w N PS ARCHIVE 1968 SMITH, J. "*»*. THE UNIVERSITY OF MIAMI TIDAL FLUCTUATIONS OF THE FLORIDA CURRENT BY John Alan Smith A THESIS Submitted to the Faculty of the University of Miami in partial fulfillment of the requirements for the degree of Master of Science > wt,u- Coral Gables, Florida July 1968 Thesis S593 MONTEREY, CALIF. ^- ^ DUOLEY KNOX LIBRARY NAVAL POSTGRADUATE SCHOOL MONTRREY CA 93943-5101 THE UNIVERSITY OF MIAMI TIDAL FLUCTUATIONS OF THE FLORIDA CURRENT BY John Alan Smith 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 July 1968 '-'Hi, J~ THE UNIVERSITY OF MIAMI A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science Subject Tidal Fluctuations of the Florida Current John Alan Smith Approved : Saul Broida Assistant Professor of Marine Science Chairman of Thesis Committee John A. Harrison, Dean of the Graduate School Donald R. Moore Assistant Professor of Marine Science Russell L. Snyder Assistant Professor of Marine Science Claes Rooth Professor of Marine Science Bernard D. Zetler Director, E.S.S.A. Physical Oceanography Laboratory of Miami Co-Chairman of Thesis Committee SMITH, JOHN ALAN (M.S. Physical Oceanography) Tidal Fluctuations of the Florida Current. (July, 1968). Abstract of a Master's Thesis at the University of Miami. Thesis supervised by Professor Saul Broida. This thesis is an examination of the short period fluctuations of tidal nature of the Florida Current surface flow from an analysis of direct surface current measurements made over a period of about a month in the Florida Straits during the latter portion of 1965,, The principal conclusion reached is that the surface current is modulated by a diurnal standing wave, coupling the tides of the Atlantic Ocean with those of the Gulf of Mexico, which produces a pronounced diurnal effect on the surface current fluctuation. ACKNOWLEDGMENTS This work started as a result of the interest of myself as a career Naval Officer in the procedure employed for predicting tides, and terminated with an analysis of the fluctuations of tidal influence in the Florida Current. The end is really only the beginning, I sincerely hope that others will follow, as many have preceded, in continued research of all of the fluctuations of this important current. The author is indebted to a multitude of persons for their assistance and patience during the preparation of this thesis. I am grateful to the members of my thesis committee, Drs . S. Broida, C. Rooth, R. Snyder, and D. Moore; in particular I wish to express my appreciation to Bernard Zetler, director of the E.S.S.A. Physical Oceanography Laboratory at Miami who served as my thesis committee co-chairman, without whose patient guidance and tireless enthusiasm I could not have completed this work. I also wish to acknowledge the excellent cooperation and assistance provided by R, A. Cummings, C. B. Taylor and other Coast and Geodetic Survey personnel in Rockville, Maryland for providing tidal predictions and analysis; to General Dynamics and Dr. W. S. Richardson of Nova University for making available the Florida Current data; and, to my friend and classmate, Joseph Paletta, USN, for continued encouragement throughout this period. iii The financial support for this study was provided by the Office of Naval Research. John Alan Smith Lt., U.S. Navy Coral Gables, Florida July, 1968. IV TABLE OF CONTENTS Page LIST OF TABLES . . vi LIST OF FIGURES vii CHAPTERS I. INTRODUCTION . L II. HISTORY 3 III. EXPERIMENTAL PROCEDURE. ........... 6 A. Harmonic Analysis of Tidal Currents. . . 6 B. Total Current Fluctuation Field. .... 15 IV. RESULTS 17 A. Discussion 17 B. Comparison of Results 27 V. SUMMARY AND CONCLUSIONS 29 LITERATURE CITED , 31 APPENDIX A 34 APPENDIX B 36 LIST OF TABLES TABLE Page 1. Principal Tidal Constituents 10 2. Comparison of Least-Squares Harmonic Analysis of the First Half of the Data Series with that of the Entire Series 20 3. Comparison of Results of Harmonic Analysis on the First Day Data Period Using Different Analysis Methods . 22 4. Harmonic Constants from Florida Current Data 23 5. Astronomical Data for the Period 21 November through 17 December 1965 24 6. Statistical Results and Energy Calculations for the 15 Day Period 26 VI LIST OF FIGURES FIGURE Page 1. General Dynamics Monster Buoy Location. ... 7 2. Current Velocity versus Time for the Period 21 November through 17 December 1965 in the Florida Current ... 8 3. Current Velocity versus Time for the Period 21 November through 5 December 1965 with Super- imposed Plot of the Predicted Tidal Modulation 18 4. Plot of the Residual After Tidal Modulation is Removed 19 vn 1. INTRODUCTION The pulsation of marine currents has long been a topic of major interest in the field of physical oceanography. Much of the dynamics of oceanic circulation can only be understood in terms of the velocity field and the forces acting upon it. In general, the study of current fluctuations is best considered on the basis of information concerning current velocities. Unfortunately, reliable information of this type has not been available in the past because of the inherent difficulties and expense involved in the gathering of such data. Numerous analyses of oceanic current fluctuations have of necessity been made on data over short duration periods, non-synoptic surveys, or resorted to the indirect measurement from dynamic computations. Conclusions based upon such information have often been highly speculative in regard to current fluctuations, although in many cases commendably accurate. Improved technology in the field of ocean measurement instrumenta- tion has made possible the collection of data over sufficient time in- tervals to provide meaningful results. The development of moored buoy systems in conjunction with dependable current recorders has provided a powerful tool which now permits us to commence directly examining the variation of ocean currents over long periods of time. The purpose of this paper is to examine the nature of current velocity fluctuations in the Florida Current using current speed measurements collected over a period of about a month at hourly intervals in the Straits of Florida from a moored buoy. Short period variations of tidal period will be investigated as a step towards the ultimate goal of long period fluc- tuation studies from which perhaps someday accurate