Generation of internal waves in a two-layered stratified system with a free surface by coupled mass sources

Abstract

The generation of internal waves (IWs) is of fundamental concern in numerical studies on the IWs and particularly their interaction with the currents and structure topography. In this study, a coupled mass sources (CMS) approach is proposed to generate IWs in a two-layer stratified system considering the free-surface effect. The numerical verifications are performed in the NEWTANK model solving full Navier-Stokes equations. The multi-layered VOF (ML-VOF) method is employed to track the movement of the interface and free surface simultaneously. The verifications indicate that the CMS method is capable of generating internal solitary waves (ISWs) with weak and strong nonlinearity under the free surface. The prescribed ISW can be generated at the very beginning with no obvious trailing waves compared with the commonly used gravity-collapse method. Furthermore, the free-surface soliton aroused at the top of ISW is consistent with the theoretical solution. The verifications also demonstrate that the CMS method is competent to generate ideal internal periodic waves (IPWs) in both Boussinesq and non-Boussinesq conditions considering the free-surface effect. Finally, the internal wave interaction with the currents simulated by the CMS method is discussed to demonstrate the advantages of this approach.