A numerical study of the frontal region of gravity currents propagating on a free-slip boundary

We investigate numerically the three-dimensional flow near the head of gravity currents propagating along a free-slip boundary. The simulations show that two states are possible: a high-mixing state, where the flow departs from the analytic inviscid solution 0.5 channel heights downstream of the front location, and with characteristics similar to the ones observed for purely two-dimensional simulations; and a low-mixing state, where billows are weaker and appear further downstream. To access the high-mixing state, it is necessary to add a source of perturbation upstream of the head in the form of turbulence. At high values of the Reynolds number, the intensity of rms turbulent fluctuations necessary to switch to the high-mixing state is small (0.5% of the speed of propagation) and may explain why the low-mixing state has so far eluded experimental detection. In the low-mixing state, the flow becomes three-dimensional near the front due to centrifugal instabilities caused by the curved streamlines. This instability of the outer flow is coupled to overturning instabilities that develop within the heavy fluid in the head, and suppresses the formation of billows. This complex behavior, which feeds on the interplay of streamline curvature and stratification, should be considered a good model to understand how instabilities occur in other types of strongly nonlinear stratified flows.