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A quadrature method for computing nonlinear source term due to wave-wave interactions
, J. Pandurangan
Published in
Volume: 90
Issue: 6
Pages: 812 - 817
An accurate method using composite Gauss-Legendre N-point quadrature formula is presented for solving the nonlinear wave-wave interaction source term in deep waters. This method employs a polar grid in the wavenumber space with a constant geometric ratio γ and uses the scaling relation for the transfer integral. The accuracy of the method can be tested for different γs by increasing N. This increase in γ will help in calculating the nonlinear source term at less number of frequency points, resulting in reduced computation time. We also included the procedure for obtaining the nonlinear results at more number of frequency points. A study of 1D nonlinear source term S nl(f) with results of exact methods, indicates that the present results are comparable and qualitatively in good agreement with Webb-Resio-Tracy (WRT) method in spite of slight differences at higher frequencies. This slight difference is due to different polar grids employed for the input vectors in the present method, whereas they are the same in the WRT method. The present method thus considers possibilities that are not explored in the WRT method.
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