Why compensated cold-core rings look stable

In contrast to many real-ocean rings and eddies, circular vortices in idealized two-layer models tend to be highly unstable, unless their radius is made small or their baroclinicity is made artificially weak. The addition of a middle layer with uniform potential vorticity weakens vertical coupling between the upper and lower layers that enhances vortex stability and makes the vortex lifespan more realistic. It is demonstrated here that such a three-layer vortex model in so-called compensated state (without rotation in the deep layer) possesses smaller lower interface slope than the two-layer model that reduces the potential vorticity gradient in the lower layer and provides less unstable configurations. Numerical simulations of an unstable cyclone with parameters typical for cold-core ring Bob reveal strong deformations and pulsations of the vortex core in the two-layer setup, while the ring becomes only slightly deformed and looks stable when the middle layer with uniform potential vorticity is added to be consistent with observations. Enhanced vortex stability in such three-layer setup has important implications for further studies of real-ocean eddies.