The Effect of a Free Surface on the Two-Dimensional Flow of an Inviscid Density-Stratified Liquid past a Slender Body

摘要

The linearized equation governing the flow of a density-stratified liquid is used, small velocity perturbations and an exponential variation of density with height having been assumed. A dipole in channel flow with a free surface is considered. A streamwise distribution of dipoles would produce a two-dimensional body whose thickness is everywhere proportional to the local dipole strength. The lift on the body would be everywhere zero, and the body would generally be unsymmetrical top to bottom. The perturbation stream function is constructed for this singularity using Fourier integral methods. The radiation condition is applied, eliminating the infinite energy upstream. Far downstream of the singularity a system of internal waves exists, and a single surface wave (decaying hyperbolically with depth) may appear. Expressions are given for the drag associated with these waves. A vortex in channel flow with a free surface also is considered, and expressions for the perturbation stream function and the wave drag are given. The use of image methods in studying free surface problems is discussed. (Author)