Asymmetric velocity boundary conditions lead to zonal flow in centrifugal convection

Abstract

We perform direct numerical simulations of rapidly rotating annular centrifugal convection to investigate how mixed (asymmetric) velocity boundary conditions and geometric curvature shape the flow organisation and heat transfer. Motivated by the quasi-two-dimensionalisation under strong rotation and the long spin-up required for large-scale states, we employ two-dimensional simulations and consider four boundary-condition sets: no-slip/no-slip (INON), no-slip/stress-free (INOS), stress-free/no-slip (ISON) and stress-free/stress-free (ISOS). For fixed geometry with the radius ratio $\eta=0.5$ and over the Rayleigh number $Ra\in[10^6,10^9]$, the heat transfer is strongest for ISOS, followed by INOS and INON, while ISON exhibits a pronounced suppression as a strong zonal flow aligned with the rotation develops. In the three cases dominated by large-scale circulation, the Nusselt number $Nu$ follows an effective classical-type scaling close to $Nu\sim Ra^{0.27}$, whereas the zonal-flow branch displays a much weaker scaling $Nu\sim Ra^{0.1}$ and strong flow anisotropy with the large difference between the radial and azimuthal Reynolds numbers $Re_r\ll Re_\varphi$. A dissipation analysis shows that zonal-flow formation is accompanied by a transition from boundary-layer-dominated dissipation to a relatively low and uniform bulk dissipation, consistent with shear-induced plume suppression. By varying the radius ratio $\eta$, we demonstrate that increasing $\eta$ weakens curvature asymmetry and destabilises the zonal-flow state, leading to roll-dominated convection in the planar limit, and we relate the accompanying bulk-temperature asymmetry to the boundary heat flux asymmetry using a free-convective boundary-layer model.