Barotropic Instability of Midlatitude Zonal Jets on Mars, Earth and Venus

We have used a linearized nondivergent barotropic vorticity model on a sphere to intercompare the fastest growing, barotropically unstable wave modes computed for zonal jets at high latitudes in the middle atmospheres of Venus, Earth, and Mars. Such zonal jets have been observed in the wintertime stratosphere on Earth and have been inferred from remotely sensed temperatures in the Venus middle atmosphere and in the wintertime Martian atmosphere. The comparison was done by extending the results of Hartmann for his simple analytic profile of a latitudinally varying terrestrial zonal wind to zonal wind profiles characterized by the larger Rossby numbers (Ro) appropriate to Mars and Venus. As Hartmann's results suggested, the fastest growing barotropic waves continue to grow more quickly as Ro increases. Eventually, the fastest growing mode shifts from a zonal wavenumber k = I to a k = 2 mode, both located on the poleward flank of the high-latitude jet. However, for somewhat higher Rossby numbers, the k = 2 mode on the equatorward side of the zonal jet becomes the fastest growing planetary-scale barotropic mode, and this transition is marked by a discontinuous shift to longer wave periods. The Venus high-latitude zonal jet appears remarkably close to this transition Ro. For each of the three planets, satellite-borne instruments have detected wave patterns in the thermal radiance field in the vicinity of the high-latitude zonal jets. As reported earlier for the terrestrial wintertime stratosphere by Hartmann and for Venus by Elson, these observed waves have characteristics similar to those computed for the fastest growing barotropic modes. For Mars, we find that such modes would have zonal wavenumbers I or 2, with e-folding times of 2-3 days and periods of 0.75-2.5 days; the longer period (k = 2) equatorward mode would dominate for the faster and narrower zonal jets. A poleward mode with k = I and a period of 1.2 days is the barotropic mode most likely to be consistent with the Mariner-9 IRIS observations of thermal waves above the I mb ( -20 km) level in the Martian atmosphere. 2031