Calculation of Entrainment in Density Jumps

The density jump in a two-layer channel flow of miscible fluids, in which one of the layers is infinitely deep and at rest, is analyzed using the momentum flux and mass flux conservation equations. The analysis yields simple equations relating the heights upstream and downstream of the jump with the upstream Froude number and the rate of entrainment into the moving layer, as well as a relation between the maximum possible entrainment and the upstream Froude number. The analysis also shows that when the flow down-stream of the jump is controlled by an obstruction or a contraction, the entrainment rate into the jump depends solely on the dimensionless obstruction height contraction ratio and the upstream Froude number.