The generalized kinetic equation as a model for the nonlinear transfer in third-generation wave models

Abstract

An alternative model for the nonlinear interaction term Snl in spectral wave models, the so called generalized kinetic equation (Janssen J Phys Oceanogr 33(4):863–884, 2003; Annenkov and Shrira J Fluid Mech 561:181–207, 2006b; Gramstad and Stiassnie J Fluid Mech 718:280–303, 2013), is discussed and implemented in the third generation wave model WAVEWATCH-III. The generalized kinetic equation includes the effects of near-resonant nonlinear interactions, and is therefore able, in theory, to describe faster nonlinear evolution than the existing forms of Snl which are based on the standard Hasselmann kinetic equation (Hasselmann J Fluid Mech 12:481–500, 1962). Numerical simulations with WAVEWATCH have been carried out to thoroughly test the performance of the new form of Snl, and to compare it to the existing models for Snl in WAVEWATCH; the DIA and WRT. Some differences between the different models for Snl are observed. As expected, the DIA is shown to perform less well compared to the exact terms in certain situations, in particular for narrow wave spectra. Also for the case of turning wind significant differences between the different models are observed. Nevertheless, different from the case of unidirectional waves where the generalized kinetic equation represents a obvious improvement to the standard forms of Snl (Gramstad and Stiassnie 2013), the differences seems to be less pronounced for the more realistic cases considered in this paper.