• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 List of Figures
 Introduction
 Literature search
 Spectrum formulation representing...
 Estimation and prediction of hurricane...
 Conclusion
 Appendix: Data
 Reference
 Biographical sketch














Group Title: UFLCOEL
Title: Spectral growth of hurricane generated seas
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 Material Information
Title: Spectral growth of hurricane generated seas
Series Title: UFLCOEL
Physical Description: vi, 75 leaves : ill. ; 28 cm.
Language: English
Creator: Finlayson, William S
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: University of Florida, Coastal & Oceanographic Engineering Dept.
Place of Publication: Gainesville Fla
Publication Date: 1997
 Subjects
Subject: Storm surges -- Research -- Evaluation   ( lcsh )
Hurricanes -- Research   ( lcsh )
Ocean waves -- Research   ( lcsh )
Water waves -- Research   ( lcsh )
Wind waves -- Research   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (M.S.)--University of Florida, 1997.
Bibliography: Includes bibliographical references (leaves 73-74).
Statement of Responsibility: by William Scott Finlayson.
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Bibliographic ID: UF00091081
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: oclc - 39004893

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Page i
    Acknowledgement
        Page ii
    Table of Contents
        Page iii
    List of Figures
        Page iv
        Page v
        Page vi
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
    Literature search
        Page 6
        Page 7
    Spectrum formulation representing hurricane generated seas
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
    Estimation and prediction of hurricane wave spectrum growth
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
        Page 64
        Page 65
        Page 66
        Page 67
    Conclusion
        Page 68
    Appendix: Data
        Page 69
        Page 70
        Page 71
        Page 72
    Reference
        Page 73
        Page 74
    Biographical sketch
        Page 75
Full Text




UFL/COEL-97/016


SPECTRAL GROWTH OF HURRICANE GENERATED
SEAS






by



William Scott Finlayson




Thesis


1997














SPECTRAL GROWTH OF HURRICANE GENERATED SEAS


By

WILLIAM SCOTT FINLAYSON














A THESIS PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF SCIENCE

UNIVERSITY OF FLORIDA


1997














ACKNOWLEDGMENTS

I would like to thank Dr. Ochi for his considerable patience and instruction. I

would also like to thank Dr. Mehta and Dr. Shepherd for taking time out of their busy

schedules to serve on my committee. Particularly, I am grateful to Dr. Mehta for making

my graduate education a well rounded one. I am also grateful to the United States Navy

for giving me the opportunity to continue my education. Finally, I would like to thank my

mother for supporting me in all my endeavors and I would like to acknowledge the

considerable contribution my father made to my personal and professional development.

This thesis is dedicated to his memory.















TABLE OF CONTENTS


page


ACKNOW LEDGM ENTS ............................................................................................ ii

LIST OF FIGURES............................................... ............................ ..................... ............. iv

A B STR A C T ............................................................................................................ ... vii

1 INTRODUCTION ....................................... .............................. ........................... 1

2 LITERATURE SEARCH .............................................................. ......................6

3 SPECTRUM FORMULATION REPRESENTING HURRICANE
GENERATED SEA S ........................................................... ......................... ... 8
Verification of Modified JONSWAP Spectrum ............................ ..... ........... 8
Comparison with Wave Spectra obtained from Measured Data................................11

4 ESTIMATION AND PREDICTION OF HURRICANE WAVE SPECTRUM
G R O W TH ............................................................ ..................................................58
Estimation of significant wave height........................................... ...58
Prediction of m odal frequency ........................................................ .......................62
Estimation of hurricane wave spectrum growth ................................................ .... 64

5 CON CLU SION S........................................................................... ............................68

A appendix: D ata .......................................................... ..................................................69

LIST OF REFEREN CES ......................................................... ....................................73

BIOGRAPHICAL SKETCH ........................................ ...........................75










11mo














LIST OF FIGURES


Figure page

1 Representative data wave energy spectrum normalized by OOm and analyzed piecewise
for intervals of o/com of 0.05 .............................................................................................12

2 Modified JONSWAP spectrum versus significant wave height for o/0m=0.80.............13

3 Modified JONSWAP spectrum versus significant wave height for co/Om=0.85 .............14

4 Modified JONSWAP spectrum versus significant wave height for c)/M0=0.90.............15

5 Modified JONSWAP spectrum versus significant wave height for (/0m=0.95 .............16

6 Modified JONSWAP spectrum versus significant wave height for o/(0m=1.00.............17

7 Modified JONSWAP spectrum versus significant wave height for 0o/m=1.05.............18

8 Modified JONSWAP spectrum versus significant wave height for o/m=l1.10............19

9 Modified JONSWAP spectrum versus significant wave height for co/0m= 1.15.............20

10 Modified JONSWAP spectrum versus significant wave height for o/0m= 1.20...........21

11 Modified JONSWAP spectrum versus significant wave height for o0/0m=1.25 ..........22

12 Modified JONSWAP spectrum versus significant wave height for co/0m=1.30.........23

13 Modified JONSWAP spectrum versus significant wave height for O/0om=1.35 ..........24

14 Modified JONSWAP spectrum versus significant wave height for )/c0m=1.40...........25

15 Modified JONSWAP spectrum versus significant wave height for o/0om=1.45...........26

16 Modified JONSWAP spectrum versus significant wave height for )/o0m=1.50...........27

17 Modified JONSWAP spectrum versus significant wave height for co/Cm=l1.55...........28

18 Modified JONSWAP spectrum versus significant wave height for o/o)m=1.60...........29

19 Modified JONSWAP spectrum versus significant wave height for o/COm=1.65...........30
iv








20 Modified JONSWAP spectrum versus significant wave height for co/0m=1.70...........31

21 Modified JONSWAP spectrum versus significant wave height for (o/0m=1.75...........32

22 Modified JONSWAP spectrum versus significant wave height for co/Om=1.80...........33

23 Modified JONSWAP spectrum versus significant wave height for (o/COm=1.85 ...........34

24 Modified JONSWAP spectrum versus significant wave height for co/0m=1.90...........35

25 Modified JONSWAP spectrum versus significant wave height for (o/COm=1.95...........36

26 Modified JONSWAP spectrum versus significant wave height for 0o/Om=2.00...........37

27 Modified JONSWAP spectrum versus significant wave height for co/om=2.05...........38

28 Modified JONSWAP spectrum versus significant wave height for o/0m=2.10...........39

29 Modified JONSWAP spectrum versus significant wave height for Co/(0m=2.15 ...........40

30 Modified JONSWAP spectrum versus significant wave height for co/m=2.20...........41

31 Modified JONSWAP spectrum versus significant wave height for co/Om=2.25...........42

32 Modified JONSWAP spectrum versus significant wave height for /Om=2.30 ...........43

33 Modified JONSWAP spectrum versus significant wave height for c)/om=2.35...........44

34 Comparison between Modified JONSWAP and measured spectrum for Hurricane
B elle, H =3.2 m ................................................................................................... 47

35 Comparison between Modified JONSWAP and measured spectrum for Hurricane
B elle, H s=6.1 m ................................................................................................... 48

36 Comparison between Modified JONSWAP and measured spectrum for Hurricane
B elle, H s=7.1 m .........................................................................................................49

