ADAO90 342 DAVID W TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CE-ETC F/9 13/10

MODIFIED JONSWAP SPECTRUM DEPENDENT ONLY ON WAVE HEI HT AND P-ETC(U)NAY 80 V T LEE, S L BALES

UNCLASSIFIED DTN SRDC/O-0918-010 NL

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1111.2.5 _____ ___V P N..'

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I

- DAVID W. TAYLOR NAVAL SHIP7 a

RESEARCH AND DEVELOPMENT CENTERBetheda, Maryland 20084

A MODIFIED JONSWAP SPECTRUM DEPENDENT ONLY

ON WAVE HEIGHT AND PERIOD

2 by

a Wah T. Leez< andI Susan L. Bales

APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITEDz

a

>-

SHIP PERFORMANCE DEPARTMENTCILC-

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53

I-cJo

LLJ0

a My18 DTNSRDC/SPD-09 18-011 o My18

cmi

NO OCB60230 2I)

r4

4

MAJOR OTNSRDC ORGANIZATIONAL COMPONENTS

DTNSRDC

COMMANDER 00

TECHNICAL DIRECTOR01

OFFICER-IN-CHARGE OFFICER-IN-CHARGECARDEROCK ANNAPOLIS

051 04

SYSTEMSDEVELOPMENTDEPARTMENT

11

SHIP PERFORMANCE AVIATION AND

DEPARTMENT SURFACE EFFECTSDEPARTMENT

15 16

COMPUTATION,STRUCTURES MATHEMATICS ANDDEPARTMENT LOGISTICS DEPARTMENT

17 18

SHIP ACOUSTICS PROPULSION ANDDEPARTMENT AUXILIARY SYSTEMS

DEPARTMENT19 27

SHIP MATERIALS CENTRALENGINEERING INSTRUMENTATIONDEPARTMENT DEPARTMENT

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N

"Development of Consistent Natural Environment Parameter Sets for CombantantCapability Assessment (CCA)," by Lee and Bales, Report DTNSRDC/SPD-0795-02 (Mar 1980)

Errata

1. P. 7 - fourth line in second paragraph should read "Li and Xi are latitude and 4

longitude in degrees, respectively"

T!DAVID W. TAYLOR NAVAL SHIP RESEARCH ANNAPOLIS LABORATORY

AND EVELPMET CETERANNAPOL S. MO 21402AND DEVELOPMENT CENTER CARDEROCK LABORATORYHEADQUARTERS BETHESDA. MO 20084

BETHESDA, MARYLAND 20084 IN REPLY REFER TO:J* 1568:WTL

560513 August 1980

From: Commander, David W. Taylor Naval Ship R&D Center

To: Commander, Naval Sea Systems Command (Code 32R)

Subj: Forwarding of Report

Ref: (a) Ship Seakeeping Research and Development Program NAVSEA SF 43 421 202

Encl: (1) DTNSRDC Ship Performance Department Report DTNSRDC/SPD-0918-01, "AModified JONSWAP Spectrum Dependent Only on Wave Height and Period,"by W.T. Lee and S.L. Bales, May 1980 (2 copies)

1. In accordance with reference (a), enclosure (1) is forwarded for yourinformation and retention.

GRANT R. HAGENBy direction

Copy to:Initial Distribution List

-- LJK.

UNCLAS SI F IEDSECURITY CLASSIFICATION OF THIS PAGE (When Date Entered)

