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We investigate the coupling effect of buoyancy and shear based on an annularcentrifugal Rayleigh-B\'enard convection (ACRBC) system in which two cylindersrotate with an angular velocity difference. Direct numerical simulations areperformed in a Rayleigh number range 10^6 \le Ra \le 10^8, at fixed Prandtlnumber Pr=4.3, inversed Rossby number Ro^{-1}=20 and radius ratio \eta=0.5. Theshear, represented by the non-dimensional rotational speed difference \Omega,varies from 0 to 10, corresponding to an ACRBC without shear and a radiallyheated Taylor-Couette flow with only the inner cylinder rotating, respectively.A stable regime is found in the middle part of the interval of \Omega, anddivides the whole parameter space into three regimes: buoyancy-dominatedregime, stable regime, and shear-dominated regime. Clear boundaries between theregimes are given by linear stability analysis. In the buoyancy-dominatedregime, the flow is a quasi-two-dimensional flow on the r\varphi plane; asshear increases, both the growth rate of instability and the heat transfer isdepressed. 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 shearcan stabilize buoyancy-driven convection and reveals the complex couplingmechanism of shear and buoyancy, which may have implications for fundamentalstudies and industrial designs.

From Sheared Annular Centrifugal Rayleigh-B\'enard Convection to  Radially Heated Taylor-Couette Flow: Exploring the Impact of Buoyancy and  Shear on Heat Transfer and Flow Structure