Modeling shallow water waves

Shallow Water Waves and Solitary Waves

Glossary Deep water A surface wave is said to be in deep water if its wavelength is much shorter than the local water depth. Internal wave A internal wave travels within the interior of a fluid. The maximum velocity and maximum amplitude occur within the fluid or at an internal boundary (interface). Internal waves depend on the density-stratification of the fluid. Shallow water A surface wave i...

Magnetohydrodynamic Shallow Water Waves: Linear Analysis

We present a linear analysis of inviscid, incompressible, magnetohydrodynamic (MHD) shallow water systems. In spherical geometry, a generic property of such systems is the existence of five wave modes. Three of them (two magneto-Poincaré modes and one magneto-Rossby mode) are previously known. The other two wave modes are strongly influenced by the magnetic field and rotation, and have substant...

Shallow Water Waves over Polygonal Bottoms

The traditional shallow water model for waves propagating over varying bathymetry depends for its derivation on the asymptotic analysis of a Dirichlet-Neumann operator. This analysis however is restricted to smoothly varying topographies. We propose an adaptation to one dimensional polygonal bottoms using the conformal mapping idea of Hamilton and Nachbin. The asymptotic analysis of the Dirichl...

Visual simulation of shallow-water waves

A commodity-type graphics card (GPU) is used to simulate nonlinear water waves described by a system of balance laws called the shallow-water system. To solve this hyperbolic system we use explicit high-resolution central-upwind schemes, which are particularly well suited for exploiting the parallel processing power of the GPU. In fact, simulations on the GPU are found to run 15–30 times faster...

Nonlinear edge waves and shallow-water theory