iREPORT DOCUMENTATION PAGE READ INSTRUCTIONSREPORT_______________PAGE_ BEFORE COMPLETING FORM

I. REPORT NUMER GOVT ACCESSION No. 3. RECIPIENT'S CATALOG NUMBER

TNSRDC/SPD-0918-1jt TITLErr-w5rsmv- -- $. TYPE Of REPORT & PERIOD COVERED

,A MODIFIED J SPECTRUM DEPENDENT ONLYON'1A IEIGHT AND PERIODS , Ina I .,

SPERFORMING D REPORT NUMBER

7. AUTNOR(s) . CGW!RACT OR GRANT NUMUER(a)

ah T. Lee Susan ,./ales

PERFORMING ORGANIZAtION NAME AND ADDRESS .PR07'.r -

Ship Performance Department AREA 4 WORK UNIT NUMBERS

David W. Taylor Naval Ship R&D Center (See reverse side)Bethesda, Maryland 20084

11. CONTROLLING OFFICE NAME AND ADDRESS REPORT VATE

Naval Material Command mmy §8CWashington, D.C. 20360 13. NUMBER L

14. MONITORING AGENCY NAME A AODRESS(I, different from Controlling OfIce) IS. SECURITY'-LASS. (of this report)

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IS. SUPPLEMENTARY NOTES

IS. KEY WORDS (Conlnue on reveres le If necessar ad lftsfI ft block rtmiber)

JONSWAP Spectrum HindcastSpectral Ocean Wave Model (SOWM)FetchWave EnergySpectral Dens ity

20. ABSTRACT (Continue an reveres esie It necoesr a" Idellif by block number)

--- For simplicity as well as consistency with the current state-of-the-artin seakeeping performance assessment, a wave spectral formulation for fetch-limited ocean areas which is dependent only on the significant wave heightand modal wave period Is desirable. A modified version of the JONSWAPspectrum is therefore derived, but as Is the case with the usual fetch-dependent JONSWAP spectrum, It contains too much energy for fetches above

(Continued on reverse side)Do IOA 1473 EDITION OF I NOVSOOTE CLASSIFD

JNsN o1o2-L.0.o6,. UNCLAS S IFI EDSECURITY CLASSIFICATION Of TNIl PAGE ( e ofl MoIds)

L- 4 ',

UNrLASSIFIFDSECUNITY CLASSIFICATION OF THIS PAGE () tea Dma Knaeo,.

(Block 10)

Project Number 62543NJk Nu.mb.er% SF 43 421 202 and SF 43 421 001Work Unit Numbers 1504-100 and 1500-104

(Block 20 continued)

- about 40 nautical miles. This inconsistency is probably due to certainparameter relationships which are all based on least squares fits.Therefore, a new parameter,J_< is developed to replace the usualparameter, correcting for the parameter's nonuniversality.

/

'

UNCLASSIFIEDSECURITY CLASIFICATION OF THIS PAGEf(bhe DArn at

I"I

• ..++, 4

TABLE OF CONTENTS

Page

LIST OF FIGURES ..... ..... ........................... III

LIST OF TABLES ..... .... ........................... ... ivNOTATION . . . . . . . . . . . . . . . vF

ABSTRACT .... ..... .. .............................. .. ..

ADMINISTRATIVE INFORMATION .... ... ..................... . ...

INTRODUCTION .... ..... .... ........................... I

MODIFICATION OF THE JONSWAP SPECTRUM ..... ... ................ 2

0 PARAMETER ..... .... .... ............................. 5

APPLICATIONS OF THE MODIFIED JONSWAP SPECTRUM ...... ............ 6

VALIDATION OF MODIFIED FORMULATION ..... ... ................. 7

CONCLUDING REMARKS ......... .. ......................... 7

REFERENCES .... ......... ............................. 9

APPENDIX - DESCRIPTION OF COMPUTER PROGRAM JONI .... ............ 21

LIST OF FIGURES

I - Description of Five Defining Parameters of theJONSWAP Spectrum .... .... .. ........................ i

2 - Comparisons of JONSWAP Theoretical and ActualSignificant Wave Height and Fetch Relationships ........... ... 12

3 - Determination of 8 for Modified JONSWAP Spectrum .......... ... 13

4 - Determination of Small 8 for Modified JONSWAPSpectrum .... .... .. ............................ ... 14

5 - Typical Modified JONSWAP Spectra for SignificantWave Heights of 2 and 5 m ..... .................... .... 15

6 - Typical Modified JONSWAP Spectra for SignificantWave Heights of 3 and 7 m ...... .................... ... 16

7 - Modified JONSWAP Spectral Relationships BetweenModal Wave Period, Fetch, and Wind Speed .... ............ ... 17

i ili

•A

8 - Modified JONSWAP Spectral Relationships Between Pg

Significant Wave Height, Fetch, and Wind Speed. .. ........ 17

9 - Comparisons Between Modified JONSWAP Spectraand Measured Spectra .. ... ......... .......... 18

