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Results pertaining to numerical solutions of the Hasselmann kinetic equation(HE), for wind driven sea spectra, in the fetch limited geometry, arepresented. Five versions of source functions, including the recently introducedZRP model, have been studied, for the exact expression of Snl andhigh-frequency implicit dissipation, due to wave-breaking. Four of the fiveexperiments were done in the absence of spectral peak dissipation for variousSin terms. They demonstrated the dominance of quadruplet wave-wave interaction,in the energy balance, and the formation of self-similar regimes, of unlimitedwave energy growth, along the fetch. Between them was the ZRP model, whichstrongly agreed with dozens of field observations performed in the seas andlakes, since 1947. The fifth, the WAM3 wind input term experiment, usedadditional spectral peak dissipation and reproduced the results of a previous,similar, numerical simulation, but only supported the field experiments formoderate fetches, demonstrating a total energy saturation at half of that ofthe Pierson-Moscowits limit. The alternative framework for HE numericalsimulation is proposed, along with a set of tests, allowing one to selectphysically-justified source terms.

Limited fetch revisited: comparison of wind input terms, in surface waves modeling