predictions and forecasting of the Gulf Stream System and its associated effect on climate may be gained. It is evident that our knowledge of long- period variations will remain unsatisfactory until the short-period oscillations have been sufficiently described and explained. II. HISTORY The pulsations of tidal origin of the Florida Current have long been a subject of interest and speculation. As early as the mid 1800's, Pillsbury on BLAKE undertook the admirable task of occupying six an- chor stations between Fowey Rocks, Florida and Gun Cay, Bahama Islands, devoting over 1100 hours in observing the Florida Current at this section in the course of two summers (Pillsbury, 1891). The longest continuous anchorage was for a period of 166 hours . He found monthly variations related to the declination of the moon and daily oscillations of tidal origin in the Florida Current, the latter amounting in some instances to a variation as large as 128 cm/sec. He reported two periods of increase and two periods of decrease in the Florida Current speed during the period of a lunar day. In April 1937, Parr anchored ATLANTIS for a series of five hydro- graphic stations which were successively occupied for twenty-four hour periods in the Straits of Florida between Fowey Rocks and Gun Cay (Parr, 1937). He reported from analyzing hourly surface current speeds that there was up to a 50 cm/sec fluctuation of the speed of the Florida Current that was apparently caused by tidal forces. He found both diurnal and semidiurnal variations with the latter predominant. From May 1950 to May 1951 the U.S. Navy Hydrographic Office recorded hourly Loran fixes from oil tankers traveling between Cape Hatteras and the Key West vicinity. From an analysis of over 5000 observations, it was concluded that there was an apparent tidal perio- dicity in the surface current flow (O'Hare et_ a_l, 1953). An attempt was made to screen the tanker survey data for a semidiurnal tidal periodicity, but the results obtained were inconclusive, In 1951 Murray attempted to analyze velocity fluctuations in the Florida Current by making numerous crossings between Miami and Gun Cay utilizing the Geomagnetic Electrokinetograph (GEK) (Murray, 1952). He was unable to detect any apparent periodicity in the fluctuations of the Florida Current, but pointed out the inherent difficulties involved with attempting to observe periodicities from scattered GEK observations From December 1952 to November 1953, GEK fix stations were oc- cupied between the Miami Sea Buoy and Gun Cay. An attempt was made to study tidal fluctuations in the Florida Current by plotting 187 GEK measurements against time (Hela and Wagner, 1953), The data seemed to indicate the existence of a tidal fluctuation, although the fluc- tuations were strongly masked by non- tidal effects. From studies of electric potential measurements between Key West, Florida and Havana, Cuba, Wertheim was able to show evidence of the diurnal tidal influence in the transport through the Florida Straits (V'ertheim, 1954). He found that the ratio of the amplitudes of the harmonic coefficients for the tidal components M2, S2, K^ and 0^ were in between those of the semidiurnal Atlantic tide at Miami and the diurnal Gulf of Mexico tide at Galveston, confirming the dependence of the transport on both tidal systems. Webster analyzed a large amount of GEK data for both the Straits of Florida and off Onslow Bay, North Carolina. He concluded that although it was probably rash to ascribe the velocity fluctuation of the Florida Current predominantly to tidal causes, the periods of the fluctuations observed were in the order of one day (Webster, 1961). Recently Schmitz and Richardson utilized a least square harmonic analysis on transport data acquired over a period of three years using the free instrument technique across a section of the Florida Current (Schmitz and Richardson, 1967). Based on the limited data available, they indicate that it is possible that fluctuations of tidal period are the major modulation of the Florida Current transport. Their estimates of tidal coefficients for transport amplitudes are 3.5 + 1 (106M,3 Sec"1) for M2, Oi and KL, and 1.5 (106M.3 sec"1) for S2. III. EXPERIMENTAL PROCEDURE GENERAL During the latter portion of 1965 a General Dynamics ocean buoy was moored for testing and evaluation in the Straits of Florida at a location as shown in Figure L. From the period November 20 to December 18, 1965, the buoy was equipped with a rotary current meter placed im- mediately beneath the water surface, installed by Dr. William Richardson. Current speed data for one minute averages taken ap- proximately each hour were telemetered to the mainland and recorded. Also available for this period are wind speed, wind direction, baro- metric pressure and the significant wave height at the time of re- cording. Current direction is considered as essentially steady in the North-South orientation of the Florida Current at this location. A plot of current velocity versus time is illustrated by Figure 2. Cursory examination of Figure 2 reveals fluctuations of current speed in the order of 30 cm/sec with apparent periodicity. Since the periodicity appears to be largely on the order of 24 hours and can be initially presumed to be due to tidal effects, it was decided to con- duct a harmonic analysis on the data to determine if the fluctuations were indeed due largely to the tidal effects. A. HARMONIC ANALYSIS OF TIDAL CURRENTS Harmonic analysis is a method for describing periodic phenomena in which values of the dependent variable repeat themselves at equal intervals of time. The first practical application of harmonic analysis Figure 1. General Dynamics Monster Buoy Location 10' 7'.)' - -- - — -^ CO' . .11 .*£ )^s- diiilmniirr m\.\l ° I F I 4 m: 44 ii &M I 'W ' I . MONSTER BUOY LONG-79" "'SI. 2'W 310 |0»* ,, »' /'3 "1 M > \ ' '' •PI' nr , •> 'p£ * *:rv. -J '7.\ ',t?v>M - »\» » M 1 U. /• " -'A V> ' v 1 \ ,*5 /.»■ • ^ ,. \" W • ':* h*oL2 ,i'», \ : \ Inii (SVr'BofGn Fl fi(— )30.« J1KUJM •. \ •". 50" »•) ! 150 ' ,7 --v-^-' ! "I 4, 4 / / ."r tiouih Hi •h"" - 1 ,(VIJ-f" i " I I I lac tm I4M II 0(C riliHiM'.vi'.ic, i as ,i > 431 . li \- '. ,. ' «•<■»">•■ -'A " I jfc4*jj^*;* \i c«tc»t 4 49 X "X.virT^TTc-r*/'^ oat U{J] i « ! ! " it u «« srV— -30' X V \\ ' ," ' 2i » a VC.'&G.S.ll] ..'