Igor Palymskiy

The problem of 2-D and 3-D convection of viscous and incompressible fluid between two horizontal stress-free isothermal planes at heating from below has been considering. It is received that in 3-D turbulent convection the mean vorticity scale decreases at growing supercriticality, but in 2-D convection the mean vorticity scale grows and it does the 2-D convection more large-scale and smooth. The growing of the mean vorticity scale at increasing supercriticality $r$ in 2-D convection is conditioned by the red (inverse) energy cascade formed at $r > 4000$ and transferring the kinetic energy from generation scale to the large scales. The appearance of the red cascade is conditioned by additional conservation law for enstrophy in 2-D flows.

Two- and three-dimensional turbulent convectional flows of viscous incompressible fluid in a horizontal layer are studied numerically. The layer is heated from below and its boundaries are assumed to be free of shear stresses. For temperature pulsations the Kolmogorov spectrums $k^{-5/3}$ and $k^{-2,4}$ are found. In the two-dimensional case the Obukhov-Bolgiano spectrum $k^{-11/5}$ and the spectrum $k^{-5}$ for the velocity pulsation are obtained. The spectrum $k^{-5}$ was predicted theoretically for large-Prandtl-number liquids. The results presented in the paper are in good agreement with experimental data and organically extend the numerical results obtained by other researches.