Numerical study of the breaking of an internal soliton and its interaction with a slope

Abstract The full Navier-Stokes and diffusion equations are applied to study the breaking of an internal soliton on the continuously stratified pycnocline in a two-layer system and its interaction with a slope. First, these equations are solved numerically to study the limiting height and breaking of the soliton in the case of constant total depth. Breaking occurs when the particle velocity in a region of flow field exceeds the wave celerity. This results in a gravitational instability with a patch of dense water entraining into the upper layer in the lee of the wave. The numerically determined breaking criterion is supported by an estimate using the first-order Korteweg-de Vries (KdV) theory. Then, the model is used to examine the interaction of the soliton with a slope-shelf topography and a uniform slope. In both cases, the relative depths of the layers change at the turning point along the slope. Mechanisms of the wave breaking and wave propagation processes for both cases are described. Scaled bottom stresses and total wave run-up on the slope are also presented.