10 - Comparisons Between Modified JONSWAP, Bretschneider,and HIndcast Wave Spectra. .... ......... ....... 19

LIST OF TABLES

I- Significant Wave Heights for Varying Values of y. ... ...... 20

2 - Computer Program JON] .. .... ......... ......... 22

3 -Output from Program JONI .......... 2

IV

-ALIZ

NOTATION

f Wave frequency, cycles , sec "! or Hertz

f Frequency corresponding to the peak of the wave spectrum,cycles - sec-I

-2g Acceleration due to gravity, 9.8087 m • sec

m Spectral moment of order zero

S (f),S (w) Long-crested wave spectral density ordinates

U Wind speed, at 10 m above ocean surface

X Fetch

Significant wave height, average of one-third highestw) /3 double amplitudes

T 0Modal wave period, period corresponding to the frequencyof the peak of wave spectrum

aPhillip's constant

B A constant dependent on the significant wave height andmodal wave period

y Ratio of the maximal spectral energy to the maximum of thecorresponding Pierson-Moskowitz spectrum

aa b Left, right side widths of spectral peak of JONSWAPspectra

Wave frequency, radians • sec

v

ABSTRACT

For simplicity as well as consistency with thecurrent state-of-the-art in seakeeping performanceassessment, a wave spectral formulation for fetch-limited ocean areas which is dependent only on thesignificant wave height and modal wave period isdesirable. A modified version of the JONSWAPspectrum is therefore derived, but as is the casewith the usual fetch-dependent JONSWAP spectrum, itcontains too much energy for fetches above about 40nautical miles. This inconsistency is probably dueto certain parameter relationships which are allbased on least squares fits. Therefore, a newparameter, 0, is developed to replace the usual aparameter, correcting for the parameter's nonuni-versality.

ADMINISTRATIVE INFORMATION

This report was prepared under the sponsorship of the Conventional

Ship Seakeeping Research and Development Program, funded under Project

Number 62543N and Block Number SF 43 421 202 and the Ship Performance and

Hydromechanics Program, funded under Project Number 62543N and Block

Number SF 43 421 001. It is identified by Work Unit Number 1504-100 and

1500-104, respectively, at the David W. Taylor Naval Ship Research and

Development Center (DTNSRDC).

INTRODUCTION

The primary goals of the Joint North Sea Wave Project (JONSWAP), which

originated in 1967, were to measure the growth of waves under limited fetch

conditions and to analyze attenuation of waves propagating into shallow

water, see References I and 2.* The fetch dependence of the measured one-

dimensional frequency spectra was investigated by parameterizing them with

an analytic function derived by least squares fit techniques. The resulting

function, currently the most widely used spectrum for representing fetch-

limited seas, is known as the JONSWAP spectral density equation and is

given by 2

S~~~ 4f - -g(2~ 5 5xF .(.(4- 4l Lef) " (2- f exp , xp 2f 2 m 2_-sec

*A complete listing of references is given on page 9.

... . . .. . .. .. . ... ... .....-...

which reflects the five parameters of fo a, y, oa and ob shown in Figure

1. f is the wave frequency in cycles sec 1 f Is the frequency at the

spectral peak, and g is the acceleration due to gravity. In this report,

a "mean" JONSWAP spectrum has been used, so that y is 3.3, aa is 0.07 and

ob is 0.09. The two parameters, a and f0 are dependent on the wind speed

and fetch such that

a= 0.076 -0.22 (2)

andfo 0 (3)

0

where

7 - (4)U

andS i0 - 33, X < 104

0

X is the fetch in nautical miles. The wind speed U is taken to be at an

elevation of 10 m above the surface and is In units of knots.

The JONSWAP spectral form represents a generalization of the Pierson-

Moskowitz form by inclusion of fetch as an additional parameter to wind

speed. If a is 0.0081 and y is 1 in equation (1), the JONSWAP spectral

form is identical to the Pierson-Moskowitz form. In general, the JONSWAP

spectrum contains more peak energy than the corresponding Pierson-Moskowitz

spectrum for the same values of a and fo, see Figure 1.

