Energetics and mixing efficiency of lock-exchange gravity currents using simultaneous velocity and density fields

A series of laboratory experiments on energy-conserving gravity currents in a lock-exchange facility are conducted for a range of Reynolds numbers, Re = U(F)h/upsilon = 485-12270, where U-F is the front velocity of the current, h the current depth, and upsilon the kinematic viscosity of the fluid. The velocity and density fields are captured simultaneously using a particle image velocimetry-planar laser induced fluorescence system. A moving average method is employed to compute the mean field and a host of turbulence statistics, namely, turbulent kinetic energy (K), shear production (P), buoyancy flux (B), and energy dissipation (epsilon) during the slumping phase of the current. The subsequent findings are used to ascertain the quantitative values of mixing efficiency, Ri(f), Ozmidov length scale (L-o), Kolmogorov length scale (L-k), and eddy diffusivities of momentum (k(m)) and scalar (k(rho)). Two different forms of Ri(f) are characterized in this study, denoted by Ri(f)(I) = B/P and Ri(f)(II) = B/B+epsilon. The results cover the entire diffusive regime (3 < Re-b < 10) and a portion of the intermediate regime (10 < Re-b < 50), where Re-b = epsilon/upsilon N-2 is the buoyancy Reynolds number that measures the level of turbulence in a shear-stratified flow, with N being the Brunt-Vaisala frequency. The variation of turbulence quantities, (P) over bar (z), (B) over bar (z), and (epsilon) over bar (z), along the depth of the current shows a marked increase at the interface of the ambient and current fluids, owing to the development of a shear-driven mixed layer. Based on the changes in the turbulence statistics and the length scales, it is inferred that the turbulence decays along the length of the current. The mixing efficiency monotonically increases in the diffusive regime (Re-b < 10) and is found to be <(Ri(f)(I))over bar> approximate to 0.15 and <(Ri(f)(II))over bar>( )approximate to 0.2 in the intermediate regime. Using the value of <(Ri(f)(II))over bar>, the normalized eddy diffusivity of momentum is parameterized as k(m)/upsilon.Ri(g) = 1.2Re(b), where Ri(g) is the gradient Richardson number, and the normalized eddy diffusivity of scalar is parameterized as k(rho)/upsilon = 0.2Re(b).