Influence of the angle between the wind and the isothermal surfaces on the boundary layer structures in turbulent thermal convection

Olga Shishkina, Sebastian Wagner, Susanne Horn

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Abstract

We derive the asymptotes for the ratio of the thermal to viscous boundary layer thicknesses for infinite and infinitesimal Prandtl numbers Pr as functions of the angle β between the large-scale circulation and an isothermal heated or cooled surface for the case of turbulent thermal convection with laminar-like boundary layers. For this purpose, we apply the Falkner-Skan ansatz, which is a generalization of the Prandtl-Blasius one to a nonhorizontal free-stream flow above the viscous boundary layer. Based on our direct numerical simulations (DNS) of turbulent Rayleigh-Bénard convection for Pr=0.1, 1, and 10 and moderate Rayleigh numbers up to 108 we evaluate the value of β that is found to be around 0.7πfor all investigated cases. Our theoretical predictions for the boundary layer thicknesses for this β and the considered Pr are in good agreement with the DNS results.
Original languageEnglish
Article number033014
Number of pages6
JournalPhysical Review E
Volume89
DOIs
Publication statusPublished - 21 Mar 2014
Externally publishedYes

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