_ -ii: r^-— -^— -; ' " ''''''-'• ' ' '—- ----- 40' (CONTINUCO :\Q' CH CHAftr I. ^ i 20 10 rnrmn'l i ;o' • Figure 2. Current Velocity versus Time for the Period 21 November through 17 December 1965 in the Florida Current. 121 NOV I 22 I 23 I 24 I 25 I 26 I 27 I 2 8 I 29 I 30 HORIZONTAL SCALE: I— I =12 HRS VERTICAL SCALE H = 5.1444 cm/sec 12 I 13 I 15 I 16 Figure 2. Current Velocity versus Time 9 is attributed to Lord Kelvin who in 1867 devised a method of reducing tidal height observations to harmonic constituents (Darwin, 1898). The harmonic analysis of tidal currents or of currents having tidal components is a process by which the tidal components having relations to astronomical conditions are separated into elementary harmonic components or constituents . Each constituent represents a cyclical change during a particular period calculated from astronomi- cal data, The constituents are in reality a substitution of hypotheti- cal tide-producing satellites (having either fixed circular or ellip- tical orbits around the earth parallel to the equator) for the actual tide-producers, the moon and the sun. Theoretically, there are a large number of tidal constituents needed to accurately resolve the complicated motions of the moon and the sun into simple components. Generally, however, in any given location most of these are of small amplitude, and all but a few may be disregarded for practical purposes. The major constituents used to determine the principal features of tidal currents are listed in Table 1 along with their respective periods. Although the amplitudes and phases of the tidal constituents are modified by local causes, the period of the constituents is defined by the configuration and periodic relative motions of the earth-sun-moon system, and is invariable. In order to determine the tidal constituents listed in Table 1, observa- tions over a complete period of about fifteen days are required to separate the individual diurnal and semidiurnal constituents with a fair degree of accuracy. It has been proposed that extremely accurate measurements coupled with an extremely low noise level would permit the analysis of shorter periods (Munk and Hasselman, 1965), but such data 10 Table 1. Principal Tidal Constituents w ►J PQ < CO CO 5m Pm co >M 33 Q O M Pi W a, N O .X1 5m CO ^M o co M 0) a. P w co 2 O M H Pm rH Oi u CO w o en H w H M H O o til CO CM 00 o> 00 CM u co CO CO i— i 3 co cj CO J-l CO -1-1 e o 01 CO E cO C CO -H co 33 ai co O 43 O" -u ■U > CO O 3 >i S cy r-M 0) SM -o CO C Ol 0) CO 43 C 4-1 c co O "O o c e 3 i o I I— I J-l Qi 03 CO < cu 2 >m 4J =3 -H J o) .a hJ 4-» o < P-, H O S £* o o CN o o d CO a, oi ■H 43 43 J-> co G O O 4J ■u co co Sm -" co cu o> >-i 42 01 CM E S CO CO 4-J CO cu 43 43 4-i 4-1 c co 3 5-i CO CO CO .-■ cq co I cu ai O < a, I—! o s P-. 01 CM CO 00 CM 00 c •H O 00 4-1 c CO 0) 43 u Ol 43 0) o a. CO co O cu s-i 4-1 CM CO ^H 01 3 O 6 m •H O CO 4-4 I I CU u > rH -i-4 H 4-1 Cm cj M co J Sm hJ 4-1 w S-l oi to < c 2 3 P r-4 |J Pd w o OS < Ol o> 00 •H S-i a CM 2 CO H w p H M H CO O c_> <: M co ca CO CNJ o o W CM 00 uo CM o ON CO S-i CO r-H a CO 3 a, r-i •H ■— I • u 03 0) 01 C3 C 43 u •H Sm 4-) S-l 5-i 3 o Cm •H CO <4H X ■U Ol C Ol 43 M CU > 4-1 os CO •i-l c CU 4-1 CO 3 m CJ 4-1 r-4 a CO C cu 5-1 o> Ol Pi 4-1 CO 43 i CU 4-J i ,— 1 5-1 o CO D- c 1— 1 3 o < CO Pm M OS U < 13 z M p Pi J PM 01 CO 0) 03 43 -C 4-J c a G •H c 0 c CU •rH X> >H 43 4-1 c 3 •H 03 QJ CO 5m G O •N CO O CM CO •H CM 01 H4J O -a O -H •H CO C 4-1 c O a •H 00 03 Cm T3 c O G •H ^M CO Sm W c O- >H •\ CO m "3 Oi a; 00 CO C 00 C cu 03 •rJ ■H XI 5m u ■r( •N Ol 3 4-J c a T3 0 O a •rJ 4-1 S-i CO 4-J CO Qu QJ 03 c c CO C ■rl S*. O 00 .— ) CO O c O XI B ■r-t CU u X uo 3 3 • cu TJ 43 r>. c O H 4-1 3 CM -a D. O 43 c CO O 03 M CO cu Sm 01 3 4-J O O Sm J^ o CO 43 S E 3 4-J cr Sm 43 iH O 4-t mH 4-J C ■r) 3 CO 3 UM 03 CU ^J S 01 4J 01 co 03 S-i Sm CO 0 4-J X, CO X a. ^ 4-1 CU CO CO G -o Sm ■H 4M 03 •iM oo UH CO e CO •I-) , Cm CM 0 r^- O 03 CO •H e 4M CO CO 4-J -O ■r-i ^M -rH 03 G CO 03 0 43 C 3 3- 0 O cu i£H CX 03 O 43 S O CU B 3 o 2 11 is not as yet available for the Florida Current. The harmonic constants sought for each of the major tidal con- stituents are amplitude and phase lag. Once determined, the constit- uents are then recombined and the resultant is the predicted tidal component of the current. Mathematically in tidal current analysis, a finite trigonometric sum is fitted to a set of current data in which there is a partial tidal periodicity. A finite number of points will exist since the current data will exist only at discrete points. Therefore, the data may be fitted by a finite number of sine and cosine curves. Solving for the five constituents in Table 1, this can be represented by Z(t1 ' Z(„) + ^CKSln Wnt+bnCOSwnt] + B„ (1) (t) (o) n=r where Z.n = periodic variate with time. (eg. current velocity), Z, = mean value of the variate, (o) n = the identification of the tidal constituent in equation (1), W = the angular velocity of the n constituent (Wn = -=~~ where T is the period of the constituent), t = time, a and b„ = Fourier coefficients for each constituent, n n and R = the residual m The harmonic Fourier coefficients for the series are solved from 2 N ar, =4 <^/ s Sin W t, (2) n N £ (t) n k N k = l 2 V1 and bn = N %^ Z(t) C0S Wn fck (3) 12 where t, = discrete points in time at which the data was collected, and N = the total number of data points. It is convenient to combine the sines and cosines of equation (1) which belong to the same n constituent (Gerges, 1966) into a single term An Sin (Wn tk + 0n) yielding 5 (t) = Zo + l^An Sin &*** + 0n) (4) where An = tan2 + bn2] 7 and On = — arctan tt- . Dn An is called the amplitude and 0 the phase of the n constituent. In tidal analysis, A of the major tidal constituents is cor- rected by a node factor which compensates for the effects of the variation in the moon's node in each 18.6 year cycle, and is also cor- rected for interference effects in the analysis from other constituents These include significant lesser constituents which sometimes may not be resolved from the actual data because of the length of the data series, but which may be inferred from the solved constituents. This is permitted by the fact that although the amplitude and phases of the tidal constituents at any location differ considerably from their theoretical equilibrium theory values, amplitudes and phases of the constituents of nearby frequencies at any place have relations that, in general, agree fairly closely with the relations of their theoreti- cal coefficients. (Schureman, 1941). 