A numerical study of the Whitham equation as a model for steady surface water waves

DOI10.1016/j.cam.2015.09.018zbMath1343.76038OpenAlexW2193899814MaRDI QIDQ898954

David P. Nicholls, Henrik Kalisch, Handan Borluk

Publication date: 21 December 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2015.09.018

zbMATH Keywords

Stokes wavesWhitham equationcosine collocation methodnumerical bifurcation analysistransformed field expansions

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Spectral methods applied to problems in fluid mechanics (76M22) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items

A direct construction of a full family of Whitham solitary waves ⋮ The Whitham equation with surface tension ⋮ Modulational instability in the Whitham equation with surface tension and vorticity ⋮ Convective wave breaking in the KdV equation ⋮ Symmetry and decay of traveling wave solutions to the Whitham equation ⋮ Modulational Instability in the Whitham Equation for Water Waves ⋮ Stability of traveling wave solutions to the Whitham equation ⋮ Solitary waves in dispersive evolution equations of Whitham type with nonlinearities of mild regularity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Reconstruction of the pressure in long-wave models with constant vorticity
• Particle dynamics in the KdV approximation
• Traveling waves for the Whitham equation.
• Efficient enforcement of far-field boundary conditions in the transformed field expansions method
• Traveling water waves: Spectral continuation methods with parallel implementation
• A Legendre-pseudospectral method for computing travelling waves with corners (slope discontinuities) in one space dimension with application to Whitham's equation family
• A uniqueness result for periodic traveling waves in water of finite depth
• A numerical approach to blow-up issues for dispersive perturbations of Burgers' equation
• The Whitham equation as a model for surface water waves
• Remarks on the full dispersion Kadomtsev-Petviashvli equation
• Stable, high-order computation of traveling water waves in three dimensions
• Long wave approximations for water waves
• The long-wave limit for the water wave problem I. The case of zero surface tension
• On the existence and stability of solitary-wave solutions to a class of evolution equations of Whitham type
• A Rigorous Numerical Analysis of the Transformed Field Expansion Method
• An existence theory for water waves and the boussinesq and korteweg-devries scaling limits
• The initial-value problem for the Korteweg-de Vries equation
• High-Order Methods for Incompressible Fluid Flow
• Modulational Instability in the Whitham Equation for Water Waves
• Global Bifurcation for the Whitham Equation
• On analyticity of travelling water waves
• Variational methods and applications to water waves
• Stability of high-order perturbative methods for the computation of Dirichlet-Neumann operators
• Stability of traveling wave solutions to the Whitham equation

This page was built for publication: A numerical study of the Whitham equation as a model for steady surface water waves