The slow motion of a flat plate in a viscous stratified fluid

Abstract

The existence of a ‘wake’ upstream of an obstacle moving slowly through a stratified fluid has been known for some time. The present study shows that a thin, flat plate moving slowly and horizontally through a linearly stratified salt-water mixture has, in addition, a boundary layer over the plate whose thickness increases upstream from thebackof the plate.The theory assumes that the ratio of diffusivity to viscosity is small, and that the plate moves so slowly that inertia forces are negligible; under these conditions, a similarity solution is derived describing the boundary layer over the plate. The study also shows that salt diffusion is important in a second, thinner boundary layer whose thickness increases from the front of the plate.In the experiment, a plate was towed through a tank of linearly stratified salt water. From streak photographs of the boundary layer over the plate, it was possible to confirm quantitatively the similarity solution and to infer at very slow velocities the presence of the thin diffusion boundary layer.