The Turbulent Schmidt Number

We analyze a large database generated from recent direct numerical simulations (DNS) of passive scalars sustained by a homogeneous mean gradient and mixed by homogeneous and isotropic turbulence on grid resolutions of up to 4096(3) and extract the turbulent Schmidt number over large parameter ranges: the Taylor microscale Reynolds number between 8 and 650 and the molecular Schmidt number between 1/2048 and 1024. While the turbulent Schmidt number shows considerable scatter with respect to the Reynolds and molecular Schmidt numbers separately, it exhibits a sensibly unique functional dependence with respect to the molecular Peclet number. The observed functional dependence is motivated by a scaling argument that is standard in the phenomenology of three-dimensional turbulence