Browse by author
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).
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
URL: https://doi.org/10.1017/jfm.2022.761
DOI: 10.1017/jfm.2022.761
ePrints DOI: 10.57711/a12p-qc66
Altmetrics provided by Altmetric
