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Abstract:
Radial unstable stratification is a potential source of turbulence in the cold regions of accretion disks. To investigate this thermal effect, here we focus on two-dimensional Rayleigh–Bénard convection in an annulus subject to radially dependent gravitational acceleration g∝1/r. Next to the Rayleigh number Ra and Prandtl number Pr, the radius ratio η, defined as the ratio of inner and outer cylinder radii, is a crucial parameter governing the flow dynamics. Using direct numerical simulations for Pr=1 and Ra in the range from 107 to 1010, we explore how variations in η influence the asymmetry in the flow field, particularly in the boundary layers. Our results show that in the studied parameter range, the flow is dominated by convective rolls and that the thermal boundary-layer (TBL) thickness ratio between the inner and outer boundaries varies as η1/2. This scaling is attributed to the equality of velocity scales in the inner (ui) and outer (uo) regions. We further derive that the temperature drops in the inner and outer TBLs scale as 1/(1+η1/2) and η1/2/(1+η1/2), respectively. The scalings and the temperature drops are in perfect agreement with the numerical data.
