Mixing and entrainment in inclined gravity currents

We explore the dynamics of inclined temporal gravity currents using direct numerical simulation, and find that the current creates an environment in which the flux Richardson number, gradient Richardson number and turbulent flux coefficient are constant across a large portion of the depth of the outer layer. Changing the slope angle modifies these mixing parameters, and the flow approaches a maximum Richardson number of approx. 0.15 as the angle tends to zero, for which the entrainment coefficient E->0.

The turbulent Prandtl number remains O(1) for all slope angles, demonstrating that E->0 is not caused by a switch-off of the turbulent buoyancy flux. Instead, E->0 occurs as the result of the turbulence intensity going to zero as the angle tends to zero, due to the flow requiring larger and larger shear to maintain the same level of turbulence. We develop a conceptual model which is in excellent agreement with the DNS data.