The Neumann–Michell theory of ship waves

Abstract

The classical Neumann–Kelvin (NK) linear potential flow model of 3D flow about a ship hull steadily advancing in calm water is reconsidered, and a modified theory—called Neumann–Michell (NM) theory—is given. The main difference between the two theories is that the line integral around the ship waterline that occurs in the classical NK boundary-integral flow representation is eliminated in the NM theory. Specifically, the integrand of the waterline integral in the NK theory is $${G\phi_x-\phi G_x}$$ , where x is the coordinate along the ship length, $${\phi}$$ is the flow potential, and G is the Green function associated with the Kelvin–Michell linear free-surface boundary condition. It is shown that the term $${G \phi_x}$$ does not appear in a consistent linear flow model. Furthermore, the term $${\phi G_x}$$ can be eliminated using a mathematical transformation, which amounts to an integration by parts.