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

•The lowest Rayleigh number R¯C at which stationary convection can occur, in an algebraic closed form is obtained.•An algebraic system for finding the lowest Rayleigh number R¯¯C at which oscillatory convection can occur, for any values of the fluid and salt Prandtl numbers, is introduced.•Via the introduction of a new field, conditions guaranteeing the onset of steady or oscillatory convection are given in algebraic closed form in the cases P1=1P1=1 or Pr  =1 or P1Pr=1P1Pr=1.•Conditions guaranteeing that R¯¯C

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 Pr, P1 – 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 P1=1P1=1 or Pr=1 or P1Pr=1P1Pr=1, stability conditions in algebraic closed form are obtained. Linear stability is recovered as non-linear global asymptotic stability via the Auxiliary System Method.