Nonlinear Shallow-Water Waves with Vertical Odd Viscosity

Nonlinear edge waves and shallow-water theory

Nonlinear refraction-diffraction of waves in shallow water

The parabolic approximation is developed to study the combined refraction/diffraction of weakly nonlinear shallow-water waves. Two methods of approach are used. In the first method Boussinesq equations are used to derive evolution equations for spectral-wave components in a slowly varying two-dimensional domain. The second method modifies the K-P equation (Kadomtsev & Petviashvili 1970) to incl...

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...

On Nonlinear Water Waves in a Channel

Numerical Simulation of a Weakly Nonlinear Model for Water Waves with Viscosity

The potential flow equations which govern the free–surface motion of an ideal fluid (the water wave problem) are notoriously difficult to solve for a number of reasons. First, they are a classical free– boundary problem where the domain shape is one of the unknowns to be found. Additionally, they are strongly nonlinear (with derivatives appearing in the nonlinearity) without a natural dissipati...