Waves Due to a Moving Oscillatory Surface Pressure in a Stratified Fluid

Abstract

The initial value problem of waves generated by an oscillatory pressure distribution moving uniformly on the free surface of a two-layer fluid is solved. The integral representations of the waves both on the free surface and on the surface of separation are obtained. By a passage to the limit t → ∞, the steady-state solution of the problem is derived through an asymptotic evaluation of these integrals at large distances. It is noticed that stratification sharply changes the number and the character of the progressive waves and also introduces two critical speeds instead of one as found in homogeneous fluid. At these speeds the solution becomes singular.