MODIFICATION OF THE JONSWAP SPECTRUM

In previously completed ship seakeeping analyses, e.g., see Reference

3, in which the ship's operations in fetch-limited waters has to be

assessed, it has been customary to apply the JONSWAP spectrum, defined by

wind speed and fetch as given in equation (1). However, for simplicity as

well as consistency with the current state-of-the-art in seakeeping per-

formance assessment, a JONSWAP expression which Is dependent only on the

two parameters, significant wave height and modal wave period, is also

2

desirable. In order to achieve this, the following steps have been

carried out. Eliminating the dimensionless frequency f from equations

(3) and (5),

Su 3.5 k-0. 33g 6u = I.. (6)

f

where~Ifo =- (7)

00

or

U 3 3.5 X 0 "33g T0 (8)

The fetch dependence of the dimensionless total energy in the wave spectrum

Is given as

2mog

mo = . (9)U

Furthermore, another fetch empirical relationship is well represented by

the following relation

,, 1.6 (10-7)R, R < 104 (10)

where mo Is the spectral moment of order zero. Significant wave height

(Qw)i/3 can be defined as

Q1) /32()/ 4 Vo orm - 1 (11)W1/3 0 0

and substituting into equation (9) gives2 2

- (¢w) 1/3 gQ)o/ 2 I u 2 (12)

Combining equations (8) and (12),

1 2 2- (¢w) 113 g0 16(3.5 x'0 33g To)4 (13)

3

__ _ _ __ _

T.. . +, .. , W I+'+ I € ' ;L+,,++ .+..

Eliminating the term m from equations (10) and (13) yields0

1.6 (io) = 16(w)132 2(14)16 (3.5 X g0 33g TO)

or

R-032 Q 2 2603. 082R"" 2 - ( w) /3 (15)

2 4g 0

This equation can also be written in the form

-0.22 222.92 (w)1/3 1.375• (16)

1.375 2.750

Substituting R into equation (2)

r- ) 1.375-

a = 0.076L i. 3 7 W 7 (17)

or1. 375

16.942 Q w)/3a= 1.375 2.75 (18)

9 T0

The JONSWAP equation can now be rewritten in terms of (Qw)/ and T asw1/ 0

1.375 dx- - To"12= 16.942 Q w) /,q g2 (21)-4 f5 exp 2 [y 20

9135T2.75 g 2r) exp I .25(fT o)Q y2a2L~S¢(f) = 1. 375 T 7

2m -sec (19)

Equation (19) can be further rewritten to be more compatible with the

usual Bretschneider spectral density formulation as well as most ship

response calculation procedures by converting f to w, the circular frequency

In radians • sec 1 , and taking y - 3.3,

4

(.375 To2.75 g xp .25 3.

m -sec (20)

where

o - 0.07 for < (21)

oroiuu =oT 1 (22)a = 0.09 for -E-> (22

TTo

0 PARAMETER

The modified JONSWAP spectrum given by equation (20) contains more

energy than it is theoretically supposed to for the same values of sig-

nificant wave height and modal wave period when these two parameters are

used to define the spectrum. Figure 2 provides an illustration of the

difference in significant wave height at the same fetch for winds of 20

and 30 knots. The solid line represents the theoretical relationship

between significant wave height and fetch for those wind speeds. The

dashed line represents the values which are actually computed from the

spectral area when the given fetch and wind speed are specified in the

usual JONSWAP formulation given in equation (I). The difference between

the solid and dashed lines represents a rather noticeable increase in

significant wave height for fetches above 40 nautical miles. The diffi-

culty arises due to the fact that the absolute value of a is not universal,

as was first suggested by Phillips, and also as described by Ewing in

Reference 4. While the f and X data are well defined In the linear re-

gression fits, see equations (5) and (10), there Is a large scatter for

*This inconsistency is also present when the usual JONSWAP formula-

tion, given in equation (1), Is applied and is particularly noticeable for

fetches above about 40 nautical miles.

