Turbulent density transport in the mixing layer of an unsteady gravity current

Abstract

Turbulent mixing is a key process influencing the dynamics of subaqueous gravity currents. In this study, the evolution of the local turbulent mixing dynamics along a lock-exchange gravity current propagating over a mild slope is statistically investigated by ensemble-averaging and spanwise-averaging 200 large eddy simulation results at two time steps characteristic of the slumping and inertial phases of the current's propagation. Premultiplied velocity and density transport spectra are computed and confirm that vertical turbulent mixing is mainly due to the large-scale structures – i.e. Kelvin-Helmholtz billows – with smaller scale turbulence acting to homogenise the density field. We show that, unlike large-scale oceanic underflows, the head holds a substantial portion of the total turbulent transport flux (~ 25%), and the decrease of the local vertical density transport flux in the body scales exponentially with distance from the head, when normalised by the current's length. Finally, the vertical density transport flux is shown to be well predicted by an eddy-viscosity model after appropriate tuning of the model constants.