On gravity currents in stratified ambients

Abstract

Detailed numerical simulations were conducted of gravity currents released from a lock and propagating at the bottom of a linearly stratified ambient. The objective is to test the predictions of the recent theoretical analysis by Ungarish [M. Ungarish, J. Fluid Mech. 548, 49 (2006)] concerning the dependency of the front velocity (Froude number, Fr) on the stratification parameter (S) and height ratio (a). The functional dependence of the front velocity on S is found to agree with the theoretical results for weak stratification, although the numerically obtained front velocities lie below the predicted values, as a result of viscous effects. Simulations for deeply submerged currents (small a) in strongly stratified ambients (S>0.5) show that the front velocities deviate from the fastest predicted theoretical solution, but fall within the range of the slower solutions found by Ungarish. This observation supports the theoretical prediction concerning (a) the existence of multiple solutions; and (b) the selection of the slowest solution as the front velocity in a nonforced time-dependent flow. The computational results point to the action of internal waves as the cause for the reduced front velocity. The numerical results also confirm the prediction that the thickness ratio of current to ambient is less than one half, and decreases with S.