Forces and Moments on a Ship Moving in a Shallow Channel

The method of matched asymptotic expansions is applied to the problem of a ship moving with constant velocity in a channel of rectangular cross section. The depth of the channel is presumed small so that a linearized shallow-water solution is developed. The ship is assumed to be slender and is replaced in the outer region by a distribution of sources and vortices. As in earlier theories for slender bodies translating in shallow water, the source strength is proportional to the change in cross-sectional area of the ship. An integral equation must be solved to find the vortex strength. Using the source and vortex strengths, expressions are developed for the side force, yaw moment, sinkage, and trim. Numerical results are presented which show good agreement with experimental results.