Instabilities of a steady, barotropic, wind-driven circulation

We explore the stability characteristics of a single, barotropic, wind-driven gyre as a function of the strength of the wind forcing and the size and shape of the basin. We find steady solutions for the barotropic flow in a basin driven by a steady wind stress over a range of values of the Reynolds number and the strength of the wind stress. For those solutions that are close to the stability boundary, we examine the form of the most unstable normal mode. We find that for sufficiently weak forcing, the form of the first instability seen is an instability of the western boundary current. However, for larger values of the forcing, the first instability to set in, as the Reynolds number is reduced, is centered on a standing meander that forms on the continuation of the boundary current after it has left the boundary. Both types of instability are oscillatory. There are several different modes of standing meander instability each associated with Rossby wave-like disturbances in the eastern half of the basin. Each of these modes is most unstable when its frequency is close to a resonance with a basin mode with similar spatial scales.