The Neumann-Michell theory of ship waves

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 , where x is the coordinate along the ship length, 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 does not appear in a consistent linear flow model. Furthermore, the term can be eliminated using a mathematical transformation, which amounts to an integration by parts.