We derive scaling relations for the thermal dissipation rate in the bulk and in the boundary layers for moderate and large Prandtl number (Pr) convection. Using direct numerical simulations of Rayleigh-Bénard convection, we show that the thermal dissipation in the bulk is suppressed compared to passive scalar dissipation. The suppression is stronger for large Pr. We further show that the dissipation in the boundary layers dominates that in the bulk for both moderate and large Pr. The probability distribution functions of thermal dissipation rate, both in the bulk and in the boundary layers, are stretched exponential, similar to passive scalar dissipation.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): Project No. k1052
Acknowledgements: We thank A. Pandey, A. Guha, and R. Samuel for useful discussions. Our numerical simulations were performed on Shaheen II at Kaust Supercomputing Laboratory, Saudi Arabia, under the Project No. k1052. This work was supported by the research Grant No. PLANEX/PHY/2015239 from Indian Space Research Organisation, India, and by the Department of Science and Technology, India (Grant No. INT/RUS/RSF/P-03), and the Russian Science Foundation, Russia (Grant No. RSF-16-41-02012), for the Indo-Russian project.