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

Changhong Zhi, Ke Chen ^∗, Yunxiang You
Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, China

Received 12 January 2018; received in revised form 24 March 2018; accepted 19 April 2018
Available online 1 May 2018

Abstract
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.
© 2018 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )

Keywords: Internal solitary waves; Two-layer fluid system; Slope-shelf topography; Theoretical model.