A wavelet-based attempt is made to estimate the nonlinear interactions for wind wave spectra using Haar wavelets. The nonlinear interactions have been synthesized using the orthogonal basis of the Haar wavelets. The analysis of the nonlinear interactions using wavelets provides an easy way of computing the transfer integral in the Webb–Resio–Tracy’s (WRT) method. The one-dimensional and two-dimensional results confirm the applicability of the wavelets to the nonlinear wave–wave interactions and the approach of multi-resolution analysis ensures the convergence and the accuracy. © 2016, Springer International Publishing Switzerland.

Prabhakar V

Mathematics

School of Advanced Sciences

Chennai Campus

Hariharan S

Department of Communication Engineering

School of Electronics Engineering

Vellore Campus

Uma G

Fulltext

Vellore Institute of Technology (VIT) is a private university located in&nbsp;Tamil Nadu, India. Founded in 1984, as Vellore Engineering College, the institution offers 20 undergraduate, 34 postgraduate, four integrated and four research programs. It has campuses in Vellore, Amravati, Bhopal and Chennai.

VIT is one of the top ranked private universities in India according to NIRF, THE and QS Rankings.&nbsp;Govt. of India has recognized&nbsp;VIT, Vellore as an&nbsp;Institution of Eminence. This has allowed VIT to take independent quality initiatives and move up in world ranking.

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VIT University

Journal of Ocean Engineering and Marine Energy

A numerical method using Hybrid functions which are the orthogonal polynomials, formed from the combination of Block pulse function and Lagrange basis polynomial (HBL) are employed for the estimation of nonlinear energy transfers (NLT) occurring between set of four waves at finite water depths. The advantages and properties of HBL functions provide an easy way for estimating the quadruplets arising in NLT. The manuscript focuses on two aspects, namely sensitivity and efficiency of NLT at finite depths due to HBL. The sensitivity of NLT at finite depths to number of points on the locus curve, for various directional spectra, are studied in detail. With decreasing water depth (i) the locus curve grows and thus magnitude of NLT increases (ii) increase the number of points on the locus curve to achieve reliable (or) accurate results and (iii) the peak frequency starts shifting towards the left side of the spectrum. The efficiency of the HBL method to NLT is substantiated by comparison with the currently used Trapezoidal rule. Convergence results of NLT are established in both frequency and direction. The method is tested for its suitability in both circular and sector grids and the results confirm its adaptability to NLT. The method is validated against the methods implemented in the Wave models such as WRT and Discrete Interaction Approximation. © 2018, Springer International Publishing AG, part of Springer Nature.

Hybrid functions for nonlinear energy transfers at finite depths

A wavelet approach for computing nonlinear wave–wave interactions in discrete spectral wave models

Journal	Data powered by TypesetJournal of Ocean Engineering and Marine Energy
Publisher	Data powered by TypesetSpringer Science and Business Media LLC
ISSN	2198-6444
Open Access	No