This work examines the instabilities of steady circulations driven by stationary single-gyre wind forcing in closed rectangular basins with different aspect ratios. The stratified ocean is modeled with quasi-geostrophic 1.5-layer (equivalent-barotropic) and two-layer models. As friction is reduced, a stability threshold is encountered. In the vicinity of this threshold, unstable steady states and their unstable eigenmodes are determined. The structures of the eigenmodes and their associated energy conversion terms allow us to characterize the instabilities. In each case, the loss of stability is associated with an oscillatory instability. Several different instability mechanisms are observed. Which of these is responsible for the onset of instability depends upon the basin aspect ratio and the choice of stratification (1.5- or two-layer). The various mechanisms include instability of the western boundary current, baroclinic instability of the main recirculation gyre, instability of a standing meander located downstream of the main recirculation gyre and a complex instability involving several recirculations and the standing meander. The periods of the eigenmodes range from several months to several years depending upon the kind of instability and type of model. Additional insight into the western boundary current and baroclinic gyre instabilities is provided by an exploration of the stability of (a) the Munk boundary layer flow in 1.5- and two-layer models in an unbounded north-south channel, and (b) an isolated baroclinic vortex on an f-plane.
Berloff, P., and S. P. Meacham. 1998. "On the stability of the wind-driven circulation." Journal of Marine Research 56, (5). https://elischolar.library.yale.edu/journal_of_marine_research/2297