Global non-linear stability in double diffusive convection via hidden symmetries

Via a new strategy, the global non-linear stability in double diffusive convection in porous layers (heated from below and salted from above), is investigated. The condition, necessary and sufficient, either for the absence of subcritical instabilities or for the global non-linear stability is obtained by (1) discovering symmetries hidden in the Darcy–Boussinesq equations; (2) introducing “symmetrizable double or triply diffusive convections”.

► Global non-linear stability in double diffusive convection in porous media is studied.
► A new strategy aimed to discover hidden symmetries is used.
► Necessary and sufficient conditions for global stability are found.
► Symmetries hidden in the Darcy–Boussinesq equations are discovered.
► Symmetrizable double or triply diffusive convection are investigated.