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Bénard convection in a slowly rotating penny-shaped cylinder subject to constant heat flux boundary conditions

Lookup NU author(s): Emeritus Professor Andrew Soward



This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND).


We consider axisymmetric Boussinesq convection in a shallow cylinder of radius L and depth H( L), which rotates with angular velocity Ω about its axis of symmetry aligned to the vertical. Constant heat flux boundary conditions, top and bottom, are adopted, for which the onset of instability occurs on a long horizontal length scale provided that Ω issufficiently small. We investigate the nonlinear development by well-established two-scale asymptotic expansion methods. Comparisons of the results with the direct numerical simulations (DNS) of the primitive governing equations are good at sufficiently large Prandtl number σ . As σ is reduced, the finite amplitude range of applicability of the asymptotics reduces in concert. Though the large meridional convective cell, predicted by the DNS, is approximated adequately by the asymptotics, the azimuthal flow fails almost catastrophically, because of significant angular momentum transport at small σ , exacerbated by the cylindrical geometry. To appraise the situation, we propose hybridmethods that build on the meridional streamfunction ψ derived from the asymptotics. With ψ given, we solve the now linear azimuthal equation of motion for the azimuthal velocity v by DNS. Our ‘hybrid’ methods enable us to explain features of the flow at large Rayleigh number, found previously by Oruba et al. (J. Fluid Mech., vol. 812, 2017, pp. 890–904).

Publication metadata

Author(s): Soward AM, Oruba L, Dormy E

Publication type: Article

Publication status: Published

Journal: Journal of Fluid Mechanics

Year: 2022

Volume: 951

Print publication date: 25/11/2022

Online publication date: 02/11/2022

Acceptance date: 26/08/2022

Date deposited: 18/11/2022

ISSN (print): 0022-1120

ISSN (electronic): 1469-7645

Publisher: Cambridge University Press


DOI: 10.1017/jfm.2022.761

ePrints DOI: 10.57711/a12p-qc66


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