The two-dimensional wake–shear layer forming behind a rectangular-based forebody with independent ambient streams on either side of the forebody is examined by direct numerical simulation. Theoretical aspects of global modes and frequency selection criteria based on local and global stability arguments are tested by computing local stability properties using local, time-averaged velocity profiles obtained from the numerical simulations and making the parallel-flow approximation. The theoretical results based on the assumption of a slightly non-parallel, spatially developing flow are shown to provide a firm basis for the frequency selection of vortex shedding and for defining the conditions for its onset. Distributed suction or blowing applied at the base of the forebody is used as a means of wake flow modification. The critical suction velocity to suppress vortex shedding is calculated. It is shown that local directional control (i.e. vectoring) of the near-wake flow is possible, but only when all global modes are suppressed.