On the ultimate regime of Rayleigh--Bernard convection
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 4, pp. 61-67

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A two-dimensional and non-stationary convection of a viscous incompressible liquid in a vertical narrow channel during down heating is discussed. A new asymptotic regime of convection with a linear dependence of Nusselt and Reynolds numbers on the Rayleigh number was derived. The asymptotic law derived can be considered as an addition to the fundamental root law.
Keywords: convection; asymptotic regime; Rayleigh number; Prandtl number; spectrum; linear instability.
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     author = {I. B. Palymskiy},
     title = {On the ultimate regime of {Rayleigh--Bernard} convection},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
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     publisher = {mathdoc},
     volume = {7},
     number = {4},
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     url = {http://geodesic.mathdoc.fr/item/VYURM_2015_7_4_a7/}
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I. B. Palymskiy. On the ultimate regime of Rayleigh--Bernard convection. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 4, pp. 61-67. http://geodesic.mathdoc.fr/item/VYURM_2015_7_4_a7/