Turbulent Prandtl number from isotropically forced turbulence

Turbulent motions enhance the diffusion of large-scale flows and temperature gradients. Such is often parameterized by coefficients turbulent viscosity ( $\nu _{t}$ ) thermal diffusivity $\chi that are analogous to their microscopic counterparts. We compute imposing sinusoidal velocity gradients on a flow measuring response system. also confirm our results using experiments where imposed allowed decay. To achieve this, we use weakly compressible three-dimensional hydrodynamic simulations isotropically forced homogeneous turbulence. find diffusion, as well ratio Prandtl number, $\textit {Pr}_{t} = \nu _{t}/\chi , approach asymptotic values at sufficiently high Reynolds Péclet numbers. do not significant dependence {Pr}_{t}$ number {Pr} /\chi$ . These findings in stark contrast from $k{-}\epsilon$ model, which suggests increases monotonically with decreasing {Pr}$ The current relevant for ongoing debate on, example, nature very-low- regimes stellar convection zones.