Flow on a beta‐plane driven by a steady localised anticyclonic forcing of potential vorticity (or equivalently a mass source) is considered as a simple model of the Asian monsoon flow in the upper troposphere. Previous authors have noted that the response may be steady, or unsteady, according to the magnitude of the forcing, with the unsteadiness manifested as westward eddy shedding. A detailed study of the transition between steady and eddy‐shedding regimes reveals a third regime ('break up'), for intermediate forcing magnitude, where the flow is steady in the neighbourhood of the forcing, but the westward extending plume of low potential vorticity breaks up into isolated anticyclonic vortices some distance away from the forcing region. A related spatio‐temporal instability problem for flow on a beta plane is specified and analysed. The flow can be stable, convectively unstable or absolutely unstable. It is argued that these three stability regimes correspond to the steady, break‐up and eddy‐shedding regimes for the forced flow and good quantitative correspondence between the regimes is demonstrated by explicit solution of the spatio‐temporal stability problem. Snapshots of the stream function and potential vorticity response in quasi‐geostrophic single‐layer experiments forced with a steady, localised mass source. The response transitions between different states (steady, break‐up and shedding), defined in terms of temporal and spatial variability, when varying the magnitude F0 or length‐scale r0 of the forcing. The different behaviours can be explained by the spatio‐temporal stability properties of the steady linear response and a transition of the system into an absolutely or convectively unstable regime.