Hydrodynamic Interactions Between Ships in Shallow Water

Abstract

A method is developed for predicting the forces and moments acting on a vessel due to the hydrodynamic interactions between Vessels in a passing situation. The lateral separation between the vessels is assumed large so that the vessels are in each other's far field. The speed of the interacting vessels is small so that the free surface effects are neglected. The water depth is assumed small so that the ship is close to the bottom. Two cases are investigated, namely, the case when the ship touches the bottom (two dimensional problem), and the case when there is a slight gap beneath the keel (shallow water problem. &&The general problem is solved using the method of matched asymptotic expansions. In the far field, the body and vorticity in the unsteady wake region are represented by a distribution of sources and vortices. As typical of slender body theories, the source strength can be directly related to the body geometry. The vorticity must be determined by the solution of a pair of coupled singular integral equations. The integral equations are solved by a successive approximation scheme. The side forces and yaw moments are calculated using the source and Vortex strengths. &&Numerical results are presented. Due to the lack of experimental data, comparison with experimental results are made for the two dimensional problem only. Qualitative agreements between the numerical and experimental results are indicated.