Hamiltonian models for the propagation of irrotational surface gravity waves over a variable bottom

Abstract

A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the surface waves are presented in Hamiltonian form. Specific scaling of the variables is selected which leads to approximations of Boussinesq and KdV types taking into account the effect of the slowly varying bottom. The arising KdV equation with variable coefficients is studied numerically when the initial condition is in the form of the one soliton solution for the initial depth.

18 pages, 6 figures, 1 table

References in corpus (6)

• Nearly-Hamiltonian Structure for Water Waves with Constant Vorticity
• The Dynamics of Flat Surface Internal Geophysical Waves with Currents
• Long wave expansions for water waves over random topography
• On the dynamics of internal waves interacting with the equatorial undercurrent
• Generalised Fourier Transform and Perturbations to Soliton Equations
• Solitons of shallow-water models from energy-dependent spectral problems

Cited by in corpus (5)

• Hamiltonian approach to modelling interfacial internal waves over variable bottom
• Surface waves over currents and uneven bottom
• Nonlinear two-dimensional water waves with arbitrary vorticity
• Hamiltonian model for coupled surface and internal waves over currents and uneven bottom
• Perturbation of Traveling Boussinesq Solitons by Periodic Bathymetry