5'

. . . . .. . . w - .. .. .M I • . .

4I

absolute values of X larger than 10 , Consequently, the basic form of

equation (2), and hence equation (18), is not universal at relatively high

waves and periods. To correct this anomaly, a new parameter, 0, is

developed to replace the a parameter given in the usual JONSWAP formulation.

The technique developed to compute 8 Is given In the Appendix. Figures 3

and 4 are the result and provide a for given values of significant wave

height and modal wave period. The wave parameter ranges are deliberately

broad in anticipation of any extreme occurrences such as those reported in

the North Sea. The 8 parameter assures that the specified (input) sig-

nificant wave height, see equation (18), corresponds to that which is

calculated from the integration of the resulting spectral ordinates. The

modified JONSWAP formulation given In equation (20) can now be rewritten

as

-5 [wTo/' I! To 2

27r 2aS -w8g2 u-5 exp 5 ..exp- 2- TL -"

m -sec (23)

where 8 is a constant dependent only on the significant wave height,

(Q11/3, and the modal wave period, To.

APPLICATIONS OF THE MODIFIED JONSWAP SPECTRUM

Figures 5 and 6 provide sample JONSWAP (modified) spectra for sig-

nificant wave heights of 2, 3, 5, and 7 meters and a range of modal wave

periods. As is the case with the Bretschneider formulation, equation (23)

can be applied without special regard to fetch or wind speed. The user,

upon selecting the values for significant wave height and modal wave

period (e.g., from historical wave statistics, climatology, etc.), deter-

mines 8 from Figures 3 or 4 and thence the spectrum can be developed.

Figures 3 and 4 contain a limited but realistic range of modal wave

periods for given significant wave heights for fetch limited geographies.

Table I provides comparisons of significant wave heights for different

values of y. By substituting a set of significant wave height values

(e.g., from Table 1) in the abscissa scale of Figures 3 and 4, a values

6

can be obtained for various values of y. Since a range of fetch or wind

speed values used to obtain $ could be of interest in some seakeeping

analyses (e.g., for specific ocean areas), Figures 7 and 8, developed

from computer program JONI as detailed in the Appendix, provide a com-

parison with corresponding height and period ranges.

As with the usual JONSWAP formulation, the modified expression given

in equation (23) is for long-crested seas. The cosine squared spreading

function can be used with the spectrum but insufficient data on the

directionality of wave systems in fetch-limited waters is available to

verify its applicability.

VALIDATION OF MODIFIED FORMULATION

The general shape of the modified JONSWAP spectra agree well with

the shape of the measured spectra reported for Argus Island in Reference

5. Several such comparisons are given in Figure 9. Furthermore, a total

of four spectra in the North Sea, hindcast by the U.S. Navy's Spectral

Ocean Wave Model (SOWM), see Reference 6, were randomly selected for

comparison with the modified JONSWAP formulation. The hindcasts were also

compared with Bretschneider spectra defined using the hindcast significant

wave height and modal period. Figure 10 shows these comparisons. In

general, the modified JONSWAP spectra provide a much closer approximation

to the hindcasts than do the Bretschneider spectra though secondary

spectral peaks are, of course, not well approximated due to the unimodal

restriction of the model. The modal wave period has been used as the

defining parameter of the spectra in this comparison. However, since

some hindcast spectra contained multiple peaks, average wave period

(e.g., zero crossing period) may permit a better shape definition of the

theoretical wave spectra.

CONCLUDING REMARKS

An expression of the mean JONSWAP spectrum dependent on the signifi-

cant wave height and modal wave period is derived. However, as is the

case with the usual fetch-dependent JONSWAP spectrum, it contains too much

energy for fetches above about 40 nautical miles. The inconsistency

arises due to the fact that the absolute value of a is not universal,

7

while the f and X data are well-defined in the least squares fits

(equations (5) and (10)). Further, there is a broad scatter for absolute

values of X larger than 10

B is developed to replace the a parameter given in the usual mean

JONSWAP formulation and to correct for the parameter's nonuniversality.

Figures 3 and 4 permit the determination of B for given values of signifi-

cant wave height and modal wave period. Hence, wave energy is conserved

in the modified JONSWAP formulation.

