Waves due to an oscillatory pressure on a stratifield fluid: A uniformly valid asymptotic solution

The three-dimensional axisymmetrical initial-value problem of waves in a two-layered fluid of finite depth by an oscillatory surface pressure is solved. The exact integral solutions for velocity potentials of each layer and wave elevations at the surface and interface are obtained. The uniform asymptotic analysis of the unsteady state of waves is carried out when lower fluid is of infinite depth.