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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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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-
,
53
I-cJo
LLJ0
a My18 DTNSRDC/SPD-09 18-011 o My18
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NO OCB60230 2I)
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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
28 29
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)
UNCLASS I FIIla, OECL. ASSI FIC ATI NDOWN GRADING0
SCHEDULE
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APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED
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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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