37 Comparison between Modified JONSWAP and measured spectrum for Hurricane
G loria, H =6.0 m ........................................................................................................50

38 Comparison between Modified JONSWAP and measured spectrum for Hurricane
G loria, H =8.1 m .................................................................................................51

39 Comparison between Modified JONSWAP and measured spectrum for Hurricane
Eloise, H =5.6 m .................................................................................................52

40 Comparison between Modified JONSWAP and measured spectrum for Hurricane
E lose, H =8.8 m ........................................................................................................53
v








41 Comparison between Modified JONSWAP and measured spectrum for Hurricane
Fredrick, H =4.5 m ............................................................................................... 54

42 Comparison between Modified JONSWAP and measured spectrum for Hurricane
Fredrick, H =5.5 m ............................................................................................... 55

43 Comparison between Modified JONSWAP and measured spectrum for Hurricane
Fredrick, H =8.5 m ............................................................................................... 56

44 Comparison between Modified JONSWAP and measured spectrum for Hurricane
K ate, H =10.7 m ................................................................................................... 57

45 Relationship between mean wind speed and significant wave height obtained in
various hurricanes (from Ochi, 1993) .....................................................................60

46 Relationship between mean wind speed and significant wave height, Tropical Cyclone
Gloria (solid) (Ochi, 1993) and a North Atlantic Storm (hollow) (Sneider and
Chakrabari, 1973..................................................................................................61

47 Relationship between mean wind speed and fetch................................................63

48 Dimensionless wind speed as a function of dimensionless fetch (based on Ross, 1980)
........................................... ................ ...................................................65













CHAPTER 1
INTRODUCTION

The purpose of this study is to evaluate the wave spectral energy growth of

hurricane associated seas. The best approach to achieve this goal is to analyze the shape

of wave spectra obtained from measured data at various stages of hurricane growth.

However, it is difficult in practice to derive a general conclusion by evaluating the

difference in the magnitude of energy for a specified wave frequency at different stages of

growth. One way to overcome this difficulty is to evaluate the growth of wave energy

through spectral formulation. It is then necessary to have a wave spectral formulation

which represents well the wave energy spectrum throughout the growing stage of

hurricanes. A good candidate is the Modified JONSWAP formulation developed by

Foster (1982) and Ochi (1993). However, the Modified JONSWAP formulation must be

verified to confirm it is valid over the entire frequency domain of the wave energy

spectrum for hurricane generated seas.

In order to use the Modified JONSWAP formula as the basis for evaluating the

growth of hurricane associated wave spectra, it is highly desirable to examine the validity

of the spectral formulation over the entire frequency domain. The subject is discussed in

detail in Chapter 3. A brief explanation of the Modified JONSWAP formulation for

wave spectra for hurricane generated seas is given. Most importantly, the Modified

JONSWAP formula is verified throughout the entire frequency domain. Also, wave








spectral data is compared to the Modified JONSWAP formulation and to existing spectral

formulation to show how well it agrees with observed hurricane data.

Since the Modified JONSWAP formula is a function of significant wave height

and modal frequency, and the design criterion usually specified is wind speed, a method

is prescribed in Chapter 4 to estimate modal frequency and significant wave height as

functions of wind speed. And therefore, growth of hurricane wave energy spectra can be

estimated through the Modified JONSWAP formula.

Before analyzing wave energy spectra for hurricanes, it is useful to understand the

atmospheric phenomenon which give rise to the wave energy spectra. Atlantic

hurricanes, or tropical cyclones, are most often formed from tropical low pressure

disturbances leaving the West Coast of Africa. The Atlantic Hurricane Season is from

May to November. Large convective energy from warm water feeds these tropical cells

as they are carried across the Mid-Atlantic. A characteristic Coriolis driven cyclonic

rotation develops to maintain the low-pressure disturbance as the storm becomes a

tropical depression. This rotation becomes more organized, the center's atmospheric

pressure drops, and wind speed increases. Strengthening, the tropical depression is

upgraded to a tropical storm and then to a hurricane. Based on maximum wind speeds

and, to a lesser extent, on the atmospheric pressure in the eye, these storms are classified

according to the Saffir-Simpson Scale given in Table 1.

Several favorable existing environmental conditions must be in place for a

tropical disturbance to grow to hurricane strength. Hurricanes require warm ocean waters

greater then 800 F and a large negative atmospheric temperature gradient. This

temperature gradient creates an unstable condition for moist convection and drives the










Table 1 Saffir-Simpson Hurricane Scale


Type Category Damage Pressure Winds
Hg (in) mph
Depression >35

Tropical storm 39-73

Hurricane 1 minimal >28.94 74-95

Hurricane 2 moderate 28.50-28.91 96-110

Hurricane 3 extensive 27.91-28.47 111-130

Hurricane 4 extreme 27.17-27.88 131-155

Hurricane 5 catastrophic <27.17 >155


necessary massive thunderstorms which releases thermal-energy contained in the ocean

water. Hurricanes cannot exist at distances any closer to the equator then 500 km, as a

non-negligible Coriolis force is necessary to offset the low pressure disturbance. A pre-

existing near-surface disturbance with sufficient vorticity and convergence is required.

Tropical cyclones cannot be generated spontaneously. To develop, they require a weakly

organized system with sizable rotation and low level inflow.

Although large storms can create sea-severity comparable to hurricanes, there are

characteristic atmospheric features of hurricanes which differentiate them from ordinary

large Atlantic storms. The low-pressure center, maintained by a Coriolis force, induces a

high rate of cyclonic rotation, causing extreme localized wind speeds. In contrast, this

low pressure center, known as the eye, has virtually no associated wind. The strongest

hurricanes have the lowest associated central atmospheric pressure and the smallest eye








diameter. This well defined eye can be used to track the location of the storm. Although

hurricanes can effect large areas, they are a local geostrophic phenomenon, driven by

greater atmospheric forces. Low and high-pressure fronts move hurricanes at speeds in

excess of 25 knots.

In contrast to hurricanes, ordinary storms are not as well organized and do not

have an easily defined center. Consequently, their location cannot be precisely tracked.

Ordinary storms are relatively stationary and have little rotation, so they are characterized

as having quasi-steady, non-localized winds blowing in a general direction over an

established fetch length.

To design a structure to operate in hurricane prone areas, an accurate prediction of

growth of hurricane generated wave spectra at a specific location with respect to the

storm is necessary. Because of differences in atmospheric characteristics, hurricanes

cause wave spectra to grow differently than for ordinary storms. When characterizing

hurricane associated events several factors are considered, in general, including

maximum sustained winds, radius of maximum winds, central barometric pressure,

distance to the storm, speed of the storm and others. However, it has been found that

shape and growth of wave spectra are generally dependent upon mean wind speed

measured at a known distance above the sea surface and a characteristic fetch length over

which the wind is acting. It is convenient to define the fetch length as the distance from

the eye to the design location.

