Abstract
This paper is concerned with the interaction of an internal solitary wave (ISW) at the interface of two-layer fluid and the free surface wave on top of the upper layer. It is based on the potential flow theory since internal waves are associated with large Reynolds numbers. The potential flows in the upper layer and lower layer are modeled using a multi-domain boundary element method (MDBEM). The computational model is validated with the experimental results for the profile and speed of the internal wave. The MDBEM is suitable for the simulation of ISW in both small and large density jump stratified fluid system. The wave velocity is compared with the approximate analytical theory for various ratios of the fluid densities of the two layers. In addition, the amplitude, velocity and profile of the surface wave induced by ISWs are investigated. The free surface displacement is opposite to that of the interface, and the amplitude of the surface wave increases with the amplitude and density jump. The surface wave induced by an ISW can be soliton-like wave, propagating with the constant speed of the ISW and maintaining its profile.
Highlights
Internal solitary waves are gravity waves that oscillate at the interface of a stratified fluid, rather than on its surface
The propagation and evolution of internal solitary wave (ISW) are simulated under the rigid-lid assumption and free surface boundary condition, respectively
The wave profiles and velocities calculated by multi-domain boundary element method (MDBEM) with free surface agree well with the experimental results
Summary
Internal solitary waves are gravity waves that oscillate at the interface of a stratified fluid, rather than on its surface. Donato et al (1999) analyzed the focusing of surface waves induced by internal waves, using the ray theory and more accurate nonlinear simulation. Koo (2010) simulated the interaction of internal linear periodic waves with linear free surface waves using the BEM. Gou et al (2012) studied wave diffraction in a two-layer fluid using the BEM with linear boundary conditions They found that the density ratio is an important factor for the hydrodynamic force. The relationship between ISWs and free surface waves are discussed and the detail of surface waves is analyzed in terms of amplitude and wave velocity
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