Global heat transport scaling in plume-controlled regime in turbulent Rayleigh-B\'enard convection$^1$

Previous study by Chong et al.$^2$ has introduced a normalized aspect-ratio $\Gamma/\Gamma_{opt}$ ($\Gamma_{opt}=29.37Ra^{-0.31}$) where the plume coverage at fixed $\Gamma/\Gamma_{opt}$ is invariant with respect to $Ra$ in the so-called plume-controlled regime in Rayleigh-Bénard convection. We have studied the global heat transport scaling (expressed as Nusselt number $Nu$) at fixed $\Gamma/\Gamma_{opt}$ with the Rayleigh number $Ra$ between $10^7$ and $10^{10}$ at fixed Prandtl number $Pr=4.38$ by direct numerical simulations. It is found that at $\Gamma/\Gamma_{opt}=1$ where the thermal plume becomes highly coherent and system-sized, $Nu$ exhibits the scaling $Nu-1 \sim Ra^{0.327\pm0.001}$ over three decades of $Ra$. This scaling is different from that found at $\Gamma=1$ for which $Nu-1 \sim Ra^{0.308\pm0.001}$, and this difference in scaling can be shown evidently in the compensated plots. 1. This work was supported by RGC of HKSAR (No. CUHK404513), CUHK Direct Grant (No. 3132740) and through a HKPhD Fellowship. 2. Chong, K. L., Huang, S.-D., Kaczorowski, M. \& Xia, K.-Q. 2015 Condensation of coherent structures in turbulent flows. Phys. Rev. Lett. 115, 264503.