Nonlinear thermal instability in spherical shells

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