Energetics and mixing efficiency of lock-exchange flow

Mixing efficiency between different water masses is typically assumed to be constant in diapycnal mixing parameterizations used in ocean models. As of now, most coarse resolution ocean circulation models employ a constant mixing efficiency value of 0.2 for the shear driven mixing, internal waves and bottom boundary layer parameterizations. This study investigates the energetics and mixing efficiency of the lock-exchange flow at different Reynolds numbers. The lock-exchange experiment resolves Kelvin-Helmholtz vortices and is an idealized test case for oceanic gravity currents. At first, the required spatial resolution for the direct numerical simulations (DNS) is determined in simulations at a constant Reynolds number of 3500. The evolution of background potential energy and tracer variance are used to assess model results. We found that the model spatial resolution should resolve at least the Kolmogorov scale but not necessarily the Batchelor scale if convergences of background potential energy, tracer variance and dissipation are considered. Simulations at Reynolds number of 125, 500, 1000, 2500, 3500, 5000, 6000, 10,000 show that the mixing efficiency in the lock-exchange flow is smaller than 0.2, and it saturates around 0.12 when Reynolds numbers exceed the value of 2500.