The thermal instability of a rotating fluid sphere heated within

Abstract

In this paper the problem of the thermal instability of an incompressible rotating fluid sphere heated within is considered. The equations governing the state of marginal instability are derived for the case when the motions and the associated perturbations have symmetry about the axis of rotation. The underlying characteristic value problem is solved for a slightly modified set of boundary conditions. Nevertheless, the solution obtained suffices to determine the general nature of the dependence of the lowest Rayleigh number for the onset of instability on the Taylor number T(=4ω²R⁴/v² ).