Resonant wave response to obstacle forcing in two layer fluid flow

The paper is concerned with the propagation of weakly nonlinear gravity wav es in a two layer fluid over bottom topography when the fluid is assumed to be inviscid and incompressible. Specifically, we investigate disturbances of a homogeneous critical state. As a consequence, the resulting (free surf ace or internal) wave is trapped which leads to a resonant wave response to obstacle forcing. In general the wave motion is found to be governed by a kinematic wave equation with quadratic nonlinearity where the bottom topogr aphy enters as a source term. In the case of internal waves, however, there exists a pow regime in which both quadratic and cubic nonlinear terms have to be taken into account.