Crossover of spectral scaling in thermal turbulence

The scaling ranges of temperature and velocity fluctuations in thermally driven turbulence are studied by analyzing the various contributions to the equations of motion. The crossover wave number ${\mathit{k}}_{\mathit{B}}$ between Bolgiano-Obukhov and Kolmogorov-Obukhov scaling is estimated in terms of the forcings. By evaluating the thermal and buoyant stirrings and dissipations of Rayleigh-Bénard convection experiments we find ${\mathit{k}}_{\mathit{B}}$ much larger than ${\mathit{L}}^{\mathrm{-}1}$, the energy-containing scale, but smaller than (10η${)}^{\mathrm{-}1}$, the viscous scale. For computer simulation of randomly thermal driven turbulence we find ${\mathit{k}}_{\mathit{B}}$ of the order of ${\mathit{L}}^{\mathrm{-}1}$. This might explain why the Bolgiano-Obukhov scaling was observed in laboratory experiments whereas Kolmogorov-Obukhov scaling was found in computer simulation of thermally driven turbulence.