Laminar flow of a stably stratified fluid past a flat plate

Abstract

Laminar flow of a stably stratified fluid with uniform upstream velocity and density gradient past a flat plate is investigated experimentally and theoretically. In the experimental study, the flat plate, parallel to the direction of motion, is towed horizontally at uniform speeds in a tank of stratified salt water at uniform density gradients. The horizontal velocity in front of, above, and behind the flat plate is measured with a flow visualization technique. One of the striking phenomena is the strong upstream influence (the upstream wake) of an obstacle in a flow of stably stratified fluid when the gravity effect is comparable to, or more than the inertial effect. The velocity profiles of the upstream wake and boundary layer above the flat plate are wavy and found to be governed by the ratio of Reynolds number Be to Richardson number Ri. The problem is also analysed theoretically with Boussinesq's approximation and two-parameter perturbation expansions for the upstream wake and the boundary layer. The solutions for the upstream wake and for the boundary layer are compared with measurements.