Since hurricanes center are rapidly moving, wind speed at a fixed location and

fetch length change rapidly. This extreme increase in wind speed and change in fetch

length have the most profound effect on hurricane wave spectra shape and growth. In






5


contrast to normal wave spectra, hurricane wave spectra have a more pronounced peak at

the modal frequency, where more energy is contained. This is due to the rapid increase

of wind speed driving the growth. Wave energy is concentrated primarily in the

neighborhood of the peak frequency during hurricanes as contrasted with the energy

spread over a wide frequency range, including double peaks, for wave spectra obtained

during ordinary storms (Ochi, 1993). Sea-severity cannot develop in the high frequency

range as quickly as wind speed. Unlike for ordinary storms, where modal frequency

clearly migrates from higher to lower frequencies during spectral growth, hurricane wave

spectra grow predominately at lower modal frequencies. There is some leftward

migration of modal frequency with growth, but it quickly becomes concentrated at a low

frequency.













CHAPTER 2
LITERATURE SEARCH

Limited research has been done on finding a mathematical representation of

hurricane wave energy spectra. Cardone, Pierson and Ward (1976), Bretschneider and

Tamaye (1976), Young and Sobey (1981), Ross and Cardone (1978) and Young (1988)

have carried out studies on hurricane-generated seas, primarily through hindcasting and

forecasting approach. These techniques provide valuable insight, but they cannot be used

to predict growth. There have been many wave spectral formulation developed to

represent sea severity, none of which predict hurricane spectra well. The Pierson-

Moskowitz (1964), the two parameter, the three parameter, the six parameter (Ochi and

Hubble, 1976) and the JONSWAP (Hasselmenn et al., 1973) are all useful for

representing ordinary wind generated seas.

Antani (1981) compared the shape of nearly 400 hurricane wave spectra to various

mathematical formulations, such as the one parameter (Pierson and Moskowitz, 1964),

the two parameter, the three parameter, the six parameter (Ochi and Hubble, 1976) and

the JONSWAP spectra (Hasselmann et al., 1973). His results showed that the six

parameter and JONSWAP most closely represent hurricane wave spectra shape. The

JONSWAP is a better candidate in that it produces a single spectrum and was developed

based on fetch limited data. It has also been suggested as the formulation of choice for

hurricanes by Lee (1980), Ross(1976), and Whalen and Ochi (1978).





7

Foster (1982) and Ochi (1993) developed a Modified JONSWAP formula. They

analyzed data from several hurricanes and represented the original JONSWAP

coefficients in terms of significant wave height and modal frequency. Ochi (1993)

compared the Modified JONSWAP formula to wave spectra data from several hurricanes

and showed that it was a good representation of the hurricane associated wave spectrum.













CHAPTER 3
SPECTRUM FORMULATION REPRESENTING HURRICANE GENERATED SEAS

As stated in Chapter 1, the Modified JONSWAP spectral formula will be used as

the basis for evaluating wave spectral growth for hurricane generated seas is to have a

wave spectral formulation which represents hurricane generated seas at various stages of

growth. The Modified JONSWAP formulation was derived based on peak energy

hurricane data and seems to represent hurricane wave spectra well. It is important to

validate the Modified JONSWAP formula over the entire frequency domain at various

stages of hurricane growth in order to determine how well it represents hurricane

generated seas.

Verification of Modified JONSWAP Spectrum


Ochi and Foster have done considerable work in determining the coefficients for

the JONSWAP spectral formulation for hurricane generated seas. A limited explanation

is provided here to outline the process used and to illustrate assumptions made during the

derivation. For a complete understanding of the determination of these parameters the

reader is directed to Foster (1982) and Ochi (1993).

The original JONSWAP formulation is given by

2 f _1)2/ 2 ,2(1 )
S(f) = a (2 exp -1.25 '[ 2


where. y = peak shape parameter, 3.30 as an average








a = 0.076 (x)-022

a = 0.07 for ooxom

fm = 3.5 (gU)(x)-033

x = dimensionless fetch = gr/U2

r = fetch length

U = mean wind speed

Foster analyzed the values of the parameters in the original JONSWAP

formulation, Equation (1), and determined functional relationships for a and the peak

shape parameter, y. The parameter a is a function of dimensionless fetch length and, due

to the rapidly changing wind speeds, is difficult to evaluate for hurricanes. However,

analysis showed a can be presented as the function of significant wave height, Hs, and

modal frequency, fm, given in Equation (2) (Foster, 1982). The constant, a, carries the

units of (sec2/meter)2.

a = 4.5H f4 (2)

The peak energy, S(fm), of the hurricane data was determined by analyzing S(fm)

as a function of Hs and found to be represented by

S(f,) = 0.75H.34. (3)

The peak energy, at f=fm, of the JONSWAP spectrum is determined from

Equation (1) and is given as









S(f) = a(2) exp(-125). (4)


From Equations (2) through (4) the peak shape parameter, y, can be shown to be a

function of significant wave height, Hs, and modal frequency, fm, as

y = 9.5H"4f, (5)

It is noted that y was determined using peak spectral energy, which is a key feature

of this derivation. Using these relationships Equation (1) can be written as a function of

co as


S(W) =( (Hg) exp{- 1.25 } H "m 22 (6)


where a = 0.07 for cocm.

Equation (6) will be referred to as the Modified JONSWAP formulation. It was

developed by determining y from data at the modal frequency. Consequently it is highly

desirable to confirm the formulation is valid over the entire frequency domain of the

spectrum through comparison with measured data.

In order to compare spectra to each other having various modal frequencies, the

frequency range for each energy density spectrum used for the current study was

normalized by dividing by modal frequency, cm. Each spectrum was then broken into

sections from om/Om=0.80 to o)/om=2.35 at intervals of 0.05. Figure 1 demonstrates the

procedure. The result gives values of spectral energy, S(co), known for each spectrum at

80% to 235% of the modal frequency, at 5% intervals. The corresponding values of








spectral energy for each co/o, are plotted versus significant wave height in Figures 2

through 34.

On each figure is a plot of the Modified JONSWAP formula at corresponding

normalized modal frequencies. The figures illustrate how well the Modified JONSWAP

formula represents hurricane data taken during the growing stage at various sea severities

(significant wave heights) throughout the frequency domain. The figures demonstrate the

utility of the Modified JONSWAP formula. Even though derived by analyzing peak

spectral energy (o)/om=1.00, Figure 6), it agrees reasonably well with values of spectra

data throughout the normalized frequency domain. Figure 27 shows even at twice the

modal frequency, the Modified JONSWAP formula adequately agrees with data. At

0/0om>2.00 the data begins to scatter but the magnitude of S(o) is substantially reduced in

comparison with that at the peak frequency.

Comparison with Wave Spectra obtained from Measured Data


Although some examples of comparison between the wave spectra obtained from wave

data during hurricanes and the Modified JONSWAP spectral formulation are given in the

references (Ochi 1993, for example) it may be of considerable interest to show

comparisons at various stages of hurricane intensities. Included in the comparisons are

the Pierson-Moskowitz and the two parameter formulations. Since these formulations

were developed for ordinary wind generated sea it may be of interest to examine how well

they represent hurricane generated sea conditions. Figures 34 through 44 show

comparison between selected data to the Modified JONSWAP formulas.
































12 - -




10









6 -___- - - - - - - - --
















0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4




Figure 1 Representative data wave energy spectrum normalized by om and analyzed
piecewise for intervals of 0/Om of 0.05



















~ U


100.00












10.00


E

U'

0.



