Topology in Shallow-Water Waves: A Violation of Bulk-Edge Correspondence

Nonlinear edge waves and shallow-water theory

NOTES AND CORRESPONDENCE A Shallow-Water Model that Prevents Nonlinear Steepening of Gravity Waves

The shallow-water model is used as a testbench for understanding many fundamental dynamical problems (e.g. certain wave–mean interaction problems). One sometimes wants to allow large-amplitude gravity waves to propagate significant distances in such models without forming shocks. This paper presents a simple, and apparently unique, modification of the standard shallow-water model that prevents ...

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...

Rossby waves in ” shallow water ” magnetohydrodynamics

Aims. The influence of a toroidal magnetic field on the dynamics of Rossby waves in a thin layer of ideal conductive fluid on a rotating sphere is studied in the " shallow water " magnetohydrodynamic approximation for the first time. Methods. Dispersion relations for magnetic Rossby waves are derived analytically in Cartesian and spherical coordinates. Results. It is shown that the magnetic fie...

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...