EM 1110-2-1100 (Part II)
(Change 1) 31 July 2003
as a function of nondimensional fetch (Mitsuyasu 1968). This presented a problem to the "first-generation"
interpretation of wave generation physics, since it implied that energies within the equilibrium range are not
controlled by wave breaking. Fortunately, a theoretical foundation already existed to help explain this
discrepancy. This foundation had been established in 1961 in an exceptional theoretical formulation by Klaus
Hasselmann in Germany. In this formulation, Hasselmann, using relatively minimal assumptions, showed
that waves in nature should interact with each other in such a way as to spread energy throughout a spectrum.
This theory of wave-wave interactions predicted that energy near the spectral peak region should be spread
to regions on either side of the spectral peak.
(12) Hasselmann et al. (1973) collected an extensive data set in the Joint North Sea Wave Project
(JONSWAP). Careful analysis of these data confirmed the earlier findings of Mitsuyasu and revealed a clear
relationship between Phillips' α and nondimensional fetch (Figure II-2-21). This finding and certain other
spectral phenomena, such as the tendency of wave spectra to be more peaked than the Pierson-Moskowitz
spectrum during active generation, could not be explained in terms of "first-generation" concepts; however,
they could be explained in terms of a nonlinear interaction among wave components. This pointed out the
necessity of incorporating wave-wave interactions into wave prediction models, and led to the development
of second-generation (2G) wave models. The modified spectral shape which came out of the JONSWAP
experiment has come to bear the name of that experiment; hence we now have the JONSWAP spectrum,
which can be written as
2
f
&1
fp
&4
exp &
αg 2
f
2σ2
exp &1.25
γ
E(f) '
(II-2-34)
fp
(2π)4 f 5
where
α = equilibrium coefficient
σ = dimensionless spectral width parameter, with value σa for f<fp and value σb for f$fp
γ = peakedness parameter
The average values of the σ and γ parameters in the JONSWAP data set were found to be γ = 3.3, σa = 0.07,
and σb = 0.09. Figure II-2-22 compares this spectrum to the Pierson-Moskowitz spectrum.
(13) Early second-generation models (Barnett 1968, Resio 1981) followed an f-5 equilibrium-range
formulation since prior research had been formulated with that spectral form. Toba (1978) was the first
researcher to present data suggesting that the equilibrium range in spectra might be better fit by an f-4
dependence. Following his work, Forristall et al. (1978); Kahma (1981); and Donelan, Hamilton, and Hu
(1982) all presented evidence from independent field measurements supporting the tendency of equilibrium
ranges to follow an f-4 dependence. Kitaigorodskii (1983); Resio (1987,1988); and Resio and Perrie (1989)
have all presented theoretical analyses showing how this behavior can be explained by the nature of
nonlinear fluxes of energy through a spectrum. Subsequently, Resio and Perrie (1989) determined that,
although certain spectral growth characteristics were somewhat different between the f-4 and f-5 formulations,
Meteorology and Wave Climate
II-2-41
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