The calculation of wave resistance

Abstract

1. The wave resistance of a body moving in a frictionless liquid has been calculated by various methods. In a few cases it has been found directly as the resultant of the fluid pressures on the surface of the body. Another method, which has been more generally useful, involves the introduction of a certain type of fluid friction into the equation of motion. The wave resistance is then found by calculating the rate of dissipation of energy and taking the limiting value when the frictional coefficient is made vanishingly small. This method has certain important analytical advantages, nevertheless it is highly artificial. A third method, dealing directly with a frictionless liquid, consists in examining the flow of energy in the wave motion; this has hitherto been used only for two-dimensional problems when the wave motion consists of simple waves with straight parallel crests, the usual theory of group velocity being directly applicable. In the following note this method is extended to three-dimensional fluid motion. Although no new special results are obtained so far as expressions for wave resistance are concerned, it seemed of sufficient interest to obtain them by this direct method, namely, by considering the flow of energy and the rate of work across planes far in advance and far in the rear of the moving body.