Free Surface Waves on a Two-Layer Fluid Over a Step
Commun. Korean Math. Soc. 2000 Vol. 15, No. 1, 173-181
Jeongwhan Choi, Sungim Whang Korea University, Korea University
Abstract : The objective of this paper is to study two dimensional steady gravitational waves on the interface between two immiscible, inviscid and incompressible fluids bounded above by a horizontal rigid boundary and below by a rigid step. A KdV equation for the first order perturbation in an asymptotic expansion can appear. However the coefficient of the KdV theory fails in that case. By a unified asymptotic method, we overcome this difficulty and derive a modified KdV equation with forcing. We find homogeneous steady solutions and present numerical solutions.