Asymmetric velocity boundary conditions lead to zonal flow in centrifugal convection

We perform two-dimensional 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 in the quasi-two-dimensional, rotation-constrained regime. 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 equals 0.5 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mi>η</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0.5</mml:mn> </mml:math> $\eta =0.5$ and over the Rayleigh-number range italic Ra element of left bracket 10 Superscript 6 Baseline comma 10 Superscript 9 Baseline right bracket <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Ra</mml:mtext> </mml:mrow> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">[</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>6</mml:mn> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>9</mml:mn> </mml:msup> <mml:mo stretchy="false">]</mml:mo> </mml:math> $ \textit{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 where the flow remains in a roll-dominated state, the Nusselt number italic Nu <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Nu</mml:mtext> </mml:mrow> </mml:math> $ \textit{Nu}$ follows an effective classical-type scaling close to italic Nu tilde upper R a Superscript 0.27 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Nu</mml:mtext> </mml:mrow> <mml:mo>∼</mml:mo> <mml:mi>R</mml:mi> <mml:msup> <mml:mi>a</mml:mi> <mml:mrow> <mml:mn>0.27</mml:mn> </mml:mrow> </mml:msup> </mml:math> $ \textit{Nu}\sim Ra^{0.27}$ , whereas the zonal-flow branch displays a much weaker scaling italic Nu tilde upper R a Superscript 0.1 <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Nu</mml:mtext> </mml:mrow> <mml:mo>∼</mml:mo> <mml:mi>R</mml:mi> <mml:msup> <mml:mi>a</mml:mi> <mml:mrow> <mml:mn>0.1</mml:mn> </mml:mrow> </mml:msup> </mml:math> $ \textit{Nu}\sim Ra^{0.1}$ and strong flow anisotropy with a large difference between the radial and azimuthal Reynolds numbers italic Re Subscript r Baseline much less than upper R e Subscript phi <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:msub> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Re</mml:mtext> </mml:mrow> <mml:mi>r</mml:mi> </mml:msub> <mml:mo>≪</mml:mo> <mml:mi>R</mml:mi> <mml:msub> <mml:mi>e</mml:mi> <mml:mi>φ</mml:mi> </mml:msub> </mml:math> $ \textit{Re}_r\ll Re_\varphi$ . A dissipation analysis shows that zonal-flow formation is accompanied by a transition from bou