jats:titleAbstract</jats:title>jats:pFlow 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.</jats:p>