Steady and oscillatory convection in rotating fluid layers heated and salted from below

Double convection in rotating horizontal layers filled by a Navier-Stokes fluid mixture, heated and salted from below, is investigated. Onset of linear instability - for any value of the fluid and salt Prandtl numbers P-r, P-1 - either via the Routh-Hurwitz conditions or via steady or oscillatory convection, is characterized. Introducing a new field connecting the perturbation fields to the temperature and salt concentration, in the cases P-1 = 1 or P-r = 1 or P1Pr = 1, stability conditions in algebraic closed form are obtained. Linear stability is recovered as non-linear global asymptotic stability via the Auxiliary System Method.