Jumps in layered miscible fluids

Abstract

Experiments with hydraulic jumps in a layered flow with a small density difference at the interface are described. Two different configurations are examined, with shear between the fluids either upstream or downstream of the jump. It is shown that when the shear stress on all interfaces is small enough for there to be no mixing either the theory which assumes hydrostatic pressure on the face of the jump or that which assumes energy conservation in one of the layers describes the results. In the experiments for a jump in the lee of a towed obstacle this condition is always satisfied, but for a jump advancing into stationary layers it is only satisfied when the ratio of the height behind the jump to that in front is less than about 2. Beyond this limit there is mixing behind the first wave of the undular jump and the flow behaves like the head of a gravity current. The theory with energy conservation in one layer is extended to the case of a stationary jump, and for this case it is shown that for a given downstream control an approximate value of the fluid entrained can be computed.