1.3 0 is corrected for equilibrium arguments for starting times (to Zeta) in accordance with astronomical stages, and likewise cor- rected for interference effects from other tidal constituents to (Kappa). There are a variety of methods available for solving for the tidal constituents. In the classical form of tidal analysis, a series of current observations is divided into periods equal to the known period of each individual tidal constituent Each period is then further sub-divided into a number of equal parts called the constituent hours which are numbered consecutively starting with zero at the initial instant for each period, Thus, the phase of each constituent and its overtides (harmonics) will be the same for a fixed instant in all sub-divisions having the same number, but all other constituents will have different phases (Dronkers, 1961). By summing and averaging all velocities which are observed at a fixed instant in each sub- interval (constituent hour) with the same number, the effect of all other components having incommensurable speeds as well as random noise will be predominantly eliminated. Convenient stencils are available to perform the separation of the various constituents from the current data recorded on proper forms. Each constituent is examined separately, and then the interference effects from other constituents are calculated and used to modify the results. A detailed description of the mechanics of this approach may be found in Schureman, 1941. This method of hand analysis becomes quite laborious and time consuming for all but the shortest of time series, but for over fifty years had been the estab- lished method of determinirg tidal constituents. The classical approach has been computerized in recent years with 14 the only major improvement (other than in computing speed) being that successive equally spaced data is multiplied by sines and cosines of angles incremented by the exact angular speed of each constituent, whereas with the hand analysis, successive values are allocated by stencil to the nearest constituent hour and then later corrected for this approximation by the application of suitable augmenting factors. Another modern technique has now largely been adopted which is known as the least- squares method of tidal analysis. Such an approach utilizes a program which specifies the frequencies of the constituents which are being sought, and the harmonic coefficients of the tidal constituents are then determined simultaneously so that the average values of the residuals squared is a minimum. Correcting the results for node factors or the equilibrium arguments for the starting times remains the same as in the traditional approach. Comparative tests show that the harmonic constants for the same set of constituents are slightly more accurate utilizing the least- squares method as opposed to the classical approach (Zetler and Lennon, 1967). The greatest advantage in using the least-squares method, how- ever, is that it requires neither equally spaced data nor a synodic period, whereas the traditional Fourier tidal analysis requires both equally spaced data and a quasi-synodic period of the principal con- stituents (Zetler e_t al_, 1965). In as much as in oceanographic data collection these latter conditions are usually difficult and sometimes impossible to fulfill, the least-squares method of analysis is often the only method which may be used to determine the tidal constituents. The least-squares method has now been adopted by the Coast and Geodetic Survey for the analysis of data series of one year's duration and is 15 sometimes used with shorter series. B. TOTAL CURRENT FLUCTUATION FIELD Over a series of current measurements, the mean value of current speed is given by: v~ = vi^/N v~ = mean current speed v~ = speed at any observation N = total number of observations The degree to which numerical data tend to spread about a mean value is termed the variation or dispersion of the data. One measure of the dispersion of the data is the standard deviation, s, which is often termed the root mean square deviation and which is defined by s = <(v - v^)2 ^^ N The variance, which is another method of measuring the spread or dispersion of the variate with reference to the mean, is defined as the square of the deviation or s , and the energy of all of the fluc- tuations of the current over a series of time is equal to the variance. The energy contributed by any periodic component of the fluctuation 2 2 field is equal to 1/2 (an + bn ), where an and bn are the Fourier coefficients of any periodic component over the period of investigation. (For derivation, see Appendix A). Parseval's Theorem tells us that the energy of a composite wave is composed of the sum of the energies of each of the distinct harmonic constituents of the waves of different frequencies making up the basic wave (Ippen, 1966). Thus, from any current fluctuation field, the per- centage of total energy due to periodic fluctuations may be calculated and compared to the total energy of all of the fluctuations, and the total energy contributed by individual periodic components may be 16 determined. 17 IV. RESULTS A plot of current velocity versus time for the period 21 November through 17 December 1965 obtained from the General Dynamics Monster Buoy in the Florida Straits was presented in Figure 2. Figure 3 presents a plot of current velocity versus time with a superimposed plot of the predicted tidal component of the current from the results of this analysis. The predicted tidal current is plotted about the mean current (167.05 cm/sec) indicating the predicted Florida Current in the absence of fluctuations of a non-tidal nature. Figure 4 is a plot of the residual after the predicted tidal component of the fluc- tuations of the Florida Current has been removed. Hourly values for current speed, wind speed and wind direction for the 15 day period are tabulated in Appendix B. A. DISCUSSION As can be seen from Figure 2, the second half of the current data series is of much poorer quality than the first half. Gaps in the record were due to telemetry and recording failure. The intense abrupt fluctuations seem to be indicative of a gradual failure of the current meter. Data obtained from the first fifteen days of this period is continuous, and the current meter one minute speed averages were available for each hour. An initial computer analysis of the entire data series utilizing a least-squares program indicated that the diurnal tidal constituents, 18 Figure 3. Current Velocity versus Time for the Period 21 November through 5 December 1965 with Super- imposed Plot of the Predicted Tidal Modulation. 