The slow transverse motion of a flat plate through a non-diffusive stratified fluid

Abstract

We consider the two-dimensional flow produced by the slow horizontal motion of a vertical plate of height 2b through a vertically stratified (ρ = ρ₀(1 - βz)) non-diffusive viscous fluid. Our results are valid when U² [Lt ] Ub/ν [Lt ] 1, where U is the speed of the plate and ν the kinematic viscosity of the fluid. Upstream of the body we find a blocking column of length 10⁻²b⁴/(Uν/βg. This column is composed of cells of closed streamlines. The convergence of these cells near the tips of the plate leads to alternate jets. The plate itself is embedded in a vertical shear layer of thickness (Uν/βg)^1/3. In the upstream portion of this layer the vertical velocities are of order U and in the downstream portion of order Ub/(Uν/βg)^1/3 ([Gt ] U). The flow is uniform and undisturbed downstream of this layer.