Implementing new nonlinear term in third generation wave models

The non-linear interaction term is one of the three key source functions in every third-generation spectral wave model. An update of physics of this term is discussed. The standard statistical/phase-averaged description of the nonlinear transfer of energy in the wave spectrum (waveturbulence) is based on Hasselmann’s kinetic equation [1]. In the derivation of the kinetic equation (KE) it is assumed that the evolution takes place on the slow O(e−4) time scale, where e is the wave steepness. This excludes the effects of near-resonant quartet interactions that may lead to spectral evolution on the ’fast’ O(e−2) time scale. Generalizations of the KE (GKE) that enable description of spectral evolution on the O(e−2) time scale [2–4] are discussed. The GKE, first solved numerically in [4], is implemented as a source term in the third generation wave model WAVEWATCHIII. The new source term (GKE) is tested and compared to the other nonlinear-interaction source terms in WAVEWATCH-III; the full KE (WRT method) and the approximate DIA method. It is shown that the GKE gives similar results to the KE in the case of a relatively broad banded and directional spread spectrum, while it shows somewhat larger difference in the case of a more narrow banded spectrum with narrower directional distribution. We suggest that the GKE may be a suitable replacement to the KE in situations where ’fast’ spectral evolution takes place