The onset of convection by thermal instability in spherical shells

Abstract

In this paper the problem of the thermal instability of an incompressible sphere consisting of an inviscid core and a viscous mantle is considered, and it is shown that the pattern of convection which sets in, at marginal stability, in the mantle shifts to harmonics of the higher orders as the thickness of the mantle decreases. Thus, when the mantle extends to a depth of half the radius of the sphere, the harmonics of orders three and four set in about simultaneously, while the harmonic of order five follows very soon afterwards. The bearing of this result on the problem of convection in the earth's mantle and of the interpretation of the earth's topographic features is indicated.