The stability of Mars' annular polar vortex

The Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here we investigate the stability of a Mars-like annular vortex using numerical integrations of the rotating shallow water equations. We show how the mode of instability and its growth rate depends upon the latitude and width of the annulus. By introducing thermal relaxation towards an annular equilibrium profile with a time scale similar to that of the instability, we are able to simulate a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere. This time scale, typically 0.5-2 sols, is similar to radiative relaxation time scales for Mars’ polar atmosphere. We also demonstrate that the persistence of an annular vortex is robust to topographic forcing, as long as it is below a certain amplitude. We hence propose that the persistence of this barotropically unstable annular vortex is permitted due to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.