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