Isolated marginally stable geophysical vortices

12 pages, 6 figures, 2 appendixes, supplementary movies https://doi.org/10.1017/jfm.2017.440Long-term marginal stability of a new family of isolated oceanic vortices is analysed. Sign reversal of the radial gradient of the potential vorticity anomaly, as implied by the isolation requirement, leads to vortex unsteadiness but does not break the coherence of the vortex, which remains marginally stable even for high absolute Rossby numbers . The marginally stable vortices are characterized by a zero amount of potential vorticity anomaly on every isopycnal. The marginally stable final state is an unsteady vortex whose inner one-signed potential vorticity anomaly experiences revolution, rotation, precession and nutationPartial support for this study was obtained through project CTM2014-56987-P (Spanish Ministry of Science and Innovation)Peer Reviewe