195 190 185 i 180 175 f 169 165 / 159 154 149 144 139 134 cm/sec 21 NOV I 22 NOV I 23 NOV I 24 NOV I 25 NOV I 26 NOV I 27 NOV I 28 NOV I 29 NOV I 30 NOV I I DEC I 2 DEC I 3 DEC I 4 DEC I 5 DEC PREDICTED TIDAL CURRENT OBSERVED CURRENT HORIZONTAL SCALE: I 1= 12 HRS VERTICAL SCALE: H = 5.1444 cm/sec Figure 3. Current Velocity versus Time with Superimposed Plot of Predicted Tidal Modulation 19 Figure 4. Plot of the Residual After Tidal Modulation is Removed. 04.9 S.E. 14.3 W.N.W. 13.6 N.W. S.E. HORIZONTAL SCALE: I— I = 12 HRS VERTICAL SCALE: H =5.1444 cm/sec 12.9 S.E. 12.2 S.SE 11.7 S.SE. 27 NOV | 28 NOV I 29 NOV | 30 NOV WIND DATA (MPH) 10.8 87 10.6 17.0 S.S.W. N.W. N.N.E. W. N.E. 22 3 N.E 2 DEC 20.7 S.E 3 DEC 19.7 S.SE. 4 DEC 5 DEC 101 11.5 S.S.W. EN.E S.E. Figure 4. Plot of the Residual After Tidal Modulation is Removed . 20 Table 2. Comparison of Least-Squares Harmonic Analysis of the First Half of the Data Series with That of the Entire Series. TABLE 2 Comparison of least-squares harmonic analysis of the first half of the data series with that of the entire series 1. 15 DAY ANALYSIS Kl 01 (360 Data Entries) Amplitude* Phase Amplitude* Phase 0.11 59. 8° 0.12 273.5° 2. ENTIRE DATA SERIES Kl 01 (596 Data Entries) 0.15 43.5° 0.13 296.5° * Amplitude is in knots __ Note: Amplitudes and phases are values prior to correcting for equilibrium argument, interference effects, etc. These comparative results will slightly differ from those found elsewhere in this paper as during the above analysis the constituent N2 was included in the calculations. 21 Ki and 0^, are the predominant contributors to the tidal fluctuations of the current. The results of the least -squares analysis for the diurnal constituents for the first fifteen days and the entire period are compared in Table 2. That the phase angles change comparatively little between the two separate analyses is indicative that the amplitudes of the diurnal tidal components are in fact real and not due to random fluctuations. Because the second half of the data series was of marginal reliability, it is not included in the remainder of the analysis. Table 3 indicates that three techniques for solving for the major tidal constituents produce, as previously discussed, relatively small differences. These differences are accounted for in the method of each technique. The Fourier computer analysis was selected for determining the harmonic constants for the data series. The final results are contained in Table 4. A total of 24 constituents, of which 20 were inferred from the major constituents, were then recombined to produce the predicted tidal modulation of the Florida Current for the period 21 November through 5 December 1965 The predicted plot of tidal modulation is shown superimposed on the basic current data in Figure 3. Astronomical data for the period is given in Table 5. It can be seen that the predicted tidal modulation is in agreement with the astro- nomical data for the period. The additive effect of ML? and Sp on 22 November is not readily apparent due to the semi-diurnal components being over-shadowed by K^ and 0-, as they approach phase agreement on 26 November. The predominant diurnal modulation becomes negligible as K, and 0i come into opposition on 3 December leaving only semi-diurnal 22 Table 3. Comparison of Results of Harmonic Analysis on the First 15 Day Data Period Using Different Analysis Methods . 00 c •H CO 3 "O o •I-l s-l CD a CO 4-1 CO "O ^ CO "D m i— < CO "O 4J O CO rC >-l 4.) •H 01 4-i e CU CO ,C "H CO 4-1 CO >* w C i-H J O CO PQ c < CO CO H ■H CO 4-1 >. c i—4 a; CO u C > i—i CO c < •a c CO 33 a> CO o CO Cm vO in r^- 0) O CO • CO o X, o Cm CO CN 0 00 * CO o CO r-^ CM CO • ■ A uO r~» Cm m LO m oo o co o o a CU u «0 CO 3 •H cr ca w >■ 1 i—i ■u to to c CIS < cu -i CM 00 CM o in CM CO o CO o CO o u CU 4-1 3 PL, CO E •rH o CO CJ >> 1—4. u CO 0) c •H m O o o 4-1 U o •r-l 5-4 a CO cu 3 i—4 CO > cu U CO c cu > •H 00 ■ CO u CO 01 4-> 4-1 CO cu o co C rC •\ ^ a, 00 4-J c T3 u •H c cu CO <4-i C M-4 CU CO CU > cu •r-l XI cu £30 3 u 4-J c CO •r-4 ai •i-t 1—1 Sm &< cu CU E ■4-1 13 CO 5-1 3 cu 4-1 cu 4-4 •H X c i—l H ■H a E < 0) 4-J o # z 23 Table 4. Harmonic Constants from Florida Current Data. TABLE 4 Harmonic constants from Florida current data CONSTITUENT** AMPLITUDE (H) (cm/ sec) KAPPA*** (a.) DIURNAL CONSTITUENTS Ki 5.710 24,49° 0i 5.551 12.25° ?l 1.888 24.49° Ql 1.075 6.13° Jl 0.437 30.61° Ml 0.396 18 37° 00i 0.237 36.74° RHOi 0.211 6.98° 2QL 0.144 0.00° (b.) OTHER CONSTITUENTS M2 3.400 114.95° S2 2.500 309.40° S6 1.101 159.88° K2 0.679 309.40° M6 0.664 277.76° N2 0.658 203.68° S4 0.458 236.23° M4 0.304 41.08° Ms 0.278 290,55° T2 0.149 309.40° NU2 0.129 191.79° L2 0.098 26.22c 2N2 0.087 292.41° LAMBDA2 0.026 38.13° R2 0.020 309.40° ** Nomenclature and constituent speeds are in accordance with the classical Doodson classification. *** To convert to Greenwich Epoch (G) , add the product of 79.85 times the value of the constituent subscript. 