Steady capillary-gravity waves on the interface of a two-layer fluid over an obstruction-forced modified K-dV equation

The objective of this paper is to study two-dimensional steady capillary-gravity waves on the interface between two immiscible, inviscid and incompressible fluids of constant but different densities bounded by two horizontal rigid boundaries with small symmetric obstructions of compact support at lower and upper boundaries. The derivation of the forced K-dV equation, which has been extensively studied in the literature for a single-layer fluid, fails for a two-layer fluid when the density ratio of the two-layer fluid is near the square of the depth ratio. By a unified asymptotic method, a forced modified K-dV equation is derived and new types of steady solutions are discovered. Numerical results of various solutions are also presented.