  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.
