In coastal seas and straits, the interaction of barotropic tidal currents with the continental shelf, seamounts or sills is often observed to generate large-amplitude, horizontally propagating internal solitary waves. Typically these waves occur in regions of variable bottom topography, with the consequence that they are often modeled by nonlinear evolution equations of the Korteweg-de Vries type with variable coefficients. We shall review how these models are used to describe the propagation, deformation and disintegration of internal solitary waves as they propagate over the continental shelf and slope.

We address a specific but possible situation in natural water bodies when the three-layer stratification has a symmetric nature, with equal depths of the uppermost and the lowermost layers. In such case, the coefficients at the leading nonlinear terms of the modified Korteweg-de Vries (mKdV) equation vanish simultaneously. It is shown that in such cases there exists a specific balance between the leading nonlinear and dispersive terms. An extension to the mKdV equation is derived by means of combination of a sequence of asymptotic methods. The resulting equation contains a cubic and a quintic nonlinearity of the same magnitude and possesses solitary wave solutions of different polarity. The properties of smaller solutions resemble those for the solutions of the mKdV equation, whereas the height of the taller solutions is limited and they become table-like. It is demonstrated numerically that the collisions of solitary wave solutions to the resulting equation are weakly inelastic: the basic properties of the counterparts experience very limited changes but the interactions are certainly accompanied by a certain level of radiation of small-amplitude waves.

The generation of huge amplitude internal waves by the barotropic tide in the Barents Sea at high latitudes is examined using the numerical model of the Euler 2-D equations for incompressible stratified fluid. The area considered is located between the Spitsbergen (Svalbard) Island and the Franz-Victoria Trough with a cross-section of 350 km length. There are two underwater hills about 100–150 m high on the background depth of about 300 m. It is shown that intensive nonlinear internal waves with amplitudes up to 50 m and lengths of about 6–12 km are generated in this zone. The total height of such waves is huge and they must be considered as a significant factor of the environment in this basin.