CO

1.00












0.10


m,
____ --U--





-I-















10
Significant Wave Height, H, (
Significant Wave Height, H, (m)


1 Data Modified JONSWAP Trendline


Figure 2 Modified JONSWAP spectrum versus significant wave height for o/(Om=0.80


/


'


'"






14







100.00














10.00 -1









1.00
5/


w




















0.10
110 100
01 - -Da --- - ______ - -

Significant Wave Height, H, (m)
SData Modified JONSWAP Trendline



Figure 3 Modified JONSWAP spectrum versus significant wave height for o/0m=0.85















100.00


1 10 100
Significant Wave Height, H, (m)
Data Modified JONSWAP Trendline



Figure 4 Modified JONSWAP spectrum versus significant wave height for 0/c0m=0.90















100.00 ~














S S10.00eg


10.001~ ------- -- - ~- -------- --- -- -






1--.00 ---




















1 10
1.00 -- ---- -4 -- - -------- -- _














0.10- -


Significant Wave Height, H, (m)
N Data Modified JONSWAP Trendline


igure 5 Modified JONSWAP spectrum versus significant wave height for o/om=0.95















100.00














10.00


N0
E
-i
8



w
0)

Cl)
to

1.00














0.10


Figure 6 Modified JONSWAP spectrum versus significant wave height for o/B0m=1.00


-U






_ _- U----
























10 10
Significant Wave Height, H, (m)
Data Modified JONSWAP Trendline



























'E
100.00














10.00








) __ ------ -- -- -
0
w





1.00














0.10
1 10 100
Significant Wave Height, H. (m)

[ Data Modified JONSWAP Trendline



Figure 7 Modified JONSWAP spectrum versus significant wave height for mo/0m=1.05






19







100.00














10.0010



E

















0.10
1.00 ---- -- - - ** - -














0.10 ---- -- -------- --- ----------- - - --
1 10 100
Significant Wave Height, H, (m)
Data Modified JONSWAP Trendline



Figure 8 Modified JONSWAP spectrum versus significant wave height for co/cm=1.10


























































1 10 100
Significant Wave Height, H, (m)
E Data Modified JONSWAP Trendline


Figure 9 Modified JONSWAP spectrum versus significant wave height for 0/0m=1.15
















100.00















10.00---







IRJ I



1.00
l-5


















0.10
1 10 100
Significant Wave Height, H, (m)

SData Modified JONSWAP Trendline



Figure 10 Modified JONSWAP spectrum versus significant wave height for c/om=1.20















100.00














10.00 -



















5at -- *- -- -- ---JNWA Tedln
1.00








SData Modified JONSWAP Trendline





0.10Figure Modified JONSWAP spectrum versus significant wave height for =1.25
1 10 100
Significant Wave Height, H8 (m)

Data Modified JONSWAP Trendline



Figure 11 Modified JONSWAP spectrum versus significant wave height for /(0m=1.25

















100.00















10.00

NIN




C4
E







C) -

C-O


1.00 --
















0.10
1 10 100
Significant Wave Height, H, (m)

| Data Modified JONSWAP Trendline



Figure 12 Modified JONSWAP spectrum versus significant wave height for O/0m=1.30















100.00














10.00 -














1.00-1















1 10 100
Significant Wave Height, H, (m)
0.10 ----- ------ ---- U



Data Modified JONSWAP Trendline



Figure 13 Modified JONSWAP spectrum versus significant wave height for o/cm=1.35
















100.00















10.00

SI/




C

w





1.00 --















0.10
1 10 100
Significant Wave Height, H, (m)
I Data Modified JONSWAP Trendline



Figure 14 Modified JONSWAP spectrum versus significant wave height for 0/Am=1.40














100.00













10.00


E



C
w

t5
0
v,

uJ




1.00


U?












_ _ -U_____ _






---U--- -- -




*
/ 1


i/







=- !


10 100
Significant Wave Height, H, (m)
| Data Modified JONSWAP Trendline


Figure 15 Modified JONSWAP spectrum versus significant wave height for (o/cm=1.45















100.00














10.00-


.. I










i *















0.10
1 10 1 00
Significant Wave Height, H, (m)
Co-

1.00 -- i-




-U---









0.10
10 100
Significant Wave Height, H, (m)

SData -- Modified JONSWAP Trendline



Figure 16 Modified JONSWAP spectrum versus significant wave height for co/cm=1.50






28







100.00














10.00 -





v,
I E






(0I
MI -



1.00







01 ---- -- ---- ---------I--i-I-I





0.10
1 10 100
Significant Wave Height, H, (m)
Data Modified JONSWAP Trendline



Figure 17 Modified JONSWAP spectrum versus significant wave height for o/Om=1.55
















100.00















10.00 I--


Es ----- ---__ ---- -- _






w

t5
im



1.00 -















0.10
1 10 100
Significant Wave Height, H, (m)

a Data Modified JONSWAP Trendline



Figure 18 Modified JONSWAP spectrum versus significant wave height for Co/COm=1.60















100.00














10.00


- -- - -

E









1.00














0.10
10 100
Significant Wave Height, H, (m)
Data --Modified JONSWAP Trendline



Figure 19 Modified JONSWAP spectrum versus significant wave height for O/(Om=1.65
2 ~ ~ ~ - -- -- --- -- --- -- __-- -












0.10 ---- ----- ---- ---- -- - -







Figure 19 Modified JONSWAP spectrum versus significant wave height for o)/I0m=1.65






31







10.00 -












7'




--*/--- -

1.00=




U














0.10
1 10 100
Significant Wave Height, H, (m)
0 Data Modified JONSWAP Trendline


Figure 20 Modified JONSWAP spectrum versus significant wave height for o/cm=1.70
Ug





















Figure 20 Modified JONSWAP spectrum versus significant wave height for C0/Cm=1 .70






32








10.00



















S11 N11
NI



















0.10
u5.5
^ 1 0 __- _ ^ _-------- -



















1 10 100
Significant Wave Height, H, (m)

SData Modified JONSWAPTrendline



Figure 21 Modified JONSWAP spectrum versus significant wave height for (o/om=1.75












10.00























0.10
II
























110 100
SData -ModifiedJONSWAPTrendline
u -II
C" ,/



I-











1 10 140
Significant Wave Height, H8(i)
,, ---- -- L c _---- _
uj "____ _____"_
a~~~~~ |z- ~T"~. -














0.10 ---- -----------





Figure 22 Modified JONSWAP spectrum versus significant wave height for o/Cm=1.80
















10.00



















'8




w
vi,









0.10








0.10


F-U
"II


----- ---__ _-_- ---- ---- - ---_

----- -- -J- -- --- ---- --- ---
"/













10 10
Significant Wave Height, H, (m)


Data Modified JONSWAP Trendline



Figure 23 Modified JONSWAP spectrum versus significant wave height for o/cm=1.85





































N'
v1


1.oo

w
I,
uL

o


1 10 100
Significant Wave Height, Hs (m)

S Data Modified JONSWAP Trendline



Figure 24 Modified JONSWAP spectrum versus significant wave height for o/cOm=1.90
















10.00


















> I q
ii '*


1.00 ---



C,

















0.10--
1 10 100
Significant Wave Height, H, (m)

Data -- Modified JONSWAP Trendline



Figure 25 Modified JONSWAP spectrum versus significant wave height for a0/0m=1.95














