Convective and absolute instabilities of a buoyancy-induced flow in a thermally stratified medium

Convective and absolute instabilities of the buoyancy-induced boundary layer adjacent to an isothermal vertical flat plate immersed in a linear ambient thermal stratification are investigated. Because of the ambient stratification, the mean temperature and velocity similarity profiles possess a region of temperature deficit and flow reversal. Linear stability analysis reveals the existence of convective and absolute instabilities, which are studied in terms of the governing nondimensional parameters of the problem, namely, the Prandtl number (Pr) and a modified Grashof number (G). The critical value of G=Gc at which transition to convective instability occurs has a maximum between Pr=2 and 3; for larger values, Gc is a weak function of Pr. At higher G=Ga, the flow becomes absolutely unstable. It is found that Ga increases with Pr. This tendency is related to the existence of the reverse flow due to the ambient stratification. It is shown that as the reverse flow becomes relatively more dominant, the flow is more susceptible to absolute instability.