Large-amplitude ferrofluid surface waves and jets

Solitary water waves of large amplitude generated by surface pressure

We consider exact nonlinear solitary water waves on a shear flow with an arbitrary distribution of vorticity. Ignoring surface tension, we impose a non-constant pressure on the free surface. Starting from a uniform shear flow with a flat free surface and a supercritical wave speed, we vary the surface pressure and use a continuation argument to construct a global connected set of symmetric soli...

Amplitude and Phase Variations of Surface Waves

Lateral heterogeneity of the Earth has begun to be mapped extensively by measurements of phase velocities of surface waves since the installation of global digital network. The methods used in such studies are, however, based on simple ray theory: observed phase delays are assumed to be integrations of slowness along the great circles connecting sources and receivers. On the other hand, wave th...

Overhanging interfacial gravity waves of large amplitude

Damping of large-amplitude solitary waves

Soliton damping in weakly dissipative media has been studied for several decades, usually using the asymptotic theory of the slowly-varying solitary wave solution of the Korteweg-de Vries (KdV) equation. Damping then occurs according to the energy balance equation, and a shelf is generated behind the soliton. Various examples of this process have been given by Ott & Sudan (1970) Pelinovsky (197...

Large-Amplitude Solitary Water Waves with Vorticity

We provide the first construction of exact solitary waves of large amplitude with an arbitrary distribution of vorticity. We use continuation to construct a global connected set of symmetric solitary waves of elevation, whose profiles decrease monotonically on either side of a central crest. This generalizes the classical result of Amick and Toland.