10.00













-I

CI

iil

S1.00 --
& -----U-------

















0.10

1 10 100
Significant Wave Height, H, (m)
Data Modified JONSWAP Trendline


Figure 26 Modified JONSWAP spectrum versus significant wave height for oC/cOm=2.00















10.00
















N I



o 1.00 --L
4)1
LLI
-s -- Utt- -- ---













Data -Modified JONSWAP Trendline-





0.10Figue 27 M d JP s m v s st w e h t fr
1 10 100
Significant Wave Height, H. (m)
Data Modified JONSWAP Trendline



Figure 27 Modified JONSWAP spectrum versus significant wave height for G)/am=2.05
















10.00





















U)
p 1.00 ----l
w












0.10









1 10 100
Significant Wave Height, H, (m)

SData ---Modified JONSWAP Trendline



Figure 28 Modified JONSWAP spectrum versus significant wave height for co/o0m=2.10














10.00















1 n



~ 1.o00o

SH LI
















0.10
1 10 100
Significant Wave Height, H. (m)
I Data -- Modified JONSWAP Trendline


Figure 29 Modified JONSWAP spectrum versus significant wave height for o/0m=2.15















10.00


E

E/ *


) ___I_______
o1 .oo0




0..







0.10 ---









1 10 100
Significant Wave Height, H. (m)
SData Modified JONSWAP Trendline



Figure 30 Modified JONSWAP spectrum versus significant wave height for co/m=2.20






42








10.00


















(D

t 1.00
wm





i/


u i









0.10 -
1 10 100
Significant Wave Height, H, (m)
Data Modified JONSWAP Trendline



Figure 31 Modified JONSWAP spectrum versus significant wave height for o/Om=2.25















10.00

















E

i m

S1.00 I -
c ------- U .--




















0.10-
1 10 100

Significant Wave Height, H, (m)
S Data -Modified JONSWAP Trendline



Figure 32 Modified JONSWAP spectrum versus significant wave height for co/tom=2.30
UI

II
UI

0.10 H II _____ -
1 10 10
SiniicntWae eiht H1(n
I aa-MdiidJNWA rnln


Fiue3 odfe OSWPsetumvru igiiatwaehih1fr0023






44








10.00
















E


CO

l-oo ---








I I
7E
L. ___---__s f -----_



















0.10
1 10 100
Significant Wave Height, H, (m)

a Data --Modified JONSWAP Trendline



Figure 33 Modified JONSWAP spectrum versus significant wave height for co/(m=2.35








The Pierson-Moskowitz and the two parameter spectra have been included to show how

well they represent hurricane generated wave spectra.

The two parameter and Modified JONSWAP both require a given modal

frequency and significant wave height. For the plots in Figure 34 through 44 the

corresponding modal frequency from the data presented in the figure is used. For this

reason the two parameter and Modified JONSWAP have the same modal frequency as the

data. On the other hand, the Pierson-Moskowitz formula requires only significant wave

height. Modal frequency is then a function of significant wave height.

Wave spectra data for hurricane Belle (Figures 34 through 36) and Gloria

(Figures 37 and 38) are similar in that both storms grew after several days of moderate

sea severity. For Belle at a significant wave height of 3.2m (Figure 34), a second peak

can be seen at 1 rad/sec. This represents a significant preexisting sea severity before the

hurricane. As the hurricane grows to a significant wave height of 6.1m (Figure 35) and

then to 7.1m (Figure 36) this second peak becomes small in comparison to the energy

contained at the modal frequency. As Gloria grows from a significant wave height of

6.0m (Figure 37) to 8.1m (Figure 38) a similar second peak is present and then

disappears because of energy associated with the hurricane dominates the energy pre-

existing in the spectrum.

Gloria at a significant wave height of 8.1m shows a good comparison between the

Pierson-Moskowitz, the two parameter and the Modified JONSWAP. Before Gloria

passed the NOAA buoy, a continues wind of 7-11 m/s blew for 10 days so the sea had a

sufficient amount of time to be fully developed (Pierson et al., 1958). Consequently, at

this stage in the growth of Gloria, the Pierson-Moskowitz formula predicts the same








modal frequency as the data, but slightly under predicts the shape of the spectra and

maximum energy. The two parameter formula gives similar results. Belle and Gloria

both grow significantly at their modal frequencies, which are concentrated in the lower

end of the frequency domain.

The wave spectral growth of Eloise from a significant wave height of 5.6m

(Figure 39) to 8.8m (Figure 40) shows a similar trend as that of Fredrick from 4.5m

(Figure 41) to 5.5m (Figure 42) and then to 8.5m (Figure 43). They exhibit growth

predominantly at the modal frequency, again located at lower frequencies. In all stages of

growth for all storms, the data shows spectra with a sharp peak at the modal frequency

which is represented well by the Modified JONSWAP formula. This peak becomes more

pronounced at higher significant wave heights which can be seen in Kate at a significant

wave height of 10.7m (Figure 44).

Plotting individual spectra shows the obvious advantage of using the Modified

JONSWAP formula to represent wave spectra for hurricane generated seas, as it

represents maximum energy and shape reasonably well at various hurricane intensities.

The figures show that the Pierson-Moskowitz and two parameter formulas both under

predict maximum values and give an extended shape at the modal frequency. The

Pierson-Moskowitz and two parameter formulations do not, in general, represent

hurricane generated sea state.










2.0
Belle
8/9/76
0:00 Modified
1.8 Hs=3.2m JONSWAP


Parameter

1.6



1.4


N
E 1.2 Pierson-
SMoskowitz
CO

2 1.0



I 0.8



0.6 o-



0.4-



0.2



0.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Frequency, o (rad/sec)



Figure 34 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Belle, H,=3.2 m





















7.0-




6.0-


E

CO
S5.0

E
2

I5 4.0

2)
-



3.0-




2.0




1.0




0.0
0.3


0.9 1.0 1.1


Figure 35 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Belle, Hs=6.1 m


0.4 0.5 0.6 0.7 0.8
Frequency, co (rad/sec)






49



14.0

Belle
8/9/76 o
6:00
Hs=7.1m
12.0
Modified
JONSWAP



10.0
o kowitz
Two Parameter



8.0












4.0





2.0





0.0-
I-



















0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Frequency, eo (rad/sec)



Figure 36 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Belle, Hs=7.1 m










8.0
Gloria o Modified
9/26/85 /\JONSWAP
7:00
Hs=6.0l Parameter
7.0

Pierson-
oskowitz

6.0





5.0
N




2 4.0






2.0
oo
Lu 3.0 o-

0
0

2.0 O





1.0





0.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Frequency, w (rad/sec)



Figure 37 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Gloria, H,=6.0 m










18.0



Modified
16.0
Gloria
9/26/85
14:00 o
Hs=8.lm
14.0 Parameter

Pierson-
Moskowitz

12.0


E
3 10.0




t 8.0
CO















2.0
0.0-
LU6.0------------P----------








00 00



2.0 ---- 0---------------------



0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Frequency, co (rad/sec)



Figure 38 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Gloria, H,=8.1 m










7.0
Eloise Modified
9/22/ JONSWAP
22:00
Hs=5.6m

6.0-


erson-
skowitz

5.0
5. Two arameter



N
4.0





3.0
a-




2.0





1.0





0.0
0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Frequency, o (rad/sec)



