Water waves generated by disturbance at an inertial surface

Abstract

Laplace transform technique is used to solve an initial value problem describing waves generated by a disturbance created at the surface of water covered by an inertial surface composed of a thin but uniform distribution of floating particles. Green's integral theorem produces the transformed potential function from which the form of the inertial surface is obtained as an infinite integral after taking Laplace inversion. The method of stationary phase is then employed to evaluate this integral approximately for large time and distance.