Zero Potential Vorticity Envelopes for the Zonal-Mean Velocity of the Venus/Titan Atmospheres

Abstract

The diagnostic analysis of numerical simulations of the Venus/Titan wind regime reveals an overlooked constraint upon the latitudinal structure of their zonal-mean angular momentum. The numerical experiments, as well as the limited planetary observations, are approximately consistent with the hypothesis that within the latitudes bounded by the wind maxima the total Ertel potential vorticity associated with the zonal-mean motion is approximately well mixed with respect to the neutral equatorial value for a stable circulation. The implied latitudinal profile of angular momentum is of the form M ≤ Me(cos?)2/Ri, where ? is the latitude and Ri the local Richardson number, generally intermediate between the two extremes of uniform angular momentum (Ri ? ∞) and uniform angular velocity (Ri = 1). The full range of angular momentum profile variation appears to be realized within the observed meridional?vertical structure of the Venus atmosphere, at least crudely approaching the implied relationship between stratification and zonal velocity there. While not itself indicative of a particular eddy mechanism or specific to atmospheric superrotation, the zero potential vorticity (ZPV) constraint represents a limiting bound for the eddy?mean flow adjustment of a neutrally stable baroclinic circulation and may be usefully applied to the diagnostic analysis of future remote sounding and in situ measurements