A numerical study of nonlinear energy fluxes due to wave-wave interactions Part 1. Methodology and basic results

Abstract

Nonlinear transfer due to wave-wave interactions was first described by the Boltzmann integrals of Hasselmann (1961) and has been the subject of modelling ever since. We present an economical method to evaluate the complete integral, which uses selected scaling properties and symmetries of the nonlinear energy transfer integrals to construct the integration grid. An important aspect of this integration is the inherent smoothness and stability of the computed nonlinear energy transfer. Energy fluxes associated with the nonlinear energy transfers and their behaviour within the equilibrium range are investigated with respect to high-frequency power law, peak frequency, peakedness, spectral sharpness and angular spreading. We also compute the time evolution of the spectral energy and the nonlinear energy transfers in the absence of energy input by wind or dissipated by wave breaking. The response of nonlinear iterations to perturbations is given and a formulation of relaxation time in the equilibrium range is suggested in terms of total equilibrium range energy and the nonlinear energy fluxes within the equilibrium range.