Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection

Abstract

The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh-Bénard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio $\Gamma$ of a closed cylindrical cell and the Rayleigh number $Ra$. For small and moderate aspect ratios, the global heat transfer law $Nu=A\times R{a}^{\beta }$ shows a power law dependence of both fit coefficients $A$ and $\beta$ on the aspect ratio. A minimum Nusselt number coincides with the point where the LSC undergoes a transition from a single-roll to a double-roll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations. The aspect ratio dependence of the turbulent heat transfer for small and moderate $\Gamma$ is in line with a varying amount of energy contained in the LSC, as quantified by the Proper Orthogonal Decomposition analysis. For $\Gamma \gtrsim 8$ the heat transfer becomes independent of the aspect ratio.

17 pages, 11 Postscript figures (in parts downscaled), accepted for J. Fluid Mech

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