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We investigate the coupling effect of buoyancy and shear based on an annular centrifugal Rayleigh-B\'enard convection (ACRBC) system in which two cylinders rotate with an angular velocity difference. Direct numerical simulations are performed in a Rayleigh number range 10^6 \le Ra \le 10^8, at fixed Prandtl number Pr=4.3, inversed Rossby number Ro^{-1}=20 and radius ratio \eta=0.5. The shear, represented by the non-dimensional rotational speed difference \Omega, varies from 0 to 10, corresponding to an ACRBC without shear and a radially heated Taylor-Couette flow with only the inner cylinder rotating, respectively. A stable regime is found in the middle part of the interval of \Omega, and divides the whole parameter space into three regimes: buoyancy-dominated regime, stable regime, and shear-dominated regime. Clear boundaries between the regimes are given by linear stability analysis. In the buoyancy-dominated regime, the flow is a quasi-two-dimensional flow on the r\varphi plane; as shear increases, both the growth rate of instability and the heat transfer is depressed. In the shear-dominated regime, the flow is mainly on the rz plane, and the heat transfer in this regime is greatly enhanced. The study shows shear can stabilize buoyancy-driven convection and reveals the complex coupling mechanism of shear and buoyancy, which may have implications for fundamental studies and industrial designs.

What is the final state of turbulence when the driving parameter approaches to infinity? For thermal turbulence, in 1962, Kraichnan proposed a so-called ultimate scaling dependence of the heat transport (quantified by the Nusselt number $\text{Nu}$) on the Rayleigh number ($\text{Ra}$), which can be extrapolated to arbitrarily high $\text{Ra}$. The existence of Kraichnan ultimate scaling has been intensively debated in the past decades. In this work, using a supergravitational thermal convection system, with an effective gravity up to 100 times the Earth's gravity, both Rayleigh number and shear Reynolds number can be boosted due to the increase of the buoyancy driving and the additional Coriolis forces. Over a decade of $\text{Ra}$ range, we demonstrate the existence of Kraichnan-like ultimate regime with four direct evidences: the ultimate scaling dependence of $\text{Nu}$ versus $\text{Ra}$; the appearance of turbulent velocity boundary layer profile; the enhanced strength of the shear Reynolds number; the new statistical properties of local temperature fluctuations. The present findings will greatly improve the understanding of the flow dynamics in geophysical and astrophysical flows.

We report on a three-dimensional direct numerical simulation study of flow structure and heat transport in the annular centrifugal Rayleigh-B\'{e}nard convection (ACRBC) system, with cold inner and hot outer cylinders corotating axially, for the Rayleigh number range Ra $ \in [{10^6},{10^8}]$ and radius ratio range $\eta = {R_i}/{R_o} \in [0.3,0.9]$. This study focuses on the dependence of flow properties on the radius ratio $\eta$. The temperature and velocity fields reveal that different curvatures of the inner and outer cylinders of the ACRBC system lead to asymmetric movements of hot and cold plumes under the action of Coriolis force, resulting in the formation of zonal flow. The physical mechanism of zonal flow is verified by the dependence of the drift frequency of the large-scale circulation rolls and the space- and time-averaged azimuthal velocity on $\eta$. We find that the larger $\eta$ is, the weaker the zonal flow becomes. We show that the heat transport efficiency increases with $\eta$. It is also found that the bulk temperature deviates from the arithmetic mean temperature and the deviation increases as $\eta$ decreases. This effect can be explained by a simple model that accounts for the curvature effects and the radially-dependent centrifugal force in ACRBC.

High-Rayleigh number convective turbulence is ubiquitous in many natural phenomena and in industries, such as atmospheric circulations, oceanic flows, flows in the fluid core of planets, and energy generations. In this work, we present a novel approach to boost the Rayleigh number in thermal convection by exploiting centrifugal acceleration and rapidly rotating a cylindrical annulus to reach an effective gravity of 60 times Earth's gravity. We show that in the regime where the Coriolis effect is strong, the scaling exponent of Nusselt number versus Rayleigh number exceeds one-third once the Rayleigh number is large enough. The convective rolls revolve in prograde direction, signifying the emergence of zonal flow. The present findings open a new avenue on the exploration of high-Rayleigh number turbulent thermal convection and will improve the understanding of the flow dynamics and heat transfer processes in geophysical and astrophysical flows and other strongly rotating systems., Comment: 9 pages, 4 figures, Science Advances