A third-order Boussinesq model applied to nonlinear evolution of shallow-water waves
type: Item
instance of: scholarly article
title: A third-order Boussinesq model applied to nonlinear evolution of shallow-water waves
zbMATH Open document ID: 0992.76017
author: Yinglong Zhang
author: Song-Ping Zhu
published in: Journal of Hydrodynamics. Ser. B
publication date: 2002-09-11T00:00:00Z
review text: This paper is devoted to the derivation of new third-order Boussinesq shallow water equations. These equations describe the evolution of a weakly nonlinear and dispersive wavetrain over a slowly varying bottom topography. It is shown that the new equations possess better linear dispersion characteristics. The new equations are used to study the evolution of periodic waves and the generation of higher harmonics in water of constant depth. Special attention is given to numerical computational results and to comparison between the conventional and new Boussinesq models. It is shown that the new third-order Boussinesq model enhances the spatial aperiodicity and skewness of the wave envelopes, shortens the beat distance, and thus more energy is transferred from lower harmonics to higher harmonics. The results are compared with experimental data as well as with previous results based on the conventional Boussinesq equation. The results of this paper seem to be more satisfactory than those obtained by previous authors.
Mathematics Subject Classification ID: 76B15
zbMATH DE Number: 1508362
zbMATH Keywords: parabolic approximation
zbMATH Keywords: nonlinear evolution of shallow water waves
zbMATH Keywords: third-order Boussinesq shallow water equations
zbMATH Keywords: linear dispersion
zbMATH Keywords: lower harmonics
zbMATH Keywords: higher harmonics
reviewed by: Lokenath Debnath
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1508362