A comparison of weakly and fully non-linear models of the shoaling of a solitary internal wave

This study investigates the behaviour of internal solitary waves crossing a continental slope in the presence of a seasonal thermocline. Comparisons are made between a fully non-linear computational fluid dynamics (CFD) model, and weakly non-linear theory. Previous observations suggested that the amplitudes of solitary waves are capped as they pass across the continental slope, which may be due to laminar dynamics, or due to the effect of turbulence. Across the continental slope, CFD and second order variable depth KdV (vEKdV) predictions agree well with observations of a limited change in solitary wave amplitude. First order variable depth KdV theory overpredicts the final amplitude significantly. In terms of the wave shape, the CFD modeled wave changes from a KdV shape in deep water towards an EkdV solution in shallow water, as observations suggest. The phase speed of the CFD and vEKdV waves are similar to that observed in waters of 400–500 m deep, but are slightly lower than observed in 140 m depth. CFD predictions using a standard k, ε turbulence model showed that turbulence had little effect on the amplitude. These preliminary results indicate that in this situation wave capping is due to laminar, large amplitude solitary wave dynamics and is independent of turbulent mixing.