Dependence of turbulent scalar flux on molecular Prandtl number

The dependence of turbulent scalar flux on molecular Prandtl number is studied by direct numerical simulation of statistically stationary isotropic turbulence with uniform mean gradient of temperature. Both Reynolds averaged scalar flux and subgrid scalar flux are investigated at molecular Prandtl numbers ranging from 0.1 to 3.0. In order to consider the Reynolds number effect, two cases of grid resolution are computed, i.e., 1283 and 2563, with the Taylor-scale Reynolds numbers equaling 30 and 50, respectively. The turbulent Prandtl number is used to characterize the turbulent scalar flux. It is found that both Reynolds averaged turbulent Prandtl number (simplified as turbulent Prandtl number hereafter) and subgrid Prandtl number change with molecular Prandtl number significantly. The turbulent Prandtl number has been found to be a linearly reciprocal function of molecular Prandtl number, whereas the subgrid Prandtl number takes a minimum around Pr=1. The appearance of minimum subgrid Prandtl number around Pr=1 can be well understood based on the analysis of transfer spectrum of scalar flux.