Laboratory Measurements of Differential Diffusion in a Diffusively Stable, Turbulent Flow

Laboratory experiments were performed to determine the conditions under which differential diffusion occurs and to evaluate its effect on the mixing efficiency. Diffusively stable profiles of temperature and salinity were stirred steadily by horizontally oscillating vertical rods. The two-component stratification ensures that both scalars experience the same stratification and forcing, or Richardson and Reynolds numbers. The eddy diffusivities KT and KS, for temperature and salinity, were estimated by fitting theoretical solutions of diffusion equations to measured profiles, and the mixing efficiency was computed as the ratio of the potential energy change during a stirring interval to the work done in that interval. Differential diffusion occurred for ɛa/νN2 < 300–500, where ɛa is an average dissipation rate computed from an integrated energy budget. The diffusivity ratio d = KS/KT varied between 0.5 and 1 in the range 50 < ɛa/νN2 < 500. The experiments also show that differential diffusion can significantly affect the mixing efficiency. An important dimensionless parameter is the density ratio Rρ, which is the ratio of the density change due to temperature to that due to salinity. Measurements in cases with low density ratio (Rρ ≈ 0.25) and high density ratio (Rρ ≈ 5) showed that the mixing efficiencies agreed well for weak stratification, or small Richardson number. For larger Richardson number, the efficiency for the high-density-ratio case exceeded that for the low-density-ratio case by as much as a factor of 1.5.