Turbulent Prandtl number from isotropically forced turbulence

Turbulent motions enhance the diffusion of large-scale flows and temperature gradients.Such diffusion is often parameterized by coefficients of turbulent viscosity (nu(t))and turbulent thermal diffusivity (chi(t)) that are analogous to their microscopic counterparts. Wecompute the turbulent diffusion coefficients by imposing sinusoidal large-scale velocityand temperature gradients on a turbulent flow and measuring the response of the system.We also confirm our results using experiments where the imposed gradients are allowedto decay. To achieve this, we use weakly compressible three-dimensional hydrodynamicsimulations of isotropically forced homogeneous turbulence. We find that the turbulentviscosity and thermal diffusion, as well as their ratio the turbulent Prandtl number,Pr-t=nu(t)/chi(t), approach asymptotic values at sufficiently high Reynolds and P & eacute;clet numbers.We also do not find a significant dependence of Pr(t )on the microscopic Prandtl number Pr=nu/chi. These findings are in stark contrast to results from the k-is an element of model, whichsuggests that Pr-t increases monotonically with decreasing Pr. The current results arerelevant for the ongoing debateon, for example, the nature of the turbulent flows in thevery-low-Prregimes of stellar convection zones.

Automated summary

Turbulent motions enhance the diffusion of large-scale flows and temperature gradients. We compute the turbulent diffusion coefficients by imposing gradients and measuring the system response. The turbulent viscosity and thermal diffusion approach asymptotic values at high Reynolds and Péclet numbers, and the turbulent Prandtl number is not significantly dependent on the microscopic Prandtl number.