Gravity-driven flows in a turbulent fluid

Abstract

The formation and destruction of a gravity current in a turbulent fluid is examined in laboratory experiments. The gravity current is produced by lock exchange and the fluid is kept turbulent by bubbling air from the base of the tank. When the lock is released the buoyancy forces associated with the reduced gravity g′ between the fluid on the two sides of the lock drives a counterflow, with the dense fluid slumping underneath the less-dense fluid, and a gravity current is formed. The current has a sharp density front at its leading edge, and a stable density stratification is established behind the front. The turbulence, characterized by a longitudinal turbulent diffusion coefficient K, tends to mix this stable stratification. Once the fluid is vertically mixed the gravity current front is destroyed, and the density varies smoothly with horizontal distance over a zone whose length increases with time owing to the continuing longitudinal turbulent diffusion and buoyancy driving. It is found that the gravity current propagates over a distance L1 before it is destroyed, where L1/H ≈ 0.08(g′H)½ H/K, and H is the fluid depth. At this point turbulent dissipation balances the buoyancy driving and frontogenesis is inhibited. The turbulent dispersion coefficient is found to increase with the buoyancy driving with K∞ Ri½, where Ri = g′H/q2 and q is the r.m.s. turbulence velocity fluctuations. It is also shown that when the turbulence level is reduced nonlinearities in the horizontal density gradient can sharpen up to form a front. The implications of these frontogenetical processes to the sea-breeze front and fronts in shallow seas is discussed.