Exploring the severely confined regime in Rayleigh–Bénard convection

We study the effect of severe geometrical confinement in Rayleigh–Bénard convection with a wide range of width-to-height aspect ratio x1D6E4, 1/128 x1D6E4 1, and Rayleigh number Ra, 3 10^4 Ra 1 10^11, at a fixed Prandtl number of Pr=4. 38 by means of direct numerical simulations in Cartesian geometry with no-slip walls. For convection under geometrical confinement (decreasing x1D6E4 from 1), three regimes can be recognized (Chong et al. , Phys. Rev. Lett. , vol. 115, 2015, 264503) based on the global and local properties in terms of heat transport, plume morphology and flow structures. These are Regime I: classical boundary-layer-controlled regime; Regime II: plume-controlled regime; and Regime III: severely confined regime. The study reveals that the transition into Regime III leads to totally different heat and momentum transport scalings and flow topology from the classical regime. The convective heat transfer scaling, in terms of the Nusselt number Nu, exhibits the scaling Nu-1 Ra^0. 61 over three decades of Ra at x1D6E4=1/128, which contrasts sharply with the classical scaling Nu-1 Ra^0. 31 found at x1D6E4=1. The flow in Regime III is found to be dominated by finger-like, long-lived plume columns, again in sharp contrast with the mushroom-like, fragmented thermal plumes typically observed in the classical regime. Moreover, we identify a Rayleigh number for regime transition, Ra^ = (29. 37/x1D6E4) ^3. 23, such that the scaling transition in Nu and Re can be clearly demonstrated when plotted against Ra/Ra^.