On the stability of a fluid layer containing a univariant phase transition: application to planetary interiors

Abstract

In a fluid layer containing a univariant phase change, both the minimum critical Rayleigh number for convection to occur and the corresponding convection pattern depend on the characteristics of the phase change as well as on the thickness and viscosity of the two phases which compose the layer. This paper describes a linear stability analysis for two layers which have different density, thickness and viscosity. The minimum critical Rayleigh number is found to depend strongly on both the relative thickness and viscosity of each layer. The marginally stable convection pattern also depends on the values of these two parameters. Application to planets is carried out and this analysis predicts minimum critical Rayleigh numbers and related pattern of convection which differ significantly from those predicted by previous analyses which considered two layers with the same density, viscosity and thickness. Comparison with finite amplitude calculations shows that endothermic phase transitions may evolve from single-cell convection at the onset of convection (minimum critical Rayleigh number) to layered convection at higher Rayleigh numbers. This clearly demonstrates that a steady-state finite amplitude convection pattern can be different from that predicted by linearized stability analysis.