Steep progressive waves in deep and shallow water

Quasiplanar steep water waves.

A unique description for highly nonlinear potential water waves is suggested, where weak three-dimensional effects are included as small corrections to exact two-dimensional equations written in conformal variables. Contrary to the traditional approach, a small parameter in this theory is not a surface slope, but it is the ratio of a typical wavelength to a large transversal scale along the sec...

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...

Steep. Short-Crested Waves and Related Phenomena

Steep, short-crested waves, as well as a large variety of three-dimensional propagating wave patterns have been created in laboratory, utilizing a plunging half-cone. Monochromatic waves, over a range of frequencies and amplitudes through breaking and including soliton wave groups near resonance, have been observed and studied in a small wave flume. This monochromatic wavemaker creates complex ...

Nonlinear edge waves and shallow-water theory

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...