5 f -4
5Hs2
1
exp -
S( f ) =
(B2)
4 fp
5
16 ( f / f p )
JONSWAP Spectrum
Based on an extensive analysis of data from the Joint North Sea Wave
Observation Project (JONSWAP), Hasselmann et al. (1973) proposed the
following modified form of the Pierson-Moskowitz spectrum to account for fetch-
limited conditions:
5 f -4
αg
2
exp - γ a
S( f ) =
(B3)
4 fp
(2π)4 f 5
where
0.22
U120
α = 0.076
(B4)
gF
1/ 3
U120
f p = 3.5
(B5)
gF
a = exp -( f - f p )2 / 2σ2 f p2
(B6)
σa = 0.07 for f < f p
(B7)
σb = 0.09 for f < f p
F is the fetch distance, γ is a spectral peak enhancement factor, and U10 is the
wind speed at 10 m above the mean sea level. Figure B1 shows a comparison of a
JONSWAP spectrum with γ = 3.3 with a Bretschneider spectrum for a sea state.
The JONSWAP spectrum reduces to the Bretschneider spectrum when γ is equal
to 1.0.
TMA Spectrum
The TMA spectrum is a modified version of the JONSWAP spectrum for
water of finite depth. It was proposed by Bouws, Gunther, and Vincent (1985)
based on Kitaigorodskii, Krasitskii, and Zaslavskii (1975) frequency-dependent
factor for the equilibrium range of the wave spectrum in shallow-water and
validated with data from three field studies (Texel, MARSEN, and ARSLOE). It
can be written as:
B2
Appendix B Description of Ocean Wave Spectra
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