Gravity‐Current Fronts Advancing into Horizontal Ambient Flow

Abstract

An integral model of the front of a gravity current advancing into flowing receiving fluid of slightly smaller density is presented. The analysis is an extension of that given by Benjamin in 1968 in that boundary‐layer shear and energy losses related to front propagation and ambient flow are taken into account. The number of empirical coefficients involved is reduced by requiring that the front speed relative to the receiving flow decreases with increasing flow rate of the receiving fluid, and that for zero front height in counterflow, the solution agrees with the case of the tip of an arrested density wedge. The single remaining empirical coefficient in the expression for the front speed is adopted from earlier work on lock exchange flow. The maximal height of realizable fronts, which is known to be limited to a certain fraction of the water depth, is shown to increase with the ambient velocity. Satisfactory agreement is obtained with experimental results on counterflows as well as coflows reported in the literature.