24 Table 5. Astronomical Data for the Period 21 November Through 17 December 1965= TABLE 5 Astronomical data for period 21 November through 17 December 1965* 22 November 26 November 29 November 1 December 3 December 8 December 10 December 11 December 15 December 16 December New Moon Moon farthest South of Equator Moon in apogee Moon in First Quarter Moon at Equator Full Moon Moon farthest North of Equator Moon in perigee Moon in Last Quarter Moon at Equator * From American Ephemeris and Nautical Almanac 2.5 tidal modulation of lesser than usual amplitude as M2 and S2 were in phase opposition on 1 December, Fluctuations of the observed and predicted current are in excel- lent agreement and clearly show that the tidal modulation is the major periodic fluctuation of the current during the period 23 through 30 November. During the remainder of the data series correlation with the predicted tidal modulation still remains fairly good, but the mean current speed is raised or lowered apparently in response to local wind stress or possibly in response to atmospheric variations over the water regions which are coupled to the Florida Straits, Figure 4 is a plot of the residual after the predicted tidal modulation has been removed from the data. Included is the mean local wind speed and average wind direction at the buoy location in the Straits during each day from midnight to midnight, It would appear that response of the current to wind stress from either the East or VJest is negligible, and further that the current fairly rapidly re- sponds with increased velocity to winds from southerly directions . Response of the current to northerly winds appears more complicated with the indication from this limited data series being that the cur- rent is slow to initially respond to northerly winds, but once the response commences the current speed is greatly lowered and recovery to normal conditions is quite gradual, The seemingly erratic period, 30 November through 3 December, contained the highest wind speeds and rough seas were prevalent. Table 6 presents statistical results from the 15 day analysis of the current data. During this period the tidal modulation accounted for 21.35 per cent of the total fluctuations, with the remainder being 26 Table 6. Statistical Results and Energy Calculations for the 15 Day Period. TABLE 6 Statistical results and energy calculations for the 15 day period 1. Mean Current Velocity , , 167.05 cm/sec 2 Standard Deviation ..... 15.42 cm/sec 3. Average Fluctuation ............. 9,23 per cent 4. Total Current Variance. ........... 237.90 cm2/sec2 5. Predicted Tidal Current Variance. ...... 50.79 cm /sec ^ 6. Fluctuations Due to Tidal Components 21.35 per cent 7. Percent of Item 6 Due to Major Diurnal Tidal Components (K^ and 0\) 71 per cent 8. Percent of Item 6 Due to Major Semi-Diurnal Tidal Components (M2 and S2) 20 per cent 9. Energy Contributed by Individual Tidal Constituents (cm2/sec2) KL 16.30 0i 15.40 M2 5.78 S2 .......... 3.12 Pi 1.78 Sfc 0.60 Q1 0.58 Remainder Semi-Diurnal Constituents. 0,88 Remainder Diurnal Constituents . . . 0.24 27 fluctuations of an apparent non-periodic nature* B . COMPARISON OF RESULTS The analysis of the surface current data reveals large diurnal tidal modulation of the Florida Current. This is in agreement with the tidal analysis performed on the transport of the Florida Current by Richardson and Schmitz (op_. cit. ) , and tidal analysis of transport fluctuations from studies of electric potential measurements by Wertheim (op cit. ) . It is further in agreement with Project MIMl's results where underwater acoustic signals transmitted across the Straits of Florida over long periods of time have shown prominent diurnal phase changes. (Steinberg and Birdsall, 1966), (Clark and Yarnall, 1967). Recently Zetler calculated the amplitude of the K\ tidal current in the Florida Straits required to conform to observations of the oscillating diurnal tidal water transport in the Gulf of Mexico (Zetler, 1968). The K^ amplitude of 0.11 knots found from the har- monic analysis of the Monster Buoy data is in remarkable close agree- ment to his calculated value of 0.12 knots. The following is a comparison of the phase angles of the major diurnal constituents of the tidal current with the phase angles for the tide at the Patrick Air Force Base and Miami Beach shore stations. No harmonic constants are available for tide at the Monster Buoy latitude. 28 TIDE LOCATION LATITUDE PHASE (" G) Patrick AFB 28D14' N 203 207 Miami Beach 25°46' N 245 267 TIDAL CURRENT Monster Buoy 26°01' N 284 272 If a wave is progressive, the difference in phase between tidal current and the resultant tide should be zero degrees at any location, whereas in a standing wave situation there should be a 90u difference. As can be seen, the differences found were inconsistent and probably indicate some combination of both a progressive and standing wave. Since, cotidal lines bunch up near a node and tidal constants at the latitude of the current observations are not available, the above comparison is of marginal suitability. No analysis of tidal currents at any of the shore stations is available for comparison. Zetler (1968) concluded, after consideration of the available known K\ and 0]^ phase angles at shore stations along either side of the Straits of Florida, that there is a strong indication of a longi- tudinal standing wave situation for the major diurnal tidal components in the Straits of Florida, with a node close to the latitude of Miami. The large amplitudes of the diurnal constituents of the tidal modu- lation of the Florida Current at the Hollywood latitude are in agree- ment with this concept as the tidal current related to this wave should be maximum at the node. 29 V. SUMMARY AND CONCLUSIONS During the latter portion of 1965 direct surface current measure- ments of the Florida Current were taken at hourly intervals over an approximate period of one month from the General Dynamics Monster Buoy anchored in the Straits of Florida at the Hollywood latitude. The data from this period presented the opportunity of conducting the first Florida Current tidal analysis from direct surface current measurements of sufficient duration to provide meaningful results. Harmonic analysis, of data from 15 complete days of this period confirms that the resultant tidal influence on the Florida Current surface flow does not conform to the usual Atlantic coastal tidal configuration, being instead transitional between the semi-diurnal Atlantic tide and the diurnal Gulf of Mexico tide. The tidal coupling between the Gulf of Mexico and the Atlantic Ocean with pronounced diurnal features can only at present be explained by a heretofore overlooked longitudinal diurnal standing wave in the Florida Straits. The obtainment and subsequent analysis of tide observations at ad- ditional points along the lower third of the east coast of Florida should confirm the presence of this diurnal standing wave. A fluctuation of 10 per cent of the mean surface current is given as representative of the Florida Current. Slightly more than one- fifth of this modulation is attributed to tidal influence, being the apparent major periodic modulating force of the Florida Current. It is recommended that further work be continued in this field. 