Spline-fitted measured spectrum as input for the evaluation of nonlinear energy transfer rate and its validation through accurate estimation of wave energy flux

A novel attempt has been made in the present work to fit measured wave spectra at any location using a non-parametric (spline) approach. The spline-fitted spectra and the reduced spline-fitted spectra (procedure discussed) represented the measured wave spectrum, ensuring an exact match to it. A neoteric "Gauss-Legendre quadrature method (GLQM)" (Kamalakannan and Prabhakar 2016a, b) was previously introduced to accurately estimate nonlinear transfer rates within parametric wave spectra. The spline approach has now been incorporated into the method to evaluate nonlinear transfer rates for measured spectrum considered from a location during June-September 2019-2021. Nonlinear results were demonstrated using reduced spline-fit spectra for both deep and shallow water measurements. Introducing spline approach shortens the method's computation time (up to 65%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$65\%$$\end{document}) without compromising its accuracy. The significance of this work also includes the estimation of main wave parameters such as significant wave height, wave period, and wave energy flux for reduced fitted spectra, which match well with those of buoy measurements and serve as validation. This work holds paramount significance as it achieves a precise fit for measured spectra with vanishing residual errors, thereby yielding accurate energy flux and nonlinear results well comparable to the pioneering methods in wave model.