The Smallest Temperature Scales in a Turbulent Channel Flow at High Prandtl Numbers

The object of this paper is to perform the numerical simulations of the temperature fields at low Reynolds numbers, i.e. Re_τ = 150 and Re_τ = 170.8, and at Prandtl numbers, Pr = 1 and Pr = 100. The spatial scales of the velocity field can be successfully described with DNS accuracy, meanwhile the scales of temperature fields decreasing approximately with Pr^3/2 and cannot be resolved for entire energy scalar spectra due to the computer limitations. To overcome these obstacles, filtering and damping of the highest temperature wave number modes in homogeneous directions are introduced rather than modeling the unresolved subgrid scales. First, numerical simulations at Pr = 1 are performed in order to make comparison of the temperature field described with DNS accuracy and filtered and damped temperature fields described with coarser numerical grids. Obtained results show that at least first and second order statistics are comparable to the DNS ones. Next step is to analyze this approach at two orders of magnitude higher Prandtl numbers, i.e: Pr = 100. Comparison is a little bit difficult because no real DNS of the temperature fields at such high Prandtl number has been performed so far. But we estimate that results are still accurate at least in the proximity of the wall.