Field correlations and the ultimate regime of turbulent convection
  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. 
Mahendra K. Verma, Pankaj K. Mishra, Ambrish Pandey, and Supriyo Paul
physics.flu-dyn astro-ph.SR nlin.CD