Geodesic
Numerical investigation of spectrums of three-dimensional turbulent convection
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 62-71

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The three-dimensional turbulent convectional flows of viscous and incompressible fluid in a rectangular parallelepiped numerically is simulated at heating from below. The horizontal boundaries are stress-free and isothermal. The calculated time spectrum of temperature pulsations at supercriticality is equal to 410 in centre of convective cell has a good agreement with experimental data for convection in cryogenic $He$. The Obukhov–Bolgiano spectra $k^{-11/5}$, $k^{-3}$ and $k^{-5}$ have been found for velocity pulsations. Also for temperature pulsations the Kolmogorov $k^{-5/3}$ and $k^{-2.4}$ are obtained. Such spectrums denote on temperature behavior as passive admixture and that dominant force for velocity is buoyancy. 
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     author = {I. B. Palymskiy},
     title = {Numerical investigation of spectrums of three-dimensional turbulent convection},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
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I. B. Palymskiy. Numerical investigation of spectrums of three-dimensional turbulent convection. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 10 (2010) no. 1, pp. 62-71. http://geodesic.mathdoc.fr/item/ISU_2010_10_1_a10/