Recent hindcast spectra from the North Sea, as well as actual wave

measurements from fetch-limited areas, suggest that the modified JONSWAP

spectrum may describe wave growth conditions more realistically than the

Bretschneider spectrum in fetch-limited or shallow water conditions. In

general, it is concluded that the modified JONSWAP spectrum provides a

reasonable representation of wave conditions in fetch-limited or shallow

water ocean areas.

...... .. ..... j

REFERENCES

1. Hasselmann, K. et al., "Measurements of Wind-Wave Growth and

Swell Decay During the Joint North Sea Wave Project (JONSWAP)," Deutschen

Hydrographischen Zeitschrift, A8, No. 12 (1973).

2. Hasselmann, K. et al., "A Parametric Wave Prediction Model,"

Journal of Physical Oceanography, Vol. 6, pp. 200-228 (1976).

3. Bales, S.L., "Ship Motion Predictions for the MONOB 1, Operating

in the Waters Near the Bahama Islands," Report DTNSRDC/SPD-727-Ol (Sep

1976).

4. Ewing, J.A., "Some Results from the Joint North Sea Wave Project

of Interest to Engineers," international Symposium on the Dynamics of

Marine Vehicles and Structures in Waves (Apr 1974).

5. Lazanoff, S.M., "Wave Power Spectra from Argus Island," U.S.

Naval Oceanographic Office, Report No. 0-46-64 (Dec 1964).

6. Cummins, W.E. and S.L. Bales, "Extreme Value and Rare Occurrence

Wave Statistics for Northern Hemispheric Ship Lanes," Proceedings of

SNAME STAR Symposium (Jun 1980).

