Hostname: page-component-7dd5485656-zlgnt Total loading time: 0 Render date: 2025-10-31T14:27:07.179Z Has data issue: false hasContentIssue false
  • English
  • Français

Critical torsional modes of convection in rotating fluid spheres at high Taylor numbers

Published online by Cambridge University Press:  15 February 2016

Juan Sánchez ,
Ferran Garcia  and
Marta Net
Juan Sánchez
Affiliation:
Physics Department, Universitat Politècnica de Catalunya Jordi Girona Salgado 3, Campus Nord, Mòdul B4, 08034 Barcelona, Spain
Ferran Garcia
Affiliation:
Physics Department, Universitat Politècnica de Catalunya Jordi Girona Salgado 3, Campus Nord, Mòdul B4, 08034 Barcelona, Spain
Marta Net*
Affiliation:
Physics Department, Universitat Politècnica de Catalunya Jordi Girona Salgado 3, Campus Nord, Mòdul B4, 08034 Barcelona, Spain
*
†Email address for correspondence: marta.net@upc.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical study of the onset of convection in rotating internally heated self-gravitating fluid spheres is presented. The exploration of the stability of the conduction state versus the Taylor and Prandtl numbers supplies a detailed idea of the laws that fulfil the four types of solutions obtained at low Prandtl numbers. The main result found is that axisymmetric (torsional) modes of convection are preferred at high Taylor numbers in the zero-Prandtl-number limit. This instability appears at low Rayleigh numbers and gives rise to an oscillating single vortex of very high frequency.

JFM classification

Convection: Buoyancy-driven instability Convection: Convection Geophysical and Geological Flows: Rotating flows

Information

Type
Rapids
Information
Journal of Fluid Mechanics , Volume 791 , 25 March 2016 , R1
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Al-Shamali, F. M., Heimpel, M. H. & Aurnou, J. M. 2004 Varying the spherical shell geometry in rotating thermal convection. Geophys. Astrophys. Fluid Dyn. 98 (2), 153–169.Google Scholar
Ardes, M., Busse, F. H. & Wicht, J. 1997 Thermal convection in rotating spherical shells. Phys. Earth Planet. Inter. 99, 55–67.Google Scholar
Bassom, A. P., Soward, A. M. & Starchenko, S. V. 2011 The onset of strongly localized thermal convection in rotating spherical shells. J. Fluid Mech. 689, 376–416.Google Scholar
Busse, F. H. 1970 Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44, 441–460.CrossRefGoogle Scholar
Busse, F. H. 2002 Convective flows in rapidly rotating spheres and their dynamo action. Phys. Fluids 14 (4), 1301–1313.Google Scholar
Busse, F. H. & Simitev, R. 2004 Inertial convection in rotating fluid spheres. J. Fluid Mech. 498, 23–30.Google Scholar
Carrigan, C. R. & Busse, F. H. 1983 An experimental and theoretical investigation of the onset of convection in rotating spherical shells. J. Fluid Mech. 126, 287–305.Google Scholar
Dormy, E., Soward, A. M., Jones, C. A., Jault, D. & Cardin, P. 2004 The onset of thermal convection in rotating spherical shells. J. Fluid Mech. 501, 43–70.Google Scholar
Garcia, F., Sánchez, J. & Net, M. 2008 Antisymmetric polar modes of thermal convection in rotating spherical fluid shells at high Taylor numbers. Phys. Rev. Lett. 101 (19), 194501.CrossRefGoogle ScholarPubMed
Jones, C. A., Soward, A. M. & Mussa, A. I. 2000 The onset of thermal convection in a rapidly rotating sphere. J. Fluid Mech. 405, 157–179.Google Scholar
Landeau, M. & Aubert, J. 2011 Equatorially asymmetric convection inducing a hemispherical magnetic field in rotating spheres and implications for the past Martian dynamo. Phys. Earth Planet. Inter. 185, 61–73.Google Scholar
Lehoucq, R. B. & Sorensen, D. C. 1996 Deflation techniques for an implicitly restarted Arnoldi iteration. SIAM J. Matrix Anal. Applics 17, 789–821.CrossRefGoogle Scholar
Liao, X. & Zhang, K. 2006 On the convective excitation of torsional oscillations in rotating systems. Astrophys. J. 638 (2), L113–L116.Google Scholar
Liao, X., Zhang, K. & Chang, Y. 2007 Nonlinear torsional oscillations in rotating systems. Phys. Rev. Lett. 98, 094501.Google Scholar
Net, M., Garcia, F. & Sánchez, J. 2008 On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions. J. Fluid Mech. 601, 317–337.Google Scholar
Roberts, P. H. 1968 On the thermal instability of a rotating fluid sphere containing heat sources. Phil. Trans. R. Soc. Lond. A 263 (1136), 93–117.Google Scholar
Sánchez, J., Garcia, F. & Net, M. 2016 Radial collocation methods for the onset of convection in rotating spheres. J. Comput. Phys. 308, 273–288.CrossRefGoogle Scholar
Yano, J. I. 1992 Asymptotic theory of thermal convection in a rapidly rotating system. J. Fluid Mech. 243, 103–131.Google Scholar
Zhang, K. 1992 Spiralling columnar convection in rapidly rotating spherical fluid shells. J. Fluid Mech. 236, 535–556.CrossRefGoogle Scholar
Zhang, K. 1993 On equatorially trapped boundary inertial waves. J. Fluid Mech. 248, 203–217.Google Scholar
Zhang, K. 1994 On coupling between the Poincaré equation and the heat equation. J. Fluid Mech. 268, 211–229.Google Scholar
Zhang, K., Earnshaw, P., Liao, X. & Busse, F. H. 2001 On inertial waves in a rotating fluid sphere. J. Fluid Mech. 437, 103–119.Google Scholar
Zhang, K. & Liao, X. 2004 A new asymptotic method for the analysis of convection in a rapidly rotating sphere. J. Fluid Mech. 518, 319–346.Google Scholar
Zhang, K., Liao, X. & Busse, F. H. 2007 Asymptotic solutions of convection in rapidly rotating non-slip spheres. J. Fluid Mech. 578, 371–380.Google Scholar