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Full text of "Tidal fluctuations of the Florida current."

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 
(10 6 M, 3 Sec" 1 ) for M 2 , Oi and K L , and 1.5 (10 6 M. 3 sec" 1 ) for S 2 . 



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'.)' 

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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 



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Pi 
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co 

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0) 

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co 



2 

O 

M 
H 
Pm 
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CO 

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H 

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H 

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o 



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CO 



CM 



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CM 



u 

co CO 

CO i— i 

3 



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CO -1-1 

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01 CO 

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cO C 

CO -H 



co 

33 



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O 3 

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C 4-1 

c 

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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 („) + ^CK Sln W n t+b n COSw n t] + 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 (W n = -=~~ 

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 

a r, =4 <^/ s Si n W t, (2) 
n N £ (t) n k N 

k = l 

2 V 1 
and b n = N %^ Z (t) C0S W n fc k (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 

A n Sin (W n t k + 0n) 

yielding 
5 



(t) = Z o + l^ A n Sin &*** + 0n) (4) 



where 

A n = ta n 2 + b n 2 ] 7 

and On = — arctan tt - . 

D n 

A n is called the amplitude and 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 

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 (a n + b n ), where a n and b n 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 <U 




CO M-4 




14-4 




O -H 




•H T3 




C 




o 




e 




m 




CO 




JZ 




«W 




o 




CO 




4-1 




i—4 




9 




CO 




cu 




M 



c 
o 

CO 

•r-l 

!-i 

CO 

a 
e 
o 
o 



Q 
O 

T 

H 





r^ 


o 


CU 


CM 


O 


CO 


• 


• 


CO 


r«. 


<r 


4= 


r^ 


r*» 


Pi 


CM 


CM 



a 

E 
< 



E 
< 



a. 

E 
< 



CO 

>> 

i—i 

CO 

c 

< 

•a 

c 

CO 

33 



a> 


CO 


o 


CO 


<t 


O 


CO 


• 


• 


X! 


O 


o> 


Cm 


vO 


in 





r^- 


0) 


O 


CO 


• 


CO 


o 


X, 


o 


Cm 


CO 


CN 







00 


* 


<r 


a 


o 


E 


• 


< 


O 



a> 


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 


<c 


s- 




3 




O 




h 





CO 





4-1 






C 






CU 






E 






3 






60 






V-i 






CO 






E 






3 






•i-l 






JM 






XI 






•H 






t— 4 






•H 






3 






cr 






cu 






u 






o 






iw 






00 






c 






•H 






4-1 






o 






cu 






M 






>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° 

2Q L 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° 

N 2 0.658 203.68° 

S4 0.458 236.23° 

M4 0.304 41.08° 

Ms 0.278 290,55° 

T2 0.149 309.40° 

NU 2 0.129 191.79° 

L 2 0.098 26.22 c 

2N 2 0.087 292.41° 

LAMBDA 2 0.026 38.13° 

R 2 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 cm 2 /sec 2 

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 (M 2 and S2) 20 per cent 

9. Energy Contributed by Individual Tidal 

Constituents (cm 2 /sec 2 ) 

K L 16.30 

0i 15.40 

M 2 5.78 

S 2 .......... 3.12 

Pi 1.78 

Sfc 0.60 

Q 1 0.58 

Remainder Semi-Diurnal Constituents. 0,88 

Remainder Diurnal Constituents . . . 0.24 



27 
fluctuations of an apparent non-periodic nature* 
B . COMPARISON O F 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 28 D 14' 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 90 u 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 = a R Sinwt + t> n COSwt 

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 ( a n 2 Sin 2 wtdt +1 f b n 2 COS 2 wtdt +1 fa n 
I J T 1 T J 

t) 'o 



b b SinwtCOSwtdt 



= a n 2 [^ - Sin2wt ] + b n 



[■7 - Sin2wt ] + b l r_t + Sin2wt] + a n b n [1_ Sin wt 
l' 4w 3 Q — [2 4w J, — [ 2w 



2 M T 




= a n 2 + b n 2 - a n 2 Sin2wT + b n Sin2wT + a n b n Sin 2 wT 



r *" 



"5wT 



"SwF 



5wT 



= I ( a n 2+b n 2 ) " ( a n 2 -b n 2 ) (Sin2wt) + (a n b n ) , 

2 8wt (4wT~) bln Wt 



1 ( a n 2+b n 2 ) " ( a n 2 - b n 2 > [Sin 2(2ffl T 

2 (STOttTTt) [ T } 

T ) 



+ 



(a n b n ) Sin 2 (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 


145 c 




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 


135 c 


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 


185 c 


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 


340 c 


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 


000 c 


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 


055 c 


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 


060 c 


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 


170 c 


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 


200 c 


ii 


0500 


3.0 


8 


200 c 


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 



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Jaynesville, Wisconsin