On the Thermal Instability of a Highly Rotating Fluid Sphere.

The asymptotic theory is developed for marginal convection in a fluid sphere at high Taylor numbers, T. The sphere is considered to be of uniform density and to contain a uniform distribution of heat sources. Prior to the onset of convection, it rotates as a solid body. Both axisymmetric and non-axisymmetric instabilities are considered not only for the case when the boundary of the sphere is free but also for when it is rigid. It is shown that the leading terms of the asymptotic expansions for the critical Rayleigh number, Rc, and critical wavenumber, , are independent of the nature of the boundary and, in the case of steady axisymmetric convection, are given by Rc=2O.7126T2/3, c=t.1O8TV6, TH Some results are also presented for convection through overstability.