Ship waves on a viscous fluid of finite depth

Abstract

In this paper we are concerned with the wave generation by a singular forcelet in a viscous fluid of finite depth, where the singularity is located far from the bottom and not very near the free surface. In the first part of this work, the image system of an Oseenlet bounded by a no-slip wall, is considered. It is found that the resultant velocity field can be described by a planar distribution of vertical Oseen doublets and a negative Oseenlet located at the mirror point of the singularity with respect to the plane wall. In the second part of the work we deal with the generation of waves by these solutions. By imposing the linearized free-surface conditions on the solutions obtained from the first part, the wave generated is shown to exhibit the Kelvin ship wave pattern that agrees with observation. The effects of water depth and of submergence on the wave amplitude are also investigated. ©1997 American Institute of Physics.