Internal Solitary Waves of Depression in Rapidly Varying Topography

Abstract

Internal solitary waves have been observed in oceans all over the world. This paper looks at the effect of rapidly varying topography on the propagation of internal solitary waves in the framework of the variable-coefficient extended Korteweg-de Vries equation. We consider internal solitary wave is propagating in a two-layer fluid system. Here we let the depth of the upper layer to be smaller than the depth of lower layer such that initially an internal solitary wave of negative polarity is generated. The governing equation is solved numerically using the method of lines. Numerical results show that under the influence of variable topography, internal solitary waves would fission into few smaller solitary waves, an undular bore is generated for some time before transforms into a radiation wave or the internal solitary wave loses its amplitude when propagates over a sharply varying slope.