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    Igor Palymskiy

    630064, Russia, Novosibirsk, Vatutina st., 71
    SGUTI, physics department


    Palymskiy I. B.
    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.
    Keywords: simulation, hydrodynamics, convection, energy, cascade
    Citation: Palymskiy I. B.,  About qualitative difference of solutions of two-dimensional and three-dimensional convection, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 2, pp.  183-203
    Palymskiy I. B.
    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.
    Keywords: simulation, hydrodynamics, convection, heat transfer, spectrum
    Citation: Palymskiy I. B.,  Numerical investigation of Rayleigh–Benard turbulent convection spectrums, Rus. J. Nonlin. Dyn., 2008, Vol. 4, No. 2, pp.  145-156

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