We consider a uniform-density ocean in which the depth-independent horizontal velocity is driven by a two-gyre wind. Numerical solutions of the governing vorticity equation reveal that the solutions with a flat ocean bottom differ greatly from those in which a continental shelf and slope are present along the western boundary. In the ocean basin with a western continental shelf, steady inertial circulations readily lose stability to unsteady inertial circulations that spawn eddies. However, eddies do not form in the corresponding solutions for the flat-bottom ocean. Reducing the friction leads to flat-bottom solutions that shed eddies far offshore, but still differ significantly from the corresponding continental-slope solutions, where eddies pinch off near the western boundary.
Becker, Janet M., and Rick Salmon. 1997. "Eddy formation on a continental slope." Journal of Marine Research 55, (2). https://elischolar.library.yale.edu/journal_of_marine_research/2222