On the thermal instability of a rotating fluid sphere

Abstract

In this paper the problem of the thermal instability of a self-gravitating rotating fluid sphere of constant density with internal heating is treated. A method of solving this problem is described which correctly takes into account the full set of boundary conditions. The cases when the bounding sphere is rigid and when it is free are both treated. The Rayleigh-Ritz method of approximating lowest characteristic values is used in a variation principle presented by Chendrasekhar to calculate the critical Rayleigh number as a function of the Taylor number.