Nonlinear Periodic and Solitary Water Waves on Currents in Shallow Water

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...

Nonlinear edge waves and shallow-water theory

High-Order Interaction of Solitary Waves on Shallow Water

The interaction of solitary waves on shallow water is examined to fourth order. At first order the interaction is governed by the Korteweg–de Vries (KdV) equation, and it is shown that the unidirectional assumption, of right-moving waves only, is incompatible with mass conservation at third order. To resolve this, a mass conserving system of KdV equations, involving both rightand left-moving wa...

On Nonlinear Water Waves in a Channel

Depth inversion in shallow water based on nonlinear properties of shoaling periodic waves 1

Two depth inversion algorithms applicable to coastal waters are developed, calibrated, and validated based on results of computations of periodic waves shoaling over mild slopes, in a two-dimensional numerical wave tank based on fully nonlinear potential flow theory. In actual field situations, these algorithms would be used to predict the cross-shore depth variation h based on sets of values o...