A lock exchange flow

Abstract

In this paper the interchange flow between two reservoirs connected by a contraction and containing fluid of different densities is considered. The effect of the boundary layers on the floor and walls of the contraction on the depth of flow in the contraction is discussed for the case of single layer flowing from one reservoir to the other. Next the theory for a denser layer plunging under a stationary layer is developed. In this case there is a discontinuity at the point of intersection of the surfaces of the flowing and the stationary fluids and there are three possible flow régimes depending on whether this discontinuity occurs at, downstream of, or upstream of the contraction.Finally, the case where there is an interchange flow with fluid flowing from each reservoir into the other is introduced. This latter theory parallels that developed by Wood (1968) for the case of two layers flowing from one reservoir through a contraction into another reservoir and as in this case there are two points of control, one at the position of minimum width and one (the virtual point of control) away from this position of minimum width.Experiments are described for a single layer flowing through the contraction and the results of these are used to obtain an indication of the accuracy that could be expected from the experiments with the more complicated exchange flow. The experiments with the exchange flow verified the major elements of the theory.