A new approach to study the nonlinear energy transfer rate for an observed wave spectrum using splines

Nonlinear energy transfer between wind waves in a gravity wave spectrum plays a pivotal role in the evolution of waves and was included as one of the source term (named nonlinear source term) in the third-generation (3G) wave models. The main objective of this paper is to compute the energy distribution due to nonlinear quadruplet wave-wave interactions for observed wave spectrum. This is achieved by utilizing cubic spline technique to fit and represent the theoretical as well as the measured spectra at given location. This technique is further incorporated into Gauss-Legendre Quadrature Method (GLQM) [1, 2] for computing the nonlinear source term. Results were illustrated and validated for the theoretical as well as measured spectra (single- or multi-peaked spectrum) without compromising the accuracy of the method. The significance of this work includes an improvement in the computational efficiency of the method up to 65% by employing optimal set of points of input spectrum (using a procedure discussed) without affecting the nonlinear results of the original one. GLQM (spline fitted spectra) is suitable for deep and finite water depths. Also, this work does not adhere to any assumptions for the tail factor, as the measured spectrum is directly fitted using splines.