Experimental Measurement of the Local Energy Dissipation Rate and its Balance with the Local Heat Flux in Turbulent Thermal Convection

The local energy dissipation rate $\epsilon_{u,c}$ in Rayleigh- B\'enard convection cell was measured experimentally using the particle tracking velocimetry method, with varying Rayleigh number Ra, Prandtl number Pr, and system size $H$. It is found that $\epsilon_{u,c}/(\kappa^3H^{-4})=1.05\times10^{-4}Ra^{1.55 \pm0.02}Pr^{1.15\pm0.38}$. The Ra- and H-dependency of the measured result are found to be consistent with the assumption made for the bulk energy dissipation rate $\epsilon_{u,bulk}$ in the Grossmann-Lohse model, while the Pr-dependency is not. A remarkable finding of the study is that $\epsilon_{u,c}$ balances the directly measured local Nusselt number Nu$_{c}$ in the cell center, not only scaling-wise but also in magnitude.