In the stability theory of shear layers, the term `local stability' refers to the stability properties of a particular velocity profile at a given position in the flow. When the basic flow develops the streamwise direction, e.g. in a growing boundary layer, the changing local stability properties can be mapped out downstream. If there are regions of local absolute instability then there is the possibility of a `global instability' of the entire flow. When the basic flow varies slowly in the downstream direction the global stability can be determined from the local stability. Local absolute instability is a necessary condition for the global instability of a slowly developing basic flow.
In this presentation we consider flows that undergo a sudden change in stability properties at a well-defined position, like, for example, the flow separating from the trailing edge of an aerofoil. The trailing edge acts as a junction between a boundary layer flow and a wake flow, each of which has different stability properties. We show in simple models that flow across a junction can be globally unstable even when neither of the two flows involved are locally absolutely unstable. There are many examples of engineering flows across a junction, and so in principle any of them might turn out to be globally unstable even when there is no absolute instability.