Modelling internal solitary waves in the coastal ocean

In the coastal oceans, the interaction of currents (such as the barotropic tide) with topography can generate large-amplitude, horizontally propagating internal solitary waves. These waves often occur in regions where the waveguide properties vary in the direction of propagation. We consider the modelling of these waves by nonlinear evolution equations of the Korteweg-de Vries type with variable coefficients, and we describe how these models are used to describe the shoaling of internal solitary waves over the continental shelf and slope. The theories are compared with various numerical simulations.