On mixing across an interface in stably stratified fluid

Abstract

Mixed-layer deepening in stratified fluid has been studied experimentally in mean-shear-free turbulence generated by an oscillating grid. Conditions were varied over a wide range and both two-layered and constant-gradient fluid systems were considered. It is shown that the mixed-layer deepening rate is represented well by power laws, and when local scaling is used all the data can be collapsed on an entrainment relation E = K Ri−n with n = 1.50±0.05 when Ri [gsim ] 7. This power law suggests that the turbulent kinetic energy is made available for mixing on a buoyancy timescale characteristic of eddy recoil or internal-wave breaking rather than a turbulent-eddy overturning timescale. In the constant-gradient situation internal waves are generated which radiate energy away from the interface. An evaluation of the radiated energy indicates, however, that generally energy radiation does not affect the entrainment rate. The coefficient K therefore has the same value (K ≈ 3.8) in linearly stratified fluid as in the two-layer situation. The interface thickness is found to be a function of stability, but reaches an asymptotic value of h/D = 0.055 when Ri is very large. There is some indication that the interface thickness is also a weak function of Reynolds number.

Steady state model and experiment for an oscillating grid turbulent two-layer stratified flow

“…Fig. 7(a-b) displays the time evolutions of the Ri and E for the case 7, showing the sensitivity of the model in the transient period and also supporting the value of n = 1.5 measured by Turner [10] and Hopfinger et al [18]. The overlap of the numerical simulations and the experimental results provides an alternative way to estimate n in the It is noteworthy that the experiments presented here extend the previous measurements on the E − Ri law to a broader range of Ri and E values.…”

“…There are no adjustable parameters and the results of Hopfinger and Turner [10,18], overlap the results in our setup. Furthermore, a power-law fit of all the cases provides the two additional calibration constants A = 3.8 and n = 1.5, which turns to be universal for all the experiments in this setup (for both increasing and, as we reveal in our case, decreasing Ri).…”

“…For instance, Xuequan & Hopfinger [18] and Wolanski et al [19] confirmed the findings of Turner [10], while Fernando & Long [20,21] obtained a higher value of n = 1.75 in saline stratified solutions.…”

“…Furthermore, a power-law fit of all the cases provides the two additional calibration constants A = 3.8 and n = 1.5, which turns to be universal for all the experiments in this setup (for both increasing and, as we reveal in our case, decreasing Ri). [10] and Xuequan & Hopfinger [18].…”

Study of Gas Liquid Mass Transfer in a Grid Stirred Tank

“…These relationships have been verified by a number of studies using grid stirred tanks [24,25,[33][34][35][36][37][38] When studying the influence of oscillating grid turbulence on an interface, the distance z g = H between this interface and the mean position of the grid is of great importance. As one can see from HT, velocity fluctuations' intensity is an hyperbolic function of the distance to the grid, hence they tend to a zero asymptote far from the grid.…”