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Periodical Convective Flow in Spherical Shells
Author(s) -
Futterer B.,
Hollerbach R.,
Egbers C.
Publication year - 2004
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200410222
Subject(s) - convection , prandtl number , rayleigh number , mechanics , spherical shell , natural convection , physics , bifurcation , flow (mathematics) , rotational symmetry , steady state (chemistry) , materials science , shell (structure) , chemistry , nonlinear system , quantum mechanics , composite material
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.