Wave load on submerged quarter-circular and semicircular breakwaters under irregular waves

Wave force on vertically submerged circular thin plate in shallow water

Nonlinear random wave groups interacting with a vertical wall are investigated. The analytical solution for the second-order free surface displacement and velocity potential when a high crest occurs at some fixed point on, or close to, the vertical wall is obtained. The solution is exact for any water depth, and it is given as a function of the frequency spectrum of the incident waves. It is obtained that the effects of nonlinearity strongly modify the linear structure of wave groups both in the space and the time domain. The maximum effect of nonlinearity occurs when the high wave hits the wall. Furthermore, it is shown that in finite water depth, the nonlinearity increases as the bottom depth decreases. Finally, a validation by means of Monte Carlo simulations of nonlinear random waves in reflection is given.

Mechanics of nonlinear random wave groups interacting with a vertical wall

A comparative study of the first and second order theories and Goda's formula for wave-induced pressure on a vertical breakwater with irregular waves

A second order analytical solution of focused wave group interacting with a vertical wall

Standing wave pressures on walls

A Polar Method using cubic spline approach for obtaining wave resonating quadruplets

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.

Hybrid functions for nonlinear energy transfers at finite depths

A polar method for obtaining wave resonating quadruplets in finite depths

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.

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V. Prabhakar

Papers

Standing wave pressures on walls

A Polar Method using cubic spline approach for obtaining wave resonating quadruplets

Hybrid functions for nonlinear energy transfers at finite depths

A polar method for obtaining wave resonating quadruplets in finite depths

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