Geodesic
About qualitative difference of solutions of two-dimensional and three-dimensional convection
Russian journal of nonlinear dynamics, Tome 5 (2009) no. 2, pp. 183-203.

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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.
Mots-clés : simulation, convection, cascade.
Keywords: hydrodynamics, energy 
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     author = {I. B. Palymskiy},
     title = {About qualitative difference of solutions of two-dimensional and three-dimensional convection},
     journal = {Russian journal of nonlinear dynamics},
     pages = {183--203},
     publisher = {mathdoc},
     volume = {5},
     number = {2},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2009_5_2_a2/}
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I. B. Palymskiy. About qualitative difference of solutions of two-dimensional and three-dimensional convection. Russian journal of nonlinear dynamics, Tome 5 (2009) no. 2, pp. 183-203. http://geodesic.mathdoc.fr/item/ND_2009_5_2_a2/