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Using direct numerical simulations of Rayleigh-B\'{e}nard convection (RBC)under free-slip boundary condition, we show that the normalized correlationfunction between the vertical velocity field and the temperature field, as wellas the normalized viscous dissipation rate, scales as $Ra^{-0.22}$ formoderately large Rayleigh number $Ra$. This scaling accounts for the Nusseltnumber ($Nu$) exponent to be around 0.3 observed in experiments. Numericalsimulations also reveal that the above normalized correlation functions areconstants for the convection simulation under periodic boundary conditions.

Field correlations and the ultimate regime of turbulent convection