ••-I ■p o S o o 4J 0) T3 T) •rl ;-« u •H -a o u 4J CO o bO -O cd > 0) CO o i-H •H o M u •M O O • .-I r^ cu c CO Q) o tM en 34 - z o . ■ c o •■-I ■p o u-i o ■u a. o E UJ l- « o m (Ij o 1 1 1 u> o •r-l a o !-l ■P CO O (U bO c > u 0) CO o o o O o o o o o o o C\J ro * in «3 8 8 •H M-l O S-i a 4J <-) CJ T3 o c .-I ca > o O C» cu o U -H 00 ca (Sd3i3lAJ) Hld3a 35 o G <4-l o 4= 4J P- . ^ v-x u •H 43 P. O u ■u CO o (U M • o;) -o ■u C CO CO T3 T) 1—1 TO !-i U-( (U 1 W 0) ^ (U O >-l M-l A /^v 0 y 4J (U ra 03 o ^^-^ •H CM X) s c s—^ •I-I J2 n ■u U -a o •H o ? 4J , •i-I o c r-< o 'O u c (U TO p- r^ JU u •. o CO a n C/} c C CO o u •1-1 H •u TO 4-1 M O •H o (SU3i3|i«) HldaO 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) o o CvJ o o o o in cr-p 2 < O h- Q oc "^1:^- UJ O ro h- rr < III ^ - _l o n Q. nr to"- < < CJ q: o 3NniSV0D o o T ■ - o 1 o o 1 O I o o o o o o O o N- ID IT) ^ ro CVJ — u c CO ■U) CO O CO >^ 4J •rl U O .-I (U > u u 3 CO •a C CO ;oas/,uj) idOdSNVdi u o CO CO U ■U B ctf <0 u 4J CO O XI (U > (U CO o ^ CM cv| P 00 •rl 44 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 x\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\ o q CD OO - UJ - -■> ^■ r<- cvT ^J _ o d "^ COASTLINE aNHiSVOO 3 O O Z (O Q \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\v ^ — 1 — o O — 1 — O o ft o ( ssVg/J) id0dNV8i WV3a^S SSCd 0 03 !-l O M 5-1 (U Xi >-i CO T3 CO ■u CO 4-1 •r-l u u o o- C to ■p E CO 0) w I Uj w O o > 54 0) m O C CO 0) s CM (U i-i W) •r-l 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