4/5 Kolmogorov law for statistically stationary turbulence: Application to high-Rayleigh-number Bénard convection

The Kolmogorov relation for the third-order moments of the velocity differences is generalized for the case of statistically steady turbulence and applied to the Bénard convection problem. The predicted temperature and velocity spectra are ${\mathit{E}}_{\mathit{T}}$≊${\mathit{k}}^{\mathrm{-}7/5}$ and E≊${\mathit{k}}^{\mathrm{-}11/5}$, respectively. At the smaller scales, in the dissipation range of the temperature fluctuations, the Kolmogorov range where most of the energy is dissipated is predicted. The new set of scaling exponents, which can be observed in the experiments in the small-aspect-ratio convection cells, is derived.