High Reynolds number gravity currents along V-shaped valleys

The motion of saline gravity currents propagating horizontally in a tank of rectangular upper cross section and lower V-shaped valley is investigated both by lock-exchange experiments and a box model. The experiments were performed for equal depths of heavy and light fluid on both sides of the lock gate. The density ratio of the heavy fluid to the light fluid was in the range 1.04–1.13 and the lock height to length aspect ratios ranged from 0.5 to 1.6. We show that a box model with the Froude number of the head defined using the distance from the top of the current to the bottom of the valley predicts the position of the head in close agreement with the experiments. The presence of the valley results in three major differences in the gravity current compared to that flowing along a flat bottom. These are (a) the front of the current is approximately parabolic with radius of curvature proportional to the initial depth of the current, (b) for sufficiently large time t, the velocity of the current in the V-shaped valley varies as t−1/5 compared to t−1/3 in the flat bottom case, and (c) the width of the current in the V-shaped valley decreases with time t according to t−2/5. Based on the box model, we predict that the steeper the flanks of the valley the faster the flow.