9

~~~MAX

E MAX

0 P (Pierson-Moskowitz spectrum)

E PM~I MAX

f0

Figure 1-Description of Five Defining Parameters of the JONSWAP Spectrum

kiZC5D1MG PA BLAW NOTnawU

16 fe e-h~

14. ACTUAL SIGNIFICANT WAVE HEIGHT-

THERETCALSIGNIFICANT WAVE HEIGHT

1 2 . . .. .. . . . .

I -

SM 3 KNOTS

I00

102 . 0 8 00 00 K 00 60O80T00

21

05

10 204 0 8 0 0040 60 80 0

+ 4 4 +f

+ + t i+ t + + t + + 4 -t 4 . . . . .

T + t + + I . " + + 4

T ++ + f . + +

+ + + + +

+ + I +- 4 +

+ + + +T I T

t I + +

+

t + t+ + + + +

T + + 4-++ 4t-

. . . CL+ + +1 t 4 + 4 4 1 T

t + CL

+ t +: +

-4 +4 +

4 + 4

t+ + + t

+ + f

+ .4 1 1

OD X 0t 41 .. c

+ 1-+ + + +47 '+ +

+ +

+ : * : z+ 4 + I.- c

+

+ 4 + I . . . \4 '

+ + . .. . .. ... .. z C3+ +

+ + ++ ... . ...... ......

+ .... . ..... . .77 D.01+ + ++ 4

+ 4

+* . . . . . . . . . . . . . . .

1 4 . . . . . .

. . . . . . . . . .

.. . . . . . . . .

+ : . 440-4 . . . . . . . . . +

014.1r4.444.44, . . . . . . + I + 4. . . . . . . . . . . . . . .

+1 4 . . . . . . . . .

0

5 j t 9 "'Lr, 1

m- Ts:t T t

4 IA

-4..

r44

ig- 0

LU L

f 4f

7tt

LL

+. 0

44

C4 mC

L.) 3 0ONCNM r% C4 1o

-u L*AL

0.

a% -a, - 4NL

0-: 4-

LL 0r,0 O - - to4

X- 1 1 NULAU U% W C

In

0

Go 4)I LAJ4--w -n

Ln U'

4~~C N ' t

33S- w wnvi.33dS 3AYI1 dVMSNor NV3W .

15

Zi m

cn '4-

%0-% %-W aCo4OU

-n m

LU

I! r I- r-.1 U

cc~I.

C

0>:

- z 0

a I wC 'a

%0

166

1000

600

200_

-h 100

so

S 60 7z

MODAL WAVE PERIOD, T0, SEC

Figure 7 -Modified JONSWAP Spectral Relationships BetweenModal Wave Period, Fetch, and Wind Speed

1000

100 A

0

107

;7- .,0,4

N I C

LU

C 0

~- 0 0VI

33 x'N #WI13S3V

- 18

30 I 1 i 30 I I

HINDCAST (MA 196 ) HINDCAST (MAR 1968)25 ( ) 6.7 n 25 (,)/ -I8/

T_ 11.4 SEC sc 1 - 11.4 SEC

MODIFIED JONSWAP M fODIFIED JONSWAP

20 6.7 M20 - 8 M

20--T, - 13.3 SEC 20 | To - 13.3 SEC

-RETSCHNEIDER I - BRETSCHNEIDER

W/3- 6.71 I ( -) " 8 M

i To 13.3 SEC To - 13.3 SEC

I I IIO--10 - 10-

5 5 -

0L / "-X . .. .6 .8 1.0 1.2 .2 . .6 .8 1.0 1.2

I- 4 ,ln ( q1(**) NIUIAT (KR 1"S)

W I (j,), con/3- NIMDCAST (PAR I681ii ?.SG.~(C(i,.):,, * .1n

- - - HoIIrl JOWISVAP

LlJ IT. - 7.4 SEC( ,,1~-11a .3

___ O

- * l l[ 338M - - M IqmFIO JOei$WAP___ (lS,)iII/ f * . n

I ) 1 14.8

T, 11.8 si c- MITSCM IDER

(5)1 - 3.3 A

a .4 .6 .8 .0 LI

.'I4 6 10

-- S

WAVE FREQUENCY, w, RAD SEC

Figure 10 - Comparisons Between Modified JONSWAP, Bretschneider,and Hindcast Wave Spectra.

19

iRO-

TABLE 1 - Significant Wave Heights for Varying Valves of y.

Y 1 Y - 3 Y - 3.3 Y - 5 Y - 7

1.6 2 2 2.2 2.4

3.2 3.9 4 4.4 4.8

4.9 5.9 6 6.7 7.3

6.5 7.8 8 8.9 9.7

8.1 9.8 10 11.1 12.1

9.7 11.8 12 13.3 14.5

S11.3 13.7 14 15.5 16.9

13.0 15.7 16 17.7 19.4

U 14.6 17.7 18 20.0 21.8

20

.................................... •.

APPENDIX

DESCRIPTION OF COMPUTER PROGRAM JONI

It has been shown in the preceding text that there Is a noticeable

discrepancy between the theoretical and actual significant wave heights for

fetches above 40 nautical miles when the JONSWAP spectrum is applied.

Therefore, a new parameter, 8, is used to replace the a parameter in

