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Parity-breaking flows in precessing spherical containers

R. Hollerbach1,2, C. Nore3,4,5, P. Marti1,6, S. Vantieghem1, F. Luddens3,4,5,7, and J. Léorat8

  • 1Institute of Geophysics, ETH Zürich, Sonneggstrasse 5, 8092 Zürich, Switzerland
  • 2Department of Applied Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom
  • 3Laboratoire d'Informatique Pour la Mécanique et les Sciences de l'Ingénieur, CNRS UPR 3251, BP 133, F-91403 Orsay cedex, France
  • 4Université Paris-Sud 11, 91405 Orsay cedex, France
  • 5Institut Universitaire de France, 103 bd Saint Michel, 75005 Paris, France
  • 6Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA
  • 7Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368, USA
  • 8Observatoire de Paris-Meudon, place Janssen, 92195 Meudon, France

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Phys. Rev. E 87, 053020 – Published 28 May, 2013

DOI: https://doi.org/10.1103/PhysRevE.87.053020

Abstract

We present numerical solutions of the flow in precessing spheres and spherical shells with small (ri/ro=0.1) inner cores and either stress-free or no-slip inner boundary conditions. For each of these three cases we consider the sequence of bifurcations as the Reynolds number Re=ro2Ω/ν is increased up to ∼1280, focusing particular attention on bifurcations that break the antipodal symmetry U(−r)=−U(r). All three cases have steady and time-periodic symmetric solutions at smaller Re, and quasiperiodic asymmetric solutions at larger Re, but the details of the transitions differ, and include also periodic asymmetric and quasiperiodic symmetric solutions in some of the cases.

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Phys. Rev. E 87, 053020– Published 28 May, 2013
  • Received 5 March 2013

©2013 American Physical Society

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