Effect of Molecular Diffusivities on Countergradient Scalar Transfer in a Strongly Stably Stratified Flow (Study on the Linear and Nonlinear Processes Using RDT)

Abstract

The linear Rapid Distortion Theory (RDT) is applied to stable thermally stratified air (Pr=0.7), thermally stratified water (Pr=6) and salt-stratified liquid (Sc-600) flows without mean shear. Effects of diffusivity and viscosity are included in the analysis and turbulence quanitities 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 counter-gradient scalar transfer (CGST), which transports 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 persistent downgradient scalar transfer (P-DGST) at small scales in air flows and the persistent CGST (P-CGST) at small scales in water flows can not be predicted by RDT. In a linear process, CGST occurs first at small scales and it spreads to all scales regardless ofPr orSc when the initial length scale of turbulence is sufficiently large. The results suggest that the turbulent scalar transfer at small scales in a strongly stably stratified flow is dominated by nonlinear processes and only the large-scale wave-like motions are controlled by linear processes.