Numerical investigation of large amplitude second mode internal solitary waves over a slope-shelf topography

A numerical study of the propagation and transformation of large amplitude second mode concave internal solitary waves (ISWs) over a slope-shelf topography is presented. A fully nonlinear and non-hydrostatic numerical model is employed and solved. The fluid stratification, amplitude of the incident wave, and inclination of the bottom topography are taken close to those in the northern South China Sea (SCS), where the continental slope and shelf span quite a large area. It is found that the incoming wave adjusts permanently to the changing depth in deep water without essential changes of the wave profile until it gets close to the shelf break, where the frontal face becomes flatter and the rear face steeper. A very steep wave structure is formed at the leading edge just after the wave passes by the shelf break. This steep structure does not progress into a new soliton of concave type, but slopes more and more gently. The trailing edge of the initial concave wave becomes steeper and steeper and gradually develops into a packet of convex ISWs. Finally the rear convex wave packet catches up with the frontal concave wave. The two wave systems then “merge” and travel forward steadily with almost permanent profile. No events of wave breaking occur with the model configuration close to the realistic slope-shelf of the northern SCS. Finally, amplitudes of the incident wave and inclination of the slope are varied, and different scenarios take place before and after the wave reaches the shelf break.