The Near-Field Disturbance Created by a Body in a Stratified Medium With a Free Surface

Abstract

The inviscid equations of motion for a slender body in a stratified fluid are formulated in a way which illustrates the relationship between the vorticity in the flow and the internal wave behavior. This formulation makes it clear that the problem admits a singular perturbation expansion of the solution if the density variation is small (large Vaisala length). Analytic solutions valid in the near field are obtained for the case of a finite-thickness constant thermocline. The slender body approximation is found to be invalid near the body; the use of this approximation results in a singularity behind the body which extends to infinity. The reason for the appearance of the singularity is given, and a technique for eliminating it is outlined. The effect of the singularity on the solution at the surface is found to be small. Typical behavior of the near-field surface current is presented in graphical form. The near-field surface disturbance is found to result primarily from the basic body potential flow field with corrections made as a result of the stratification.