Internal symmetric waves of two-layer fluids over an obstruction

Abstract

We study two-dimensional capillary-gravity waves on the interface between two immiscible, inviscid and incompressible fluids of different constant densities bounded by two horizontal rigid boundaries with small obstructions with compact support. A forced modified Korteweg--de Vries equation is derived as a model equation without assuming that the fluid is of constant depth at far upstream. Various new types of steady solutions have been obtained numerically.