A Numerical Study for the Nonlinear Four Wave Interactions In Deep Waters

摘要

In this paper, we present the results in deep waters for the nonlinear source term due to wave-wave interactions, represented by a 6-D Boltzmann integral, using a quadrature based method that uses a mix of both simple and composite Gauss Legendre quadrature methods for the integration parameters of the resulting triple integral. This Gauss-Legendre Quadrature Method, denoted GLQM, employs a polar grid with a constant geometric ratio A, . and uses the scaling relations for the inner transfer integral of Tracy and Resio (1982) to achieve a reduction in the computation time. The accuracy of the method has been tested for different frequency resolutions by varying.the parameter X and also for different angular resolutions. This increase in X will help in calculating the nonlinear source term at less number of frequency points without loss of accuracy, resulting in further reduction of computation time. Results are presented in which the computation time is shown less than a minute indicating that the present method can be used to choose choosing optimal points of an input polar grid for achieving both accuracy and computational efficiency.