Stability analysis for the onset of convection in rotating fluid binary mixtures in spherical shells

The stability analysis of the basic conductive state of a rotating binary mixture of two fluids bounded by spherical shells is studied. The Boussinesq approximation of the mass conservation, Navier-Stokes, energy and concentration equations is used, and results for a moderate Ekman number E = 10-3 are presented for positive and negative external compositional gradients. Preliminary results are compared with those obtained for a pure fluid in the same range of parameters. They show an important influence of the presence of a mixture on the onset of the convection for solutal Rayleigh numbers Rc at least of the order of the thermal Rayleigh number Re. On the sphere the leading eigenvectors, which give the patterns of convection, have sectorial structure like those of a pure fluid, although slightly deformed due to the presence of two components.Postprint (author's final draft