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We investigate families of finite core vortex quartets in mutual equilibrium in a two-layer quasi-geostrophic flow. The finite core solutions stem from known solutions for discrete (singular) vortex quartets. Two vortices lie in the top layer and two vortices lie in the bottom layer. Two vortices have a positive potential vorticity anomaly, while the two others have negative potential vorticity anomaly. The vortex configurations are therefore related to the baroclinic dipoles known in the literature as hetons. Two main branches of solutions exist depending on the arrangement of the vortices: the translating zigzag-shaped hetonic quartets and the rotating zigzag-shaped hetonic quartets. By addressing their linear stability, we show that while the rotating quartets can be unstable over a large range of the parameter space, most translating quartets are stable. This has implications on the longevity of such vortex equilibria in the oceans.

Hetonic quartets in a two-layer quasi-geostrophic flow: V-states and stability