Figure 39 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Eloise, Hs=5.6 m










25.0



Eloise
9/23/75
1:00 Modified
Hs=8.8m JONSWAP
20.0



Piers n-
os


S15.0


T Parameter
E



S10.0







5.0







0.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Frequency, c (rad/sec)



Figure 40 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Eloise, H,=8.8 m










4.5


Modified
JONSWAP
4.0
Fredrick
9/11/79
12:00
Hs= 4.5m
3.5


iersor& oskowitz

3.0
T Parameter



j2.5




w 2.0




1.5




1.0




0.5




0.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Frequency, o (rad/sec)



Figure 41 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Fredrick, Hs=4.5 m










7.0

Fredrick
Modified
9/11/79
5:0 AJONSWAP
15:00
Hs=5.5m a
6.0



person
skowi
5.0


SParameter

N
4.0


2


> 3.0





2.0






1.0





0.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Frequency, o (rad/sec)



Figure 42 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Fredrick, Hs=5.5 m








20.0


18.0 Modified
Fredrick JONSWAP
9/11/79
22:00
16.0 Hs=8.5m
16.0\
Pie son

14.0

T Parameter






S) 8.0 -"-- t -- \ \ A--------------


i--v--



4.0 -----------N -------
12.0






10.0





4.0






0.0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3
Frequency, a (rad/sec)


Figure 43 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Fredrick, Hs=8.5 m
Hurricane Fredrick, H=8.5 mn










35.0



Modified
ONSWAP
30.0
o\ Kate
S 11/20/85
Piers n- 117:00
osk tl Hs=10.7m


25.0



ST Parameter

20.0




15.0






10.0
10.0





5.0





0.0 1
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1
Frequency, co (rad/sec)



Figure 44 Comparison between Modified JONSWAP and measured spectrum for
Hurricane Kate, H,=10.7 m













CHAPTER 4
ESTIMATION AND PREDICTION OF HURRICANE WAVE SPECTRUM GROWTH

This chapter discusses a method for estimating the growth of sea severity

(significant wave height) and modal frequency when a hurricane is approaching a specific

location from knowledge of wind speed at that location and distance to the storm. The

method will provide significant information for design of offshore structures. As

presented in the previous chapter, hurricane-generated are represented by the Modified

JONSWAP formula given as a function of significant wave height and modal frequency.

For design use, these parameters will be presented in terms of wind speed.

Estimation of significant wave height


Ordinary storms are relatively stationary and associated wind speeds change at a

much slower rate and blow over an established quasi-steady fetch length. Wind-

generated seas in hurricanes differ from ordinary storms in that the hurricane is moving

from 5 to 12 knots with respect to a specific location. This causes a high rate of change

of wind speed blowing over a rapidly changing fetch. Ochi (1993) addressed this topic

and developed wind speed-sea severity functional relationships for two cases; the

growing stage of hurricane-generated seas in which the wind speed is increasing at an

extremely high rate but the sea severity was comparatively moderate because the sea

condition prior to the hurricane was very mild, the second is the sea condition resulting








from continuous winds of mild severity blowing for one week or longer then followed by

a storm, usually a tropical storm which has a wind speed much less then a hurricane.

For an extremely high rate of increase in wind speed following a very mild sea,

analysis shows an almost linear increase in sea severity with increase in wind speed. The

significant wave height during the growing stage of the hurricane is a function of mean

wind speed at a 10-meter level given as Equation (7) and presented in Figure 45.

H. = 0235U10 (7)

For a tropical storm following continues mild winds blowing for one week or

longer, sea severity increases rapidly with increase in wind speed. The significant wave

height-wind speed relationship seems to be approximated by Equation (8) and is

presented in Figure 46. Equation (8) is derived from the Pierson-Moskowitz formulation

corrected for a wind speed at a 10-meter height and making a narrow-band assumption.

H, = 0.237(U'0/g) (8)

Note that the Pierson-Moskowitz spectral formulation is only applicable to fully

developed seas. For the sea to become fully-developed at high wind speeds and

corresponding large significant wave heights, a significantly long duration is needed

(Pierson-Moskowitz, 1964). For example, 42 hours is required for a Uio of 20 m/s.

Hurricanes do not behave in this manner. Therefore even though the significant wave

height-wind speed relationship for the tropical storm close to that given in Equations (8).

The shape of the spectrum is different from that of the Pierson-Moskowitz spectrum. For

large wind speeds associated with hurricanes, U1o>33 m/s, Equation (8) would predict

unrealistically high significant wave heights which observation does not support.






60











60
SELOISE /
A FREDERIC
v ANITA
BELLE (100 KTS)-
50- o KATE -,
a CARMEN
CAMILLE
( ]SEVEREST
WIND SPEED
40 /*_"ZZ ------ -- ^ -----
0 (75 KTS) --H


| 3 -----------^ -------- -----

W E9
o ] Ol- HURRICANE

0) 0e o
o *0
20 -


%" % FULLY DEVELOPED SEA

10 ---





0 2 4 6 8 10 12 14
SIGNIFICANT WAVE HEIGHT IN M




Figure 45 Relationship between mean wind speed and significant wave height obtained in
various hurricanes (from Ochi, 1993)
























20


w FULLY DEVELOPED SEA
cL
0

1 o


//




0 4 8 12 16
SIGNIFICANT WAVE HEIGHT IN M






Figure 46 Relationship between mean wind speed and significant wave height, Tropical
Cyclone Gloria (solid) (Ochi, 1993) and a North Atlantic Storm (hollow) (Sneider and
Chakrabari, 1973








In summary, Equation (7) should be used to estimate significant wave height from

knowledge of wind speed at a specified location. Equation (8) applies to specific cases

involving tropical storms following several days of steady mild wind. However, it

predicts unrealistically high significant wave heights at wind speeds associated with

hurricanes.

Prediction of modal frequency


The method given here to predict a trend in change in modal frequency with

respect to wind speed is useful in representing growth of hurricane spectra. Unlike for

fully developed conditions, where modal frequency is directly related to significant wave

height, a modal frequency-significant wave height relationship is difficult to establish for

hurricane associated wave spectra. However, a relationship can be found by first

estimating the relationship between fetch length and wind speed. Then modal frequency

can be estimated through obtaining the relationship between wind speed and modal

frequency.

Figure 47 is a plot of fetch length versus wind speed for the various hurricanes

considered in this study. It shows a general fetch length wind speed relationship trend

given by Equation (9).

r = 5.4x107U;U (9)

At small fetch lengths there is a small but finite wind speed. As fetch length

decreases wind speed increases. At large wind speeds fetch length approaches 10 km, a

good approximations of the eye diameter, where wind speed is a maximum. Specifying

wind speed yields a theoretical fetch length.










500,000
0


450,000



400,000

-01-
0
350,000


0




-250,000 --' ----------- ---
300,000


0








150,000 : : :




100,000 A o
50,000 5
S. I i i r


100,000 --0---



50,000 ----------B 4^,------r=5E





10 20 30 40
Wind Speed, U10 (m/s)

o Belle u Eloise A Fredrick o Gloria a Kate


Figure 47 Relationship between mean wind speed and fetch








Next, the relationship between fetch length and modal frequency of hurricane

associated wave spectra is discussed. Ross (1976) developed a relationship between the

dimensionless modal frequency, u, and the dimensionless fetch, 6, from the analysis of

three storms. This is given in Equation (10). Data considered in the present study

compares well to this relationship. Figure 48 is a plot of data and Equation (10), which

shows good agreement.

o = 0.97.2'1 (10)

where
wUo
1-
27rg
rg
U210
U'10
Thus, from Equation (9) and (10) it is possible to estimate the modal frequency of

hurricane associated wave spectra from knowledge of wind speed.

