Modeling of turbulent Prandtl number in stationary and homogeneous stratified turbulence

The dependency of turbulent Prandtl number on the stratification stability was numerically investigated by means of direct numerical simulation of homogeneous and stratified turbulence in which the gradient Richardson number ranged from 0.05 to 0.15. It was found that the mixing efficiency was almost linearly correlated with the gradient Richardson number. By using this relation, turbulent Prandtl number was expressed by a simple model of linear function of the Richardson number. The proposed model of turbulent Prandtl number was implemented to large eddy simulation to find a better representation of the subgrid-scale diffusion coefficient for heat than the conventional constant model.