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We investigate the 2D instability recently discussed by Gallet et al. (2010)and Ilin \& Morgulis (2013) which arises when a radial crossflow is imposed ona centrifugally-stable swirling flow. By finding a simpler rectilinear exampleof the instability - a sheared half plane, the minimal ingredients for theinstability are identified and the destabilizing/stabilizing effect ofinflow/outflow boundaries clarified. The instability - christened `boundaryinflow instability' here - is of critical layer type where this layer is eitherat the inflow wall and the growth rate is $O(\sqrt{\eta})$ (as found by Ilin \&Morgulis 2013), or in the interior of the flow and the growth rate is $O(\eta\log 1/\eta)$ where $\eta$ measures the (small) inflow-to-tangential-flowratio. The instability is robust to changes in the rotation profile even tothose which are very Rayleigh-stable and the addition of further physics suchas viscosity, 3-dimensionality and compressibility but is sensitive to theboundary condition imposed on the tangential velocity field at the inflowboundary. Providing the vorticity is not fixed at the inflow boundary, theinstability seems generic and operates by the inflow advecting vorticitypresent at the boundary across the interior shear. Both the primary bifurcationto 2D states and secondary bifurcations to 3D states are found to besupercritical. Assuming an accretion flow driven by molecular viscosity only so$\eta=O(Re^{-1})$, the instability is not immediately relevant for accretiondisks since the critical threshold is $O(Re^{-2/3})$ and the inflow boundaryconditions are more likely to be stress-free than non-slip. However, theanalysis presented here does highlight the potential for mass entering a diskto disrupt the orbiting flow if this mass flux possesses vorticity.

Instability driven by boundary inflow across shear: a way to circumvent Rayleigh's stability criterion in accretion disks?