Breakdown of the Classical Equations and Existence of Hydrodynamic Instability in Single Diffusive Bottom Heavy Systems

The governing equations of Rayleigh′s classical theory (Philos. Mag.32, 1916, 529) of thermal instability of a liquid layer heated underside (or overside) break down in the parameter regime T0 α2 > 1 and the existence of some new phenomena, not yet discovered or reported in the literature to the best of our knowledge, is mathematically established in this regime with the help of a reformulation of the classical equations, T0 and α2 being some properly chosen mean temperature and coefficient of specific heat (at constant volume) variation due to temperature variation respectively.