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Differential mixing in a stratified fluid

We present an experimental and theoretical study of the effects of localized mixing on a stratified fluid contained in a reservoir. In the experiments, mixing is accomplished by means of a vertically oscillating, horizontal grid located near the water surface at one end of the reservoir. Once the grid is set in motion, a mixed layer forms immediately beneath it. As this layer deepens, a horizontal pressure gradient builds up which drives an outflow of mixed fluid into the unmixed interior of the reservoir. This outflow slows, and eventually brings to a halt, mixed-layer deepening under the grid. At this equilibrium depth, the vertical velocity of the entrainment interface induced by the outflow exactly equals the velocity at which the entrainment interface would move downwards because of mixing. This equilibrium state persists until the outflow intrusion is blocked by the far wall of the reservoir, at which time deepening resumes under the grid. Asymptotically, the fluid reaches a state in which mixed-layer deepening is independent of position.