The absolute and convective instability properties of a parallel shear flow in a stratified

fluid, confined between two parallel rigid plates is considered. The flow is assumed to be

two-dimensional, inviscid and incompressible, and is modelled using both a discontinuous

two-layer stratification profile and a continuous stratification profile. Significantly, it is

found that asymmetrically confining the flow by the two plates, and asymmetrically

positioning the density interface such that it does not occur at the centre of the shear

layer, both lead to a destabilization of the flow for a range of flow parameter values, with

an absolute instability occurring for an increased parameter range. We identify parameter

regimes for asymmetric confinement where the destabilizing effect is strong enough to

generate an absolutely unstable co-flow shear layer; this contrasts with the unconfined case

for which only absolutely unstable counter-flow shear layers exist. In the semi-confined

case (i.e. asymmetric confinement by one plate) it is found that the most unstable scenario

occurs when the plate is placed in the faster/lighter stream. The robustness of the results

found for a discontinuous density interface are confirmed using a continuous density profile.

These results give valuable new insight into a class of flows such as co-axial injectors for

high-speed fluid atomization.