Effect of Molecular Diffusivities on Countergradient Scalar Transfer in a Strong Stable Stratified Flow

Abstract

Linear rapid distortion theory (RDT) is applied to unsteady, unsheared, stable, thermally stratified air (Pr=0.7), thermally stratified water (Pr=6), and salt-stratified liquid (Sc∼600) flows. The effects of diffusivity and viscosity are included in the analysis and turbulence quantities such as turbulent scalar fluxes and their cospectra are obtained. The results are compared with previous laboratory measurements and direct numerical simulations (DNS). The results show that countergradient scalar transfer (CGST), which transports the scalar counter to the mean gradient (i.e., negative eddy diffusivity), can be predicted by linear RDT, as shown in the previous studies. However, the small-scale persistent downgradient scalar transfer (P-DGST) in air flows and the small-scale persistent CGST (P-CGST) in water flows cannot be predicted by RDT. In a linear process, small-scale CGST occurs first and then it spreads on a large-scale regardless the values of Pr or Sc; then, the small-scale fluxes change their signs to become downgradient flux again (i.e., small-scale flux oscillates with time). The results suggest that the small-scale turbulent scalar transfer in a strong, stable stratified flow is dominated by nonlinear processes, and only the large-scale wave-like motions are controlled by the linear processes.

Keywords

• stratified flow
• heat transfer
• diffusion
• rapid distortion theory