Thermal Instability of a Fluid in a Spherical Shell with Thin Layer Approximation Analysis

The thermal instability of a fluid layer confined in a spherical shell is investigated on a linear theory basis. The dependence of the critical Rayleigh number on the functional form of the gravity distribution is investigated. An asymptotic analysis is also made for very thin layer case by an expansion with R-1 where R is the radius of the inner sphere normalized by the thickness of the fluid layer. The critical Rayleigh number is obtained as [formula omitted], where λG is the density ratio of the fluid to the matter inside the inner sphere. The asymptotic expression of the Rayleigh number is shown to be a good approximation even for R of order one.