Two-dimensional nonlinear models are developed to account for abnormal surface ocean waves generation and propagation. These models are based on the KadomtsevPetviashvili equation, the 2D Benjamin-Ono equation and the 2D Gardner equation. Possible mechanisms of the waves formation suggested are the resonant interaction between semi-plane waves or waves with curved fronts or the transverse insta...

is derived for surface gravity waves with nearly-elliptic front, generalising the cylindrical KP equation for nearly-concentric waves. We discuss transformations between the derived equation and two existing versions of the KP equation, for nearly-plane and nearly-concentric waves. The transformations are used to construct important classes of exact solutions of the derived equation and corresp...

A simple, physical approximation is developed for the effect of viscosity for stable interfacial waves and for the unstable interfacial waves which correspond to RayleighTaylor instability. The approximate picture is rigorously justified for the interface between a heavy fluid (e.g., water) and a light fluid (e.g., air) with negligible dynamic effect. The approximate picture may also be rigorou...

We present a generalized optical theorem for surface waves. The theorem also applies to body waves since under many circumstances body waves can be written in terms of surface-wave modal summations. This theorem therefore extends the domain of applicability of the optical theorem from homogeneous background media to a general class of body and surface-wave propagation regimes within layered ela...

Substantial bottom topography in a basin with planetary vorticity gradients strongly affects the vertical structure of the linear topographic and planetary Rossby waves that spin up the ocean circulation. There is no barotropic mode with large amplitude topography and stratification. It is shown that the lowest frequency two-layer quasigeostrophic waves that exist with stratification, planetary...