dc.contributor.author | Moldabayev, Daulet | |
dc.contributor.author | Kalisch, Henrik | |
dc.contributor.author | Dutykh, Denys | |
dc.date.accessioned | 2016-01-06T14:49:07Z | |
dc.date.available | 2016-01-06T14:49:07Z | |
dc.date.issued | 2015-08 | |
dc.Published | Physica D : Non-linear Phenomena 2015, 309:99-107 | eng |
dc.identifier.issn | 0167-2789 | en_US |
dc.identifier.uri | https://hdl.handle.net/1956/10890 | |
dc.description.abstract | The Whitham equation was proposed as an alternate model equation for the simplified description of uni-directional wave motion at the surface of an inviscid fluid. As the Whitham equation incorporates the full linear dispersion relation of the water wave problem, it is thought to provide a more faithful description of shorter waves of small amplitude than traditional long wave models such as the KdV equation. In this work, we identify a scaling regime in which the Whitham equation can be derived from the Hamiltonian theory of surface water waves. A Hamiltonian system of Whitham type allowing for two-way wave propagation is also derived. The Whitham equation is integrated numerically, and it is shown that the equation gives a close approximation of inviscid free surface dynamics as described by the Euler equations. The performance of the Whitham equation as a model for free surface dynamics is also compared to different free surface models: the KdV equation, the BBM equation, and the Padé (2,2) model. It is found that in a wide parameter range of amplitudes and wavelengths, the Whitham equation performs on par with or better than the three considered models. | en_US |
dc.language.iso | eng | eng |
dc.publisher | Elsevier | en_US |
dc.relation.ispartof | <a href="http://hdl.handle.net/1956/16254" target="_blank">Derivation and numerical solution of fully nonlinear and fully dispersive water wave model equations</a> | en_US |
dc.rights | Attribution CC BY-NC-ND | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | eng |
dc.subject | Nonlocal equations | eng |
dc.subject | Nonlinear dispersive equations | eng |
dc.subject | Hamiltonian models | eng |
dc.subject | Solitary waves | eng |
dc.subject | Surface waves | eng |
dc.title | The Whitham Equation as a model for surface water waves | en_US |
dc.type | Peer reviewed | |
dc.type | Journal article | |
dc.date.updated | 2015-12-22T10:35:03Z | |
dc.description.version | publishedVersion | en_US |
dc.rights.holder | Copyright 2015 The Authors | en_US |
dc.identifier.doi | https://doi.org/10.1016/j.physd.2015.07.010 | |
dc.identifier.cristin | 1276954 | |
dc.subject.nsi | VDP::Matematikk og naturvitenskap: 400::Matematikk: 410::Anvendt matematikk: 413 | |
dc.subject.nsi | VDP::Mathematics and natural scienses: 400::Mathematics: 410::Applied mathematics: 413 | |