30 The obtainment of tidal current data in the Straits of Florida from a deep subsurface buoy would be particularly invaluable for analysis. Additionally, the placement of another data gathering platform in the Florida Current at about the Miami latitude for long term fluctuation study of the Florida Current would be well worth the expense. 31 LITERATURE CITED 32 CLARK, JOHN G, and J. R. YARNALL 1967. Long range Ocean Acoustics and Synoptic Oceanography, Straits of Florida Results. Contrib. No. 798, Institute of Marine Science, Univ. of Miami. Unpublished Manuscript, DARWIN, GEORGE H. 1898. The Tides. Cambridge, Mass., The Riverside Press. DRONKERS, J. 1964. Tidal Computations. New York, Interscience Publishers. GERGES, MAKRAM A. 1966. Analysis of Deep-Ocean Tidal Currents. W. H.O.I. No. 66-28. Unpublished Manuscript. HELA, ILMO and L.P. WAGNER 1954. Note on Tidal Fluctuations in the Florida Current. Institute of Marine Science, Univ. of Miami No. 54-7, pp. 14-24. Unpublished Manuscript, IPPEN, ARTHUR (ed.). 1966. Estuary and Coastline Hydrodynamics. New York. McGraw-Hill Book Co., Inc. MUNK, WALTER H. , and K. HASSELMANN 1965. Super-resolution of Tides. Studies on Oceanography, K. Yoshida, ed., University of Wash. Press, pp. 457-478. MURRAY, KENNETH M. 1952. Short Period Fluctuation of the Florida Current from Geomagnetic Electrokinetograph Observations. Bull. Mar. Sci. Gulf and Carib., 2, pp. 360-375. O'HARE, J. E., Q, H. CARLSON and W. E. TAMBLYN 1953. Some results of a Tanker Survey of the Gulf Stream. Trans. Amer. Geophysical Union, 35(3), pp. 420-430. PARR, ALBERT E. 1937. Report of Hydrographic Observations at a Series of Anchor Stations Across the Straits of Florida. Bull. Bingham Oceanogr. Coll., 6, pp. 1-62. PILLSBURY, JOHN E. 1891. The Gulfstream--A Description of the Methods Employed in the Investigation and the Results of the Research, Re- port of the Superintendent of the U.S. Coast and Geodetic Survey, Appendix 10, pp. 461-620. 33 SCHMITZ, WILLIAM J. and W. S. RICHARDSON 1967. On the Transport of the Florida Current. Nova Univ., Unpublished Manuscript. SCHUREMAN, PAUL 1941. Manual of Harmonic Analysis and Prediction of Tides. U.S. Coast and Geodetic Survey Special Pub. No. 98. STEINBERG, JOHN C. and T. G. BIRDSALL 1966. Underwater Sound Propagation in the Straits of Florida. Jour. Acoustical Society of Amer., 39 (2), pp. 301-315. WEBSTER, F. 1961. The Effect of Meanders on the Kinetic Energy Balance of the Gulfstream. Tellus 13 (3), pp. 392-401. WERTHEIM, G. K. 1954. Studies of the Electric Potential Between Key West, Florida and Havana, Cuba. Trans. Amer. Geophysical Union, 35 (6), pp. 872-882. ZETLER, BERNARD D,, M. D. SCHULDT, R. W.WHIPPLE and S. D. HICKS 1965. Harmonic Analysis of Tides From Data Randomly Spaced in Time. Jour, of Geophysical Res., _7J) (12), pp. 2805-2811. ZETLER, BERNARD D. and G. W. LENNON 1967. Some Comparative Tests of Tidal Analytical Processes. Int. Hydro. Review, 44 (1), pp. 139-147. ZETLER, BERNARD D. 1968. Tides in the Gulf of Mexico. Physical Oceanogr. Lab. Miami, Preliminary Review. Unpublished Manuscript. 34 APPENDIX A: DERIVATION OF THE ENERGY FORMULA OF A HARMONIC TIDAL COMPONENT 35 If any harmonic component of the mean current speed is represented by: v = aRSinwt + t>nCOSwt where w = 2fT i-s the angular speed of the motion, then the energy of the periodic motion may be represented by: P.E. + K.E. =1 \ \^d 1 T T 1 ( an2 Sin2wtdt +1 f bn2COS2wtdt +1 fan I J T 1 T J 0 t) 'o bbSinwtCOSwtdt = an2 [^ - Sin2wt] + bn [■7 - Sin2wt] + b l r_t + Sin2wt] + anbn [1_ Sin wt l' 4w 3Q — [2 4w J, — [2w 2 MT 0 = an2 + bn2 - an2Sin2wT + bn Sin2wT + anbnSin2wT r *" "5wT "SwF 5wT = I (an2+bn2) " (an2-bn2) (Sin2wt) + (anbn) , 2 8wt (4wT~) bln Wt 1 (an2+bn2) " (an2-bn2> [Sin 2(2fflT 2 (STOttTTt) [ T } T ) + (anbn) Sin2(2Y* (4) (OT) m T )UJ ( T )(T) I (a„2 + b 2 2 "n ) 36 APPENDIX B: FLORIDA CURRENT DATA AND ENVIRONMENTAL DATA FOR THE 15 DAY PERIOD 37 TIME CURRENT SPEED UIND SPEED WIND DATE (LOCAL) 0000 (kts) (mph) DIRECTION 11/21/65 3.1 7 120° 0113 3.4 6 135° 0203 3.6 4 120° 0258 3.5 1 130° 0401 3.5 3 120° 0500 3.5 4 100° 0600 3.6 7 100° 0657 3.4 9 110° 0800 3.4 10 100° 0902 3.4 4 120° 1000 3.4 4 100° 1100 3.5 5 120° 1200 3.7 2 145c 1300 3.7 2 120° 1400 3.9 2 200° 1503 3.4 3 200° 1600 4.0 4 180° 1700 3.7 3 190° 1800 3.6 3 190° 1900 3.0 4 220° 2001 3.2 9 200° 2110 3.3 8 200° 2206 3.3 8 220° 2303 3.3 10 220° 11/22/65 0002 3.3 11 240° 0101 3.4 11 250° 0206 3.2 17 240° 0301 3.2 17 240° 0401 3.1 6 250° 0502 3.1 16 260° 0604 3.2 14 270° 0702 3.3 12 250° 0800 3.4 10 300° 0920 3.1 12 260° 1000 3.1 14 280° 1100 3.2 10 290° 1200 3.0 13 260° 1301 3 . 4 13 260° 1400 3.4 13 272° 1500 3.2 14 270° 1600 3.3 17 325° 1700 2.8 18 300° 1800 3.5 19 310° 1900 3.4 21 325° 2002 3.2 22 330° 2104 3.3 16 330° 2204 3.4 12 330° 2303 3.4 15 325° 38 TIME CURRENT SPEED WIND SPEED WIND DATE (LOCAL) 0000 (kts) (mph) 12 DIRECTION 11/23/65 3,3 330° M 0100 3.4 15 320° II 0200 3.5 19 320° II 0259 3.4 20 320° li 0402 3.4 18 320° II 0500 3.2 19 320° II 0603 3.2 20 335° II 0700 3.2 20 340° II 0800 3.0 15 340° II 0900 2.7 12 020° II 1000 2.8 12 040° It 1100 2.7 12 030° II 1200 2.6 11 060° II 1300 2.6 12 060° II 1400 2.6 10 060° II 1500 2.6 5 070° II 1600 2.9 8 070° II 1701 2.8 8 080° II 1800 2.6 10 068° II 1900 3.2 16 110° II 2001 3.0 14 130° II 2100 3.0 17 130° II 2200 3.4 13 130° II 2302 3.2 10 120° 11/24/65 0002 3.2 13 110° ii 0110 3.2 17 120° ii 0220 3.5 11 120° ii 0300 3.4 10 120° ii 0400 3.2 12 120° ii 0500 3.5 15 120° ii 0558 3.4 15 120° ii 0700 3.5 13 115° ii 0800 3.5 12 140° ii 0900 3.2 10 140° ii 1000 3.3 11 140° ii 1100 3.1 12 135° ii 1203 3.0 15 132° ii 1300 3.4 12 140° ii 1400 3.2 13 135° M 1500 3.3 10 120° ii 1600 3.4 11 140° ii 1700 3.1 15 140° ii 1800 3.1 15 140° ii 1900 3.5 16 140° ii 2003 3.4 14 150° ii 2104 3.5 10 150° ii 2202 3.6 10 120° ii 2304 3.6 15 180° 39 TIME CURRENT SPEED WIND SPEED WIND DATE 11/25/65 (LOCAL) 0000 (kts) (mph) 20 DIRECTION 3.5 170° it 0100 3.6 18 180° ti 0201 3.8 18 180° ii 0300 3.8 20 180° it 0400 3.6 19 200° ii 0458 3.5 18 180° ii 0600 3.8 14 200° ii 0701 3.8 15 200° ii 0800 3.7 15 188° ii 0900 3.6 10 140° ii 1000 3.4 16 060° ii 1100 3.5 20 135c ii 1200 3.4 1 060° ii 1300 3.5 7 200^ ii 1400 