Study of global heat transport and plume morphology in severely-confined Rayleigh-B\'enard convection$^1$

We study systematically how severe geometrical confinement influences the global heat transport (expressed as Nusselt number $Nu$) and the plume morphology in Rayleigh-B\'enard convection (RBC) by means of direct numerical simulations. Broad ranges of width-to-height aspect-ratio ($1/128 \le \Gamma \le 1$) and Rayleigh number ($3\times10^4 \le Ra \le 10^{11}$) at fixed Prandtl number $Pr=4.38$ are considered in present study. It is found that $Nu$ exhibits the scaling $Nu-1 \sim Ra^{0.61}$ over three decades of $Ra$ at $\Gamma=1/128$ and the flow is dominated by finger-like, long-lived plume columns for such severely-confined situation. The $Nu$ scaling and the flow structures contrast sharply to that found at $\Gamma=1$ for which $Nu$ exhibits the scaling $Nu-1 \sim Ra^{0.31}$ and the flow is dominated by mushroom-like, fragmented thermal plumes. Analogy is made between the severely-confined RBC and strongly rotating RBC. 1. This work was supported by RGC of HKSAR (No. CUHK404513), CUHK Direct Grant (No. 3132740) and through a HKPhD Fellowship.