On the instability of sheared disturbances

The equation for small-amplitude disturbances to an unbounded flow of constant shear on a beta-plane has well-known solutions of a particularly simple form. In physical terms such solutions represent a flow in which absolute-vorticity contours, initially taking a wavy configuration, are deformed by the basic-state shear. Here it is shown that, at least in cases where the initial disturbance has long wavelength, the vorticity distribution predicted by such solutions eventually becomes barotropically unstable, as the shearing over of material contours leads to local reversals in the cross-stream gradient of absolute vorticity.