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Here we report some interesting new features of the spatio-temporalinstability of the incompressible plane Couette-Poiseuille flow (CPF). First ofall, this flow represents the first instance of a "non-inflectional" absoluteinstability, within constant-viscosity formulation, which is triggered when oneof the plates moves opposite to the bulk motion. More strikingly, with furtherincrease in the negative plate motion, the absolute instability ($\textrm{AI}$)transitions to an "upstream" convective instability ($\textrm{CI}^-$), whereinan unstable wave packet moves opposite to the direction of the bulk flow. Thus,the CPF exhibits a unique $\textrm{CI}^+ \to \textrm{AI} \to \textrm{CI}^-$transition, for a given Reynolds number ($Re$), where $\textrm{CI}^+$ denotesthe commonly-observed case of a "downstream" convective instability. This typeof transition has not been reported for other known examples of absolutelyunstable flows. We compute the leading and trailing edge velocities for anamplifying wave packet and find that, for the plane Poiseuille flow, both thesevelocities approach zero as $Re \to \infty$. As a result, at high $Re$, eventhe slightest of negative plate motions is sufficient to trigger $\textrm{AI}$and subsequently $\textrm{CI}^-$, as observed for the CPF. The wave-packetdispersion first increases with $Re$, followed by a decrease, which points to apeculiar "dual" role of viscosity in sustaining $\textrm{AI}$ in the CPF,namely, viscosity promotes sustenance of $\textrm{AI}$ at moderate Reynoldsnumbers but suppresses it at low and high Reynolds numbers. These results canbe well understood within the Ginzburg-Landau framework, and therefore can beexpected to have a wider applicability.

Absolute and "upstream" convective instabilities in plane Couette-Poiseuille flow