Estimation of hurricane wave spectrum growth


Hurricane wave energy spectra growth for various wind speeds is now estimated.

The following procedure may be used to estimate Hs and com needed for the Modified

JONSWAP formula; 1) Specify Uo1, 2) calculate H, using Equation (7), 3) calculate r

using Equation (9), and 4) knowing Ulo and r, calculated om using Equation (10).

Figure 49 is a plot of hurricane energy spectrum, S(co), for wind speeds from

20m/s to 60m/s and is useful in showing a trend in spectral growth. The plot shows the

characteristics of hurricane spectral growth. Modal frequency is concentrated at lower

values throughout growth and most growth takes place at the modal frequency.











1.00 I I








L ----- : I ,
u=.974-.21











: i P ! i :




0 1 ; ; : : .. 0 .1 . o
S 43


0)


0.10
:o0P
fo
0-









i f










0.01
10 100 1,000 10,000 100,000

r,=rg/Uo2
o Belle 0 Eloise A Fredrick o Gloria a Kate


Figure 48 Dimensionless wind speed as a function of dimensionless fetch (based on Ross,
1980)










60 -- =60 m/s
H=14.1 m





50
0=55 m/s
s=12.9 m




40
10=50 m/
s=11.8 m




30 -I =45 m/
S30
S//10.6
2





20


s 8.



10






0
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1
Frequency, w (rps)


Figure 49 Predicted hurricane spectrum growth showing mean wind speed and

corresponding significant wave height









To show the growth of the wave spectra with respect to significant wave height,

the Modified JONSWAP formula is differentiated with respect to significant wave height





(2)4H, exp 1.25 H. 4m


x 2 + 0.34exp (CL- if 2&}

showing growth is proportional to significant wave height at m=mm as,


SCO H1.34

and at co>> m as,


oc H.

Clearly, hurricane spectral growth occurs most predominantly at the modal

frequency.













CHAPTER 5
CONCLUSIONS

This study dealt with evaluating wave spectra energy growth for hurricane

generated seas at various stages of intensities to develop a mathematical formulation

representing a trend in the growth of the wave energy spectrum. Since it is difficult to

derive a general conclusion by evaluating the difference in the magnitude of energy for a

specified wave frequency at different intensities from analysis of spectra obtained from

field data, a mathematical formula is needed which represents hurricane wave spectra at

various stages of growth. The Modified JONSWAP formula is a good candidate, but

needed to be verified over the entire frequency domain. In Chapter 3, it was verified

throughout the frequency domain by comparison to hurricane wave spectra from

measured data and was shown to represent the wave spectrum associated with hurricane

generated seas for various stages of intensity.

The Modified JONSWAP formula is a function of significant wave height and

modal frequency. To use it to present a trend in the growth of the wave spectrum,

mathematical relationships were presented in Chapter 4 to present significant wave height

and modal frequency as functions of wind speed. Using these relationships a plot of the

trend in growth of the wave energy spectrum was given for wind speeds of 20 to 60 m/s.

The plot shows the characteristics of hurricane wave spectrum growth. Modal frequency

is located at lower values throughout and is where most growth takes place.








APPENDIX


DATA

General

The data used for this study were taken from National Oceanographic and

Atmospheric Administration's (NOAA) Data Buoys. Atmospheric and oceanographic

data has been collected by NOAA Data Buoys since the early 1970's. They are generally

located in deep water locations and collect a wide variety of atmospheric and general

oceanographic data in addition to wave data. Steele and Johnson (1977) describe the

payload and operation of the buoys. There is considerable information at the NOAA

world wide web homepage at http://www.nhc.noaa.gov. The data used consists of an

hourly energy density spectrum, significant wave height determined by integration, and

wind speed for five Atlantic and Gulf of Mexico hurricanes. The purpose of this study is

spectral growth, so the data was generally reduced to reflect increasing significant wave

height with increasing wind speed. Hurricane path information was obtained at

http://www.nhc.noaa.gov/tracks.html Following are narratives taken from yearly

NOAA Mariners Weather Logs for each storm considered.

Hurricane Belle (August 9, 1976) (Mariners Weather Log, 1977)


Belle reached hurricane strength at 1800 on 7 August, 1976 as it moved across the

Atlantic in the trade wind belt just east of the Northern Bahamas. Belle's maximum

strength was attained on August 9 with sustained winds of 105 knots and a minimum sea

level pressure of 957 mb. While moving northward, parallel to the U.S. East Coast, Belle








passed almost directly over NOAA buoy EB 15 (32N, 75.20W). The largest significant

wave height measured was 7.1 m with a wind speed of 30.7 m/s. Belle made landfall on

1000 on August 10 on southern Long Island with sustained winds of 65 knots and

minimum pressure of 980 mb. Belle caused tides three feet above normal and four to five

inches of rainfall into the mountains of New England. Five fatalities were associated

with Hurricane Belle.

Hurricane Eloise (September 22-23, 1975) (Mariners Weather Log .1976)


The disturbance from which Eloise formed left the African coast on September 6.

Winds reached tropical strength early on September 16. Eloise intensified rapidly and

reached minimal hurricane strength before it struck the northeastern coast of the

Dominican Republic. Fifty-nine deaths occurred in the area, with 34 in Puerto Rico; and

damage was estimated at $60 million. Rainfall amounts of 10-20 inches were common

over eastern and southeastern Puerto Rico. Eloise weakened as it tracked westward

across the mountains of Hispanola and eastern Cuba. By 19 September Eloise was barely

a tropical storm as it passed over the Yucatan.

Eloise began a steady strengthening north of the Yucatan Peninsula, regaining

hurricane force in the central Gulf of Mexico about 350 miles south of New Orleans on

the morning of 22 September. At 0300 on 23 September the eye passed within 10 miles

of NOAA buoy EB10 (27.50N, 88.00W). The largest significant wave height measured

was 8.8 m with a wind speed of 35.1 m/s. It continued to strengthen as it reached landfall

midway between Fort Walden Beach and Panama City, Florida, shortly after 1200 on 23

September. A sustained wind near 80 knots with a gust to 135 knots was measured on a








98 foot tower 13 miles offshore. Hurricane tides of 12 to 16 feet were measured. Four

deaths in Florida were indirectly attributed to Eloise. The hurricane caused $500 million

in loss of property and crops in Florida, Alabama and over the northeastern U.S. due to

flooding.

Hurricane Fredrick (September 11-12, 1979) (Mariners Weather Log, 1980)


Fredrick was the first hurricane to strike Mobile, Alabama directly since 1926.

The central pressure of 946 mb and maximum sustained winds of 115 knots made

Fredrick the most intense hurricane to affect Mobile this century. The highest wind

reported in the U.S. was a gust to 126 knots on Dauphin Island bridge in Alabama. The

peak storm surge of 12 feet over Gulf Shores, Alabama destroyed most of the Island. An

11 foot surge destroyed the Dauphin Island causeway. Five deaths were attributed to

Fredrick. The estimated damage totaled $2.3 billion. Data were obtained from NOAA

buoy 42003 (26.00N, 86.00W). The largest significant wave height measured was 8.9 m

with a wind speed of 37.0 m/s.

