Gravity effects in the initial value problems of water wave theory

Abstract

The theory described in this paper is directed towards obtaining a general expression for the development of the free surface of a fluid, subsequent to a given initial state and prescribed boundary conditions, as a power series in g, the gravitational acceleration. In an earlier paper [4], a result, applicable to the particular case of the entry of a thin wedge into an incompressible fluid, was obtained and gave the shape of the free surface as such a power series. This series was valid for values of the ratio ut/x < 1, where u, was the (constant) velocity of entyr of the wedge; x the horizontal distance from the vertex of the wedge; and t the times elapsed after entry. This particular problem was first investigated by Mackie [6] who derived an asymptotic solution.