The difference in turbulent diffusion between active and passive scalars in stable thermal stratification

Abstract

The difference in turbulent diffusion between active scalar (heat) and passive scalar (mass) in a stable thermally stratified flow is investigated both experimentally and numerically. The experiments are conducted in an unsheared thermally stratified water flow downstream of a turbulence-generating grid. Passive mass is released into the stable thermally stratified flow from a point source located 60 mm downstream from the grid. Instantaneous streamwise and vertical velocities, the temperature of the active scalar and the concentration of the passive scalar are simultaneously measured using a combined technique with a two-component laser-Doppler velocimeter (LDV), a resistance thermometer and a laser-induced fluorescence (LIF) method. From the measurements, turbulent heat and mass fluxes and eddy diffusivities for both active heat and passive mass are estimated. To investigate the Prandtl or Schmidt number effects on the difference in turbulent diffusion between active heat and passive mass, a three-dimensional direct numerical simulation (DNS) based on a finite difference method is applied to stable thermally stratified flows of both water and air behind the turbulence grid. The Schmidt number of passive mass in the DNS is set to the same value as the Prandtl number of active heat.

The results show that stable stratification causes a large difference in eddy diffusivities between active heat and passive mass. The numerical predictions by the DNS are in qualitative agreement with the measurements despite the assumption of the same molecular diffusivity for active heat and passive mass. The difference suggests that the assumption of identical eddy diffusivity for active heat and passive mass, used in conventional turbulence models, gives significant errors in estimating heat and mass transfer in a plume under stably stratified conditions.