Internal solitary wave transformation over the slope: Asymptotic theory and numerical simulation

The propagation and evolution of long nonlinear internal solitary waves over slope-shelf topography is theoretically and numerically studied in a two-layer fluid system of finite depth. The variable Korteweg-de Vries (vKdV) and variable extended Korteweg-de Vries (veKdV) equations are derived for the weak and moderate nonlinear waves, respectively. The numerical method is developed from finite difference/volume (FD/FV) scheme to solve the nonlinear equations. The transformation of solitary waves is observed when they propagate past the slope. The elevation of rear face of the front wave grows with the increase of the slope inclination. The results also show that the transformed waves can be described by the steady solution of the corresponding theoretical model (vKdV, veKdV) by considering the depth condition beyond the shelf.