Selective withdrawal from a layered fluid

Abstract

The selective withdrawal of a layered fluid from a reservoir has interesting properties which are not present if the stratification is continuous. The problem investigated is that of finding the ratios of the discharges from each flowing layer when the total discharge from all layers is regulated at the outlet. It is shown that the ratios are determined by the requirement that the flow be smooth at critical points in the flow, each critical point being a point at which the long-wave velocity on one of the interfaces is zero. If there are too many critical points, the flow is over-determined and becomes unsteady. It follows therefore that if the external conditions change slowly, such as in the slow draining of a reservoir, the flow alternates between intervals in which the flow ratios also change slowly and intervals in which the flow ratios oscillate unsteadily. An experiment is described in which the theoretical conclusions were tested for two-layer flow. Good agreement was obtained between theory and experiment.