On the existence of hydrodynamic instability in single diffusive bottom heavy systems with permeable boundaries

We utilize the reformulated equations of the classical theory, as derived by Banerjee et al. (J. Math. Anal. Appl.175 (1993) 458), to establish mathematically, the existence of hydrodynamic instability in single diffusive bottom heavy systems, when considered in the more general framework of the boundary conditions of the type specified by Beavers and Joseph (J. Fluid Mech.30 (1967) 197), in the parameter regime T0α2 > 1, where T0 and α2 being some properly chosen mean temperature and coefficient of specific heat (at constant volume) variation due to temperature variation respectively.