Entrainment and mixing in lock-exchange gravity currents using simultaneous velocity-density measurements

Abstract

Gravity currents modify their flow characteristics by entraining ambient fluid, which depends on a variety of governing parameters such as the initial density, Δρ, the total initial height of the fluid, H, and the slope of the terrain, α, from where it is released. It is imperative to study the entrainment dynamics of a gravity current in order to have a clear understanding of mixing transitions that govern the flow physics, the velocity mixing layer thickness, δu, and the density mixing layer thickness, δρ. Experiments were conducted in a lock-exchange facility in which the dense fluid was separated from the ambient lighter fluid using a gate. As the gate is released instantaneously, an energy conserving gravity current is formed, for which the only governing parameter is the Reynolds number defined as Re=Uhν, where U is the front velocity of the gravity current and h is the height of the current. In our study, the bulk Richardson number (inverse of Froude number, Fr), Rib = g′HUb2 = 1, takes a constant value for all the experiments, with Ub being the bulk velocity of the current defined as Ub = g′H. Simultaneous particle image velocimetry and planar laser induced fluorescence measurement techniques are employed to get the velocity and density statistics. Using the buoyancy conservation equation, a new flux-based method was formulated for calculating the entrainment coefficient, EF, near the front and head of the propagating gravity current for a Reynolds number range of Re ≈ 485-12 270 used in our experiments. At the head of the current, the results show a mixing transition at Re ≈ 2700 that is attributed to the flow transitioning from weak Holmboe waves to Kelvin-Helmholtz instabilities, in the form of Kelvin-Helmholtz vortex rolls. Following this mixing transition, the entrainment coefficient continued to increase with increasing Reynolds number owing to the occurrence of three-dimensional Kelvin-Helmholtz billows that promote further small-scale local mixing. Such a mixing transition indicates that a fully turbulent state is not reached even at Re = 12 270 and the amount of entrainment and ensuing mixing depends on the type of flow instability and presence of small-scale secondary structures. The entrainment dynamics were further substantiated using the ratio of δu and δρ. It was observed that δuδρ decreases with increasing Re and reaches a constant value of δuδρ≈ 1 at high values of Re. This trend is in contrast to the entrainment coefficient EF, which never reaches a constant value even at high enough Re. This disparity could be explained by the fact that EF accounts for small-scale scalar mixing, which is not captured by the ratio of mixing layer thicknesses. Experimentally, it was also observed that the EF value near the front of gravity current was 2-9 times higher than the head value depending on the value of the Reynolds numbers. At low Reynolds numbers, the entrainment near the front is an order of magnitude higher than the head and the value decreases with increasing Re. This could be attributed to different modes of entrainment near the front (dominated by vortical structures) and the head (dominated by turbulent flux exchange triggered by the nature of the flow instability). The results from this study improve our understanding of entrainment dynamics and would be useful in developing empirical parameterizations for mixing in stratified flows.