Neumann–Michell theory of short ship waves

Abstract

Short-wave approximations are obtained within the framework of the Neumann–Michell (NM) linear theory of potential flow around a ship that travels at a constant speed in calm water. Specifically, the integral over the ship hull surface – that determines ship waves within the Fourier–Kochin representation related to the NM theory – is approximated as a line integral around the ship waterline via Laplace’s method. This waterline-integral approximation is further approximated via Kelvin’s method of stationary phase. The short-wave asymptotic approximations obtained via successive applications of Laplace’s method and Kelvin’s method of stationary phase provide theoretical insight into short (transverse and divergent) waves created by ships that travel at low Froude numbers, and short divergent waves created by ships traveling at moderate or high Froude numbers. In particular, these analytical approximations show that short ship waves are related to the Froude number and the hull form in a fairly complicated manner.