Journal of Fluid Mechanics

Patterns of convection in spherical shells

F. H.  Busse a1
a1 Institute of Geophysics and Planetary Physics, University of California, Los Angeles

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The problem of the pattern of motion realized in a convectively unstable system with spherical symmetry can be considered without reference to the physical details of the system. Since the solution of the linear problem is degenerate because of the spherical homogeneity, the nonlinear terms must be taken into account in order to remove the degeneracy. The solvability condition leads to the selection of patterns distinguished by their symmetries among spherical harmonics of even order. It is shown that the corresponding convective motions set in as subcritical finite amplitude instabilities.

(Published Online March 29 2006)
(Received March 24 1975)