Turbulent entrainment in a gravity current

We revisit the classical entrainment experiments for gravity currents on inclined slopes (Ellison and Turner, J. Fluid Mech. 6, 423-448, 1959). We derive an entrainment relation that couples the entrainment rate E to the production of turbulence kinetic energy, the net effect of buoyancy and inner layer. Using direct numerical simulations that are run for durations long enough for the flow to reach universal self-similarity, we show that the net effect of inner layer processes on entrainment is very small and that buoyancy has an almost negligible effect on E. It is demonstrated that the dominant process causing entrainment is turbulence production due to shear. Second, we observe that for all simulations the eddy diffusivity and dissipation rate can be parameterised using the turbulence kinetic energy and shear parameter. This information can be used to derive an entrainment law which is in good agreement with the Direct Numerical Simulation (DNS) results. We discuss the potential reasons for why this result is significantly different from experiments and the classical entrainment law introduced by Ellison and Turner.