About qualitative difference of solutions of two-dimensional and three-dimensional convection

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.