3.2 4 060° ii 1500 3.2 5 060° ii 1600 3.2 5 075° it 1700 3.2 9 120° ii 1800 3.4 10 160° ii 1900 3.4 9 140° ii 2001 3.3 12 160° ii 2100 3.4 9 130° it 2201 3.4 12 150° ii 2300 3.6 10 150° 11/26/65 0000 3.5 12 170° ii 0103 3.4 10 150° ii 0200 3.4 8 180° ii 0301 3.5 7 180° " 0401 3.5 10 175° ii 0501 3.6 6 160° i; 0605 3.6 6 160° ii 0700 3.5 9 140° ii 1800 3.6 7 135° ii 0900 3.6 7 140° ii 1000 3.4 10 150° ii 1100 3.3 9 140° ii 1200 3.0 10 140° ti 1300 3.1 9 130° ii 1400 3.0 14 140° ii 1500 2.9 15 140° n 1600 3.0 12 170° ii 1700 3.0 12 170° ii 1800 3.1 18 160° ii 1857 3.0 19 175° it 2000 3.0 17 145° ii 2100 3.1 18 180° ii 2200 3.3 16 180° ii 2257 3.4 20 180° 40 TIME CURRENT SPEED WIND SPEED WIND DATE (LOCAL) 0000 (kts) (mph) 20 DIRECTION 11/27/65 3.5 190° M 0058 3.6 18 190° ii 0200 3.5 18 190° ii 0300 3.6 19 220° ii 0403 3.6 12 210° ii 0505 3.6 12 190° ii 0615 3.6 12 170° ii 1700 3.6 5 170° ii 0810 3.7 9 200° ii 0900 3.7 10 180° it 1000 3.5 10 160° ii 1100 3.6 15 170° it 1200 3.4 12 185° it 1300 3.2 14 185c ii 1400 3.1 10 200° ii 1500 3.3 6 220' n 1600 3.2 4 200° ii 1700 3.3 7 200° ii 1800 3.4 7 215° ii 1900 3.4 8 200° ii 2000 3.3 8 200° ii 2100 3.3 8 210° ii 2200 3.2 8 210° ii 2300 3.2 8 230° 11/28/65 0000 3.3 9 250° ii 0100 3.3 9 270° ii 0200 3.5 10 280° it 0300 3.6 10 330° ii 0400 3.6 10 340° m 0500 3.8 11 340° ii 0600 3.8 11 340° it 0700 3.8 10 345° it 0800 3.6 10 340° it 0900 3.8 10 340c ii 1000 3.6 10 350° ii 1100 3.4 9 345° ii 1200 3.2 8 330° ii 1300 3.0 5 340° ii 1400 3.1 3 268° it 1500 3.1 3 280° it 1600 3.1 4 270° ii 1700 3.1 6 275° ii 1800 3.2 8 280° ii 1900 3.4 10 260° ii 2000 3.3 7 280° it 2100 3.4 8 300° it 2200 3.4 12 320° ii 2300 3.6 16 340° 41 TIME CURRENT SPEED WIND SPEED WIND DATE (LOCAL) 0000 (kts) (mph; 13 D1REC HON 11/29/65 3.6 040° ii 0100 3.6 14 010° ii 0200 3.6 12 000° ii 0300 3.3 10 350° ii 0400 3.3 11 350° ii 0500 3.4 13 000° ii 0600 3.4 12 000° ii 0700 3.4 13 350° ii 0800 3.3 15 010° it 0900 3.6 11 020° ii 1000 3.8 10 000° ii 1100 3.6 10 020" n 1200 3.4 9 020° it 1300 3.3 5 020° ii 1400 3.1 3 150' ii 1500 3.1 5 220° ii 1600 3.0 9 255° ii 1700 3.2 5 240° ii 1800 3.2 8 275° ii 1900 3.3 10 280° it 2000 3.6 12 280° it 2100 3.6 12 280 ii 2200 3.7 15 290° ii 2300 3.7 18 300° 11/30/65 0000 3.6 15 310° it 0100 3.7 12 320° ii 0200 3.6 12 320° n 0300 3.5 10 000° M 0400 3.5 15 030° it 0500 3.6 14 059° ii 0600 3.7 11 060° ii 0700 3.3 17 030° it 0800 3.4 19 035° it 0900 3.5 19 350° it 1000 3.4 18 000c it 1100 3.1 14 005° ii 1200 3.4 12 000° it 1300 3.1 20 350° it 1400 3.1 22 050° ii 1500 3.0 21 050° it 1600 3.0 20 060° it 1700 3.0 20 050° it 1800 2.9 18 060° it 1900 2.7 17 060° it 2000 2.9 21 060° it 2100 3.0 20 060° it 2200 2.9 20 060° ii 2300 3.1 22 050° 42 TIME CURRENT SPEED WIND SPEED WIND DATE 12/1/65 (LOCAL) 0000 (kts) (mph) 22 DIRECTION 3.0 050° M 0100 2.8 25 060° ii 0200 3.0 24 040° it 0300 2.8 25 058° ii 0400 2.8 25 058° ii 0500 3.0 25 058° ii 0600 3.2 27 056° ii 0700 3.2 27 055c ii 0800 2.9 22 058° ii 0900 3.4 25 060° ii 1000 3.2 22 060° ii 1100 3.1 20 060° M 1200 3.0 21 060° it 1300 2.7 20 060° ii 1400 3.0 20 060^ ii 1500 3.0 19 060c ii 1600 3.0 20 080° ii 1700 2.9 16 100° ii 1800 3.0 20 100° ti 1900 2.8 20 090° ii 2000 3.0 26 110° it 2100 2.8 22 120° ii 2200 3.0 22 110° ii 2300 3.0 20 120° 12/2/65 0005 2.9 25 110° ii 0100 2.9 26 120° n 0200 2.9 22 140° ii 0300 3.0 20 110° it 0400 2.9 20 110° ii 0507 2.8 25 125° ii 0602 2.9 22 125° M 0701 2.8 20 140° ii 0800 2.7 25 130° M 0900 2.8 20 140° " 1000 2.8 25 160° ii 1100 2.8 19 150° ii 1200 3.0 20 150° ii 1300 2.6 19 160° M 1400 2.8 20 150° ii 1500 2.6 16 150° ii 160C 2.6 19 160° ii 1700 2.4 18 180° ii 1800 2.6 15 180° ii 1900 2.8 20 180° ii 2000 2.9 18 160° ii 2100 3.0 20 180° ii 2200 3.1 20 190° ii 2300 3.0 22 160° 43 TIME CURRENT SPEED WIND SPEED WIND DATE (LOCAL) (kts) (mph) DIRECTION 12/3/65 OOOO 3.0 22 160° ti 0100 2.8 20 150° 11 0200 2.8 20 140° ii 0300 2.6 24 170c ii 0400 2.7 22 190° n 0500 2,8 19 180° ii 0600 2.8 15 150° ii 0800 2.8 14 150° it 0800 3.0 20 160° ii 0900 2.9 22 160° ii 1000 3.4 25 170° ii 1100 2.7 25 170° ii 1200 2,9 25 160° ii 1300 3,0 20 180° ii 1400 3-0 21 185° ii 1500 2.9 20 180° ii 1600 3.0 20 185° it 1700 3.1 18 180° ii 1800 3.0 18 180° it 1900 3.0 18 175° ii 2000 3.0 18 190° ii 2100 3.2 14 190° it 2200 3.2 16 190° ii 2300 3.3 16 185° 12/4/65 0000 3.3 15 200° n 0100 3.2 13 200° ii 0200 3.0 9 200° ii 0300 3.0 8 200° ii 0400 2.9 8 200c ii 0500 3.0 8 200c it 0600 3.0 12 200° ii 0700 3.0 10 200° ii 0800 3.0 11 180° it 0900 3.1 12 200° ii 1000 3.1 9 190° it 1100 3.0 8 220° ii 1200 3.2 5 240° it 1300 3.2 5 220° ti 1400 3.1 7 230° ii 1500 3.1 7 240° tt 1600 3.2 4 240° ii 1700 3.2 3 280° ii 1800 3.3 4 000° tt 1900 3.2 20 065° ti 2000 3.3 16 060° it 2100 3.3 15 070° ti 2200 3.4 15 060° ti 2300 3.4 18 060° 44 TIME CURRENT SPEED WIND SPEED WIND DATE (LOCAL) 0000 (kts) (mph) DIRECTION 12/5/65 3.5 18 080° 0051 3,4 15 100° 0200 3.4 18 090° 0300 3.3 15 090° 0400 3.2 15 060° 0500 3.2 12 125° 0600 3.2 13 100° 0700 3.0 17 059° 0800 3.1 12 080° 0900 3.1 16 058° 1000 3.3 12 060" 1100 3.5 11 060° 1200 3.6 8 150° 1300 3.6 12 130° 1400 3.5 11 120° 1500 3.7 12 150° 1600 3.6 10 225° 1700 3.3 10 165° 1800 3.3 6 200° 1900 3.4 8 180° 2000 3.6 5 170° 2100 3.8 6 275° 2200 4.0 9 120° 2300 4.0 5 195° VITA Lt. John Alan Smith, USN, was born in Norwood, Massachusetts, on December 5, 1937. His parents were Arthur L. Smith and Elinor Smith. He received his elementary education in the Walpole public school system at Walpole, Massachusetts, and his secondary education at Fort Lauderdale High School, Fort Lauderdale, Florida. In September 1955, he enlisted in the United States Navy, and served in the USS NAUTILUS (SSN571) and attended the U.S. Naval Academy Preparatory School at Bainbridge, Maryland from September 1956 to June 1957. In July, 1957, he entered the U.S. Naval Academy, Annapolis, Maryland. Upon graduation in June, 1961, with a B.S., he was commissioned an Ensign in the U.S. Navy. Subsequent Naval Service included five years in the Destroyer Force of the Atlantic Fleet with attendance at Fleet ASW School at Key West, Florida, and Fleet Destroyer School at Newport, Rhode Island. He was admitted to the Graduate School of the University of Miami in September, 1966. He was granted the degree of Master of Science in July, 1968 Permanent address: 1911 North Sumac Drive Jaynesville, Wisconsin