An isolated barotropic eddy on the β-plane can be in equilibrium only if it is composed of a coupled cyclone-anticyclone system, only if it is separated by a vorticity discontinuity (free streamline) from the surrounding fluid...
Stern, Melvin E.. 1975. "Minimal properties of planetary eddies." Journal of Marine Research 33, (1). https://elischolar.library.yale.edu/journal_of_marine_research/1307