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Rapid Calculation of Nonlinear Wave-Wave Interactions in Wave-Action Balance Equation

Abstract : This paper presents an efficient numerical algorithm for the nonlinear wave-wave interactions that can be important in the evolution of coastal waves. Random sea waves of multiple frequencies always interact with each other and with the variable wind and pressure fields. As waves propagate and transform from deep to shallow water, it is generally difficult to determine the actual amount of nonlinear energy transfer that occurs among spectral waves and the atmospheric input and wave breaking. The classical derivation of the nonlinear wave energy transfer has involved tedious numerical calculations that are impractical for engineering applications. We propose in this paper a theoretically based formulation to efficiently calculate nonlinear wave-wave interactions in the spectral wave transformation equation. The proposed formulation has performed well in both idealized and real application examples. This rapid calculation algorithm indicates that the nonlinear energy transfer is more significant in the intermediate depth than in deep and shallow water conditions.