Effects of molecular diffusivities on counter-gradient scalar and momentum transfer in strongly stable stratification

Abstract

The effects of molecular diffusivities of heat and mass on the counter-gradient scalar and momentum transfer in strongly stable stratification are experimentally investigated in unsheared and sheared stratified water mixing-layer flows downstream of turbulence-generating grids. Experiments are carried out in two kinds of stably stratified water flows. In the case of thermal stratification, the difference between the turbulent fluxes of an active scalar (heat with the Prandtl number of Pr ≈ 6) and a passive scalar (mass with the Schmidt number of Sc ≈ 600) is investigated. In the case of salt stratification, the effects of the molecular diffusion of the active scalar (salt) with a very high Schmidt number of Sc ≈ 600 on the counter-gradient scalar transfer is studied. Comparisons of the effects of molecular diffusivities are also made between thermally stratified water and air (Pr ≈ 0.7) flows. Further, the effects of mean shear on the counter-gradient scalar and momentum transfer are investigated for both stratified cases. Instantaneous temperature, concentration and streamwise and vertical velocities are simultaneously measured using a combined technique with a resistance thermometer, a laser-induced fluorescence method, and a laser-Doppler velocimeter with high spatial resolution. Turbulent scalar fluxes, joint probability density functions, and cospectra are estimated.The results of the first case show that both active heat and passive mass develop counter-gradient fluxes but that the counter-gradient flux of passive mass is about 10% larger than that of active heat, mostly due to molecular diffusion effects at small scales. The counter-gradient scalar transfer mechanism in stable stratification can be explained by considering the relative balance between the available potential energy and the turbulent kinetic energy as in Schumann (1987). In thermally and salt-stratified water mixing-layer flows with the active scalars of high Prandtl and Schmidt numbers, the buoyancy-induced motions with finger-like structures first contribute to the counter-gradient scalar fluxes at small scales, and then the large-scale motions, which bring fluid back to its original levels, generate the counter-gradient fluxes at large scales. The contribution of the small-scale motions to the counter-gradient fluxes in stratified water flows is quite different from that in stratified air flows. The higher Prandtl or Schmidt number of the active scalar generates both the stronger buoyancy effects and the longer time-oscillation period of the counter-gradient scalar fluxes. The time-oscillation occurs at large scales but the counter-gradient fluxes at small scales persist without oscillating. The mean shear acts to reduce the counter-gradient scalar and momentum transfer at large scales, and therefore the counter-gradient fluxes in sheared stratified flows can be seen only in very strong stratification. The behaviour of the counter-gradient momentum flux in strong stratification is quite similar to that of the counter-gradient scalar flux.