Eur. Phys. J. B 73, 265-273 (2010)
https://doi.org/10.1140/epjb/e2009-00428-4

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

¹ Institute of Mechanics, Bulgarian Academy of Sciences, Akad G. Bonchev Str., Bl. 4, 1113 Sofia, Bulgaria
² Max-Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany

Corresponding author: vitanov@mech.bas.bg

Received: 1 August 2009
Revised: 30 October 2009
Published online: 17 December 2009

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.