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Optimum fields and bounds on heat transport for nonlinear convection in rapidly rotating fluid layer

  • Statistical and Nonlinear Physics
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Abstract

By means of the Howard-Busse method of the optimum theory of turbulence we investigate numerically the effect of strong rotation on the upper bound on the convective heat transport in a horizontal fluid layer of infinite Prandtl number Pr. We discuss the case of fields with one wave number for regions of Rayleigh and Taylor numbers R and Ta where no analytical asymptotic bounds on the Nusselt number Nu can be derived by the Howard-Busse method. Nevertheless we observe that when R > 108 and Ta is large enough the wave number of the optimum fields comes close to the analytical asymptotic result α1 = (R/5)1/4. We detect formation of a nonlinear structure similar to the nonlinear vortex discussed by Bassom and Chang [Geophys. Astrophys. Fluid Dyn. 76, 223 (1994)]. In addition we obtain evidence for a reshaping of the horizontal structure of the optimum fields for large values of Rayleigh and Taylor numbers.

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Authors and Affiliations

  1. Institute of Mechanics, Bulgarian Academy of Sciences, Akad G. Bonchev Str., Bl. 4, 1113, Sofia, Bulgaria

    N. K. Vitanov

  2. Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187, Dresden, Germany

    N. K. Vitanov

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  1. N. K. Vitanov
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Correspondence to N. K. Vitanov.

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Vitanov, N. Optimum fields and bounds on heat transport for nonlinear convection in rapidly rotating fluid layer. Eur. Phys. J. B 73, 265–273 (2010). https://doi.org/10.1140/epjb/e2009-00428-4

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  • DOI: https://doi.org/10.1140/epjb/e2009-00428-4

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