Investigation on the Nonlinear Energy Transfer Rates for Spline Fitted Wave Spectra with Varied Peakedness

Nonlinear energy transfer rate due to four-wave interactions within the energy spectrum is described by the 6-D Boltzmann integral. The solution to compute this 6-D integral is either through exact or approximate methods. Betterment of these methods is analysed based on numerical accuracy and computational efficiency. One such potential method is Gauss–Legendre quadrature method (GLQM) [10]. Parameters like tail decay index and peak enhancement factor may vary for a wave spectrum at respective locations which are essential for finding the properties of the sea state. Estimation of these parameters for wind sea and swell prediction using theoretical wave spectrum often leads to discrepancy. The focus of this paperwork is to fit a given wave spectrum consisting of significant wave height and varied peak enhancement factor or peakedness ( \(\gamma\) ) using cubic splines. Further, incorporating this spline fitted spectrum in GLQM to compute and observe the variation in the nonlinear output. Introducing splines indeed helps in fitting any given wave spectrum, thereby avoiding residual errors. This non-parametric approach also helped in improving the computational efficiency of the method without disturbing the accuracy.