Nonlinear Transfer From Wave-Wave Interactions

Nonlinear transfer from wave-wave i n teractions is an important term in the action-balance equation governing t h e e v olution of the surface-gravity-wave eld. Computation of this term, however, has hitherto been so consuming of computer resources that its full representation has not been feasible in nonparametric two-dimensional computer models of this e q u ation. This paper describes the implementation of a hybrid computational scheme, incorporating a simplication rst proposed by T h acker into the EXACT-NL Boltzmann integration scheme of Hasselmann and Hasselmann. This hybrid scheme retains EXACT-NL's symmetry, precision, and two-stage structure, but, by transferring a spectrum-independent p reintegration from the second stage to the rst, dramatically accelerates the resulting second-stage computation, enabling a relatively ecient a n d precise determination of nonlinear transfer in two-dimensional wave models. Physically, t his preintegration collects together in single hybrid interactions m ultiple interactions belonging to identical spectral-band q u adruplets. Thus all possible interactions are represented , and these interactions are represented in a uniquely ecient manner consistent with the spectral representation. We compute the coecients in the resulting second-stage hybrid sum b y essentially sorting and presumming the coecients generated by a piecewise-constant rst-stage EXACT-NL computation , using a v ariant o f E X ACT-NL that replaces the gather-scatter operations w i t h a s i m p ler bin-assignment p rocedure and e m p loys a somewhat simpler set of integration variables. By exploiting the n atural scaling of the integrand a n d p artially presumming prior to sorting, we are able to further improve the eciency of this computation for the deep-water case and to rene its integration-grid resolution almost to convergence. In wave-model computations of nonlinear transfer, vectorization on the s p atial grid points of the model and selective truncation of the hybrid sum potentially reduce the working computation time for a single model time step to well under one Cray Y-MP single-processor CPU second per hundred grid points, while preserving a remarkably faithful representation of the full transfer.