In this paper, we present a numerical method for the computation of surface water waves over bottom topography. It is based on a series expansion representation of the Dirichlet–Neumann operator in terms of the surface and bottom variations. This method is computationally very efficient using...

Considered here are Boussinesq systems of equations of surface water wave theory over a variable bottom. A simplified such Boussinesq system is derived and solved numerically by the standard Galerkin-finite element method. We study by numerical means the generation of tsunami waves due to bottom...

We describe and implement a fully discrete spectral method for the numerical solution of a class of non-linear, dispersive systems of Boussinesq type, modelling two-way propagation of long water waves of small amplitude in a channel. For three particular systems, we investigate properties of the...

Considered here is a Boussinesq system of equations from surface water wave theory. The particular system is one of a class of equations derived and analyzed in recent studies. After a brief review of theoretical aspects of this system, attention is turned to numerical methods for the...

Purpose – The purpose of this paper is to look at the UK's tidal and wave energy resources and the numerous technologies in this area. Design/methodology/approach – The paper looks at the innovations in the UK's tidal and wave energy technology. Findings – While the Government may have...

We consider the ‘classical’ Boussinesq system of water wave theory, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a horizontal channel. (We also consider its completely symmetric analog.) We...

We study the stability of a class of traveling waves in a model of weakly nonlinear water waves on the sphere. The model describes free surface potential flow of a fluid layer surrounding a gravitating sphere, and the evolution equations are Hamiltonian. For small amplitude oscillations the...

In this paper we produce numerical, genuinely three-dimensional, hexagonal traveling wave solutions of the Euler equations for water waves using a surface integral formulation derived by Craig and Sulem. These calculations are free from the requirements of either long wavelength or...