Section 13

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Periodical Convective Flow in Spherical Shells

  1. B. Futterer1,*,
  2. R. Hollerbach2,
  3. C. Egbers1

Article first published online: 13 DEC 2004

DOI: 10.1002/pamm.200410222

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PAMM

PAMM

Volume 4, Issue 1, pages 482–483, December 2004

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How to Cite

Futterer, B., Hollerbach, R. and Egbers, C. (2004), Periodical Convective Flow in Spherical Shells. Proc. Appl. Math. Mech., 4: 482–483. doi: 10.1002/pamm.200410222

Author Information

  1. 1

    Department of Aerodynamics and Fluid Mechanics, Brandenburg Technical University Cottbus, 03013 Cottbus, Germany

  2. 2

    Department of Mathematics, University of Glasgow, Glasgow, G12 8QW, United Kingdom

*Phone: +00 49 355 694893, Fax: +00 49 355 694891

Publication History

  1. Issue published online: 13 DEC 2004
  2. Article first published online: 13 DEC 2004

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Abstract

Natural convection in wide spherical shells of aspect ratio β = 1 changes in fundamental ways, when the Rayleigh number Ra reaches critical values. For low Ra the convection is steady and axisymmetric, but above a critical value it becomes timedependent, with plumes dripping of the ‘south pole’ periodically. At higher Ra these still two-dimensional convective pulses become irregular in time, the transition occuring with period-doubling bifurcation. Our numerical investigations of the flow show this transition scheme from steady to periodic to chaotic behaviour to be independent for Prandtl numbers Pr greater than 100. For decreasing Pr down to 6 the steady, axisymmetric basic state is observed up to higher and higher Ra . For β ≠ 1 the onset of periodicity appears at higher Ra , too. Small gap-width reveal a crescent-eddy type flow, wide gap-width reveal a varied kidney-shaped eddy type.

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