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Abstract:
Nonlinear transfer from wave-wave interactions is an important term in the action-balance equation governing the evolution of the surface-gravity-wave field. 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 equation. This paper describes the implementation of a hybrid computational scheme, incorporating a simplification first proposed by Thacker 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 preintegration from the second stage to the first, dramatically accelerates the resulting second-stage computation, enabling a relatively efficient and precise determination of nonlinear transfer in two-dimensional wave models. Physically, this preintegration collects together in single hybrid interactions multiple interactions belonging to identical spectral-band quadruplets. Thus all possible interactions are represented, and these interactions are represented in a uniquely efficient manner consistent with the spectral representation. We compute the coefficients in the resulting second-stage hybrid sum by essentially sorting and pre-summing the coefficients generated by a piecewise-constant first-stage EXACT-NL computation, using a variant of EXACT-NL that replaces the gather-scatter operations with a simpler bin-assignment procedure and employs a somewhat simpler set of integration variables. By exploiting the natural scaling of the integrand and partially pre-summing prior to sorting, we are able to further improve the efficiency of this computation for the deep-water case and to refine its integration-grid resolution almost to convergence. In wave-model computations of nonlinear transfer, vectorization on the spatial 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.