Hurricane Gloria (September 25-26, 1985) (Mariners Weather Log, 1986)


Gloria had its start near the Cape Verde Islands on 16 September. On 22

September, hurricane Gloria turned to the northwest as it approached the Leeward

Islands. The hurricane weakened as it passed Cape Hatteras after midnight on 27

September. Ten hours later, Gloria crossed western Long Island, New York and emerged

back over the open waters of the far North Atlantic. As Gloria again approached the East

Coast of the U.S. it passed within 60 miles of the NOAA buoy 41002 (32.30N, 75.30W) at








2000 on 26 September. The buoy measured a significant wave height of 14.3 m with a

wind speed of 25 m/s.

Hurricane Kate (November 20, 1985) (Mariners Weather Log, 1986)


Development of Kate began just northeast of the Virgin Islands when a weak

tropical wave began to interact with an upper air trough on 13-14 November. The

tropical storm began moving in a general westerly direction and reached hurricane

strength by 1800 on 16 November. Kate moved onto the north central Cuban coast on the

19th and emerged over the waters of the southeastern Gulf of Mexico. It passed the

NOAA buoy 42003 (26.00N, 86.0W) at 1700 on 20 November. The largest significant

wave height measured was 10.7 m with a wind speed of 47.3 m/s. Kate weakened

slowly before making landfall near Mexico Beach, Florida on 21 November.














LIST OF REFERENCES


Antani, J. K. (1981), "Mathematical Representation of Hurricane Associated Wave
Spectra," UFL/COEL-81/007, University of Florida, Gainesville.

Bretschneider, C. L., and Tamaye, E. (1976), "Hurricane Wind and Wave Forecasting
Techniques," Fifteenth Coastal Engineering Conference, American Society of
Civil Engineers, New York, pp. 202-237.

Cardone, V. J., Pierson, W. J., and Ward, E. G. (1976), "Hindcasting the Direction
Spectra of Hurricane-Generated Waves," Journal of Petroleum Technology, Vol.
28, 1976, pp. 385-394.

Foster, E. R. (1982), "JONSWAP Spectral Formulation Applied to Hurricane-Generated
Seas," UFL/COEL-81/004, University of Florida, Gainesville.

Hasselman, K., Barnett, T. P., Bouws, E., Carlson, H., Cartwright, D. E., Enke, K.,
Ewing, J. A., Gienapp, H., Hasselmen, D. F., Kruseman, P., Meerburg, A.,
Muller, P., Olbers, D. J., Richter, K., Sell, W., and Walden, H. (1973),
"Measurements of Wind-Wave Growth and Swell Decay during the Joint Sea
Wave Project (JONSWAP)," Deutsches Hydrographisches Institut, Hamburg.

Lee, Y. Keen (1980), "Hurricane Eloise Wave Spectra," Coastal Engineering, Vol. 4, pp.
151-156.

National Oceanographic and Atmospheric Administration, Mariners Weather Log (1976),
"Hurricane Eloise, September 13-24," Vol. 20, No. 2, p. 69.

National Oceanographic and Atmospheric Administration, Mariners Weather Log (1977),
"Hurricane Belle, August 6-10," Vol. 21, No. 2, p. 65.

National Oceanographic and Atmospheric Administration, Mariners Weather Log (1980),
"Hurricane Fredrick, August 29 September 14," Vol. 24, No. 2, p. 100.

National Oceanographic and Atmospheric Administration, Mariners Weather Log (1986),
"Hurricane Gloria, September 16 October 2," Vol. 30, No. 1, p. 9.

National Oceanographic and Atmospheric Administration, Mariners Weather Log (1986),
"Hurricane Kate, November 15-23," Vol. 30, No. 1, p. 11.








Ochi, M. K. (1993), "On Hurricane-Generated Seas," Proceedings Second Symposium
on Ocean Wave Measurement and Analysis, American Society of Civil Engineers,
pp. 374-387

Ochi, M. K. and Hubble, N. E. (1976), "Six-Parameter Wave Spectra," Proc. Fifteenth
Coastal Engineering Conference, American Society of Civil Engineers, Honolulu,
Hawaii, July 11-17.

Pierson, W. J. and Moskowitz, L. (1964), "A proposed Spectral Form for Fully
Developed Wind Seas Based on the Similarity Theory of S.A. Kitaigorodski,"
Journal of Geophysical Research, Vol. 69, No. 24, pp. 5181-5190.

Pierson, W. J., Neuman, G., and James, R. W. (1958), "Observing and Forecasting Ocean
Waves by Means of Wave Spectra and Statistics," U.S. Navy Hydrographic Office
Publication No. 603.

Ross, D. (1976), "Observing and Predicting Hurricane Wind and Wave Conditions,"
Seminar on Ocean Products and IGOSS Data Processing and Services System
(IDSS), Moscow, U.S.S.R, April 2-11.

Ross, D. and Cardone, V. J. (1978), "A comparison of Parametric and Spectral Hurricane
Wave Prediction Products," in Turbulent Fluxes through the Sea Surface, Wave
Dynamic, and Prediction, Plenum Press., New York.

Sneider, R. H. and Chakrabari, S. K. (1973), "High Wave Conditions Observed Over the
North Atlantic in March 1968," Journal of Geophysical Research, Vol. 78, No. 36,
pp. 8793-8807.

Steele, K. and Johnson, A. Jr. (1979), "Data Buoy Wave Measurements," in Ocean Wave
Climate, Plenum Press, New York, 1979.

Whalen, J. E. and Ochi, M. K. (1978), "Variability of Wave Spectra Shapes Associated
with Hurricanes," Offshore Technology Conference, Paper No. 3228, Houston,
Texas, May 6-8.

Young, I. R., (1988), "Parametric Hurricane Wave Prediction Model," Journal of
Waterway, Port, Coastal and Ocean Engineering, Vol. 114, No. 5, 1988, pp. 637-
652.













BIOGRAPHICAL SKETCH


William Scott Finlayson was born on December 27, 1969, in Alamogordo, New

Mexico and grew up in Arizona and New Mexico. He attended New Mexico State

University in Las Cruces and received a Bachelor of Science degree in mechanical

engineering in May 1991. He entered the Navy through the Navy Civil Engineer

Collegiate Program in 1989 and received his commission through Officer Candidate

School in Newport, Rhode Island, in November 1991.

After attending Civil Engineer Corps Officer School in Port Hueneme,

California, he was assigned to Marine Corps Air Station Iwakuni, Japan as the Facilities

Maintenance Officer and later as the Maintenance Control Officer, from April 1992

through April 1994. LT Finlayson reported to Naval Mobile Construction Battalion

SEVEN, Gulfport, Mississippi in April 1994 and served as Officer in Charge for Details

deployed to Sasebo, Japan, and El Salvador. He was assigned to the University of Florida

in September 1996 as part of the Civil Engineer Corps Ocean Facilities Program of the

United States Navy and will received a Master of Science degree in coastal and

oceanographic engineering in December 1997.




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