equation (20) , eg,

1.375

16.942 QT 375 2.75

where ()i, is the theoretical significant wave height in meters.

A listing of program JONI Is presented in Table 2. The purpose of

the program is to calculate 8, modal wave period, and actual significant

wave height under the spectral area. Results are plotted on Figures 3 and

4, with 8 against the actual significant wave height, (w)11/3, and the

modal period, T 0 . For example, If the significant wave height is 4.08 m,

and the modal period is 8 sec, then, by reading across the intersection at

4.08 m and 8 sec, 8 is seen to be about 0.0135. Substituting 8 value into

equation (23) and the modified JONSWAP spectral can be generated by varying

the values of w. A typical output from program JONI is presented in Table

3.

21

TABLE 2 - COMPUTER PROGRAM JON)

CHARGE *%4. LCLLUI ldb.

FTN r9ALJ,T=1 ,A=j)

SFTCU9t I NL)vF AID-)

9eRuGpkm JuNi (i4-lt19UWI:,?(tE i~~gAE=UPT

2

2 J. iS, J.cu 9 J.-

di. O (94u m1.cCt~S

CALL J~. 5xrl J1~ USi-4 O*SSsm-FT = Sr"3e

CALL ALjl-4' (,9sto-q A

Wa-jIS~'4 (-4c ).) NiF

SI.,FT=-.4 4sr: r

deUuJ LO).T[''

IUl Ioij.4 T t_'Fiu., )

2* '"411* :41?i) ~-t ei.K Sio a -VL HT. =9r,.e*i M2 ~.oFli Mkj,0L e-%Vt. 't."bc L~."LS LEfA*FI0.b//I

2 %X *r* VA *1- 14 * *j6l.b IA *,,*r i/)10-s turV4AT (-I ,)i.ver iu . n)

104 e0'41AT (*iI-"I.tJ S =*:. m M *9 1~*E*II Uo , tUr (* Si.,. .. tMT. **~*m 4 F f)

*r)LcK JJ~t?

C -----. 7wtW IT~iL I ~i~iu JU'isV.-rj hri--u. F'iJM Wljvd SPUDO ANOt)tTCI.C- ---- C.LCjL'4H1UNv 1!S i' t J1 fk iuL'4L' r* oo~JL INd tmf PI' U'dIT', Trol IALLY.C- ---- h) O~CT A PIL.,3J~ mlY,'sVdlL %rC.lI.Ltzl AL*jt-lA:.u%)p1 ANU

CSJw-4ii Flit.~. -. / CT.i ,,vvi v ~~

44

UA~~~~ ~ ~ ~ 1-%1g 9t ' ' )' Suc 9 QU

TABLE 2 -COMPUTER PROGRAM JONI (Continued)

N9iDLTCr1 U-rtfLru'-/jj/UU

5!w x 4.* ij~k (I.0@NOFTCMl*UUOJVU*Uj/&//U)*LIUUe

ALPH1A = 1/NtTP*fd

C-----t 0k a IER S--US0of IT Z 5PJELTrUm, Sr-T ALPHAZ.UUdI AFTtR THIS

dtI oo Igj.14

A'~uiz- (r -F-1 ( -r -4) /,quIF (A~461 .0. 1IVU.) 5(1)=U.IF a'IR~ .0. -LUW.) O TOJ LOU11A1f.I.l. UU IJ III

60J TO Ile

C~~ - ~ ~~J-4-K4T SpjECTiu, Sr.] (AMIIA=1.( AITLH 1ei S

C----LU.94~'4T CAw.J

C ---- tUVERT Sf CTw-j;",T 'u *02-SE,; ltwum, mi*elm).

am= sm 1I(e.oil

*FUoqTRA'4 gOUT'1 14.) w-L.,rUR.4 A LAVAAA'i414 AdILbI.(ArhJN.

A~k (.14.) -4 (A* )

20 CUNT I4J

I60,O 4(1.

23 ~ p

-LS f

TABLE 3 -OUTPUT FROM PROGRAM JON]

JONS4iAP' bPECTNuF4FETC#4 014 '0 .io -tu a J i Iu. WAVE MiT. a J.5j all.ti FTMOUAL WAVE PERI. a S.OOSECONDS bETAm .013SI0 THEORETICAL

F 7 a '4 SP

.ou" 1:!1.66 . U'.3 u QjUvuu vuuuuU

.0*6 ce.de laoo U.AU.iuu u.Qu~uji.0 di 4 '. t vi .L'u v~iquiu U.IhUUOU00ja J1.410a .~ J.jvuu ut.uoUou.04%) e~Li . j.jg~iuv vuuuut0 4F tuuuu *u~juou.036 .o *Uuuuv .uuuu

.064 k1 ., .. ,0 *Ujuu uouiol

*012 .. j .- ,so .8~

*1o 1 .4 i. *o.,' i..le

4 11 ,.eJ, I *,Iq 0.b e4114 ./Oa A u JaC44e' a .v7o~g

.114*3e V.'s I V u L, I.' aV. .I Ie 4.13 (. 14 ,3 *..141u I .. 0 ul!

I e o~i .lu.. zhiuu *nitild

3.e~u *lJjj) I *j.7j'u.2t,0fu7 . .3 1.3)p vt J.j- I Tjd

(CACULTE FRO INERAE AREA Ok SP3( oIe CUM )j

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