Thermal instability of the steady conduction state of a fluid in a spherical shell with spherically symmetric physical conditions is reviewed. Particular emphasis is given to the important roles played by the nonlinear instability of finite amplitude disturbances, and the realization of the subsequent convection patterns that are of interest in both theory and application of nonlinear flow instability is discussed. The known preferred cellular structures and their symmetries, including those that exhibit symmetries of platonic solids and those in their relation to mantle convection, are reviewed. The roles played by the Rayleigh number and the degree of spherical harmonics, which have significant influence on the structure of the preferred flow solutions, are discussed.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
TAM R 886
1998-6012
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112592
Copyright and License Information
Copyright 1998 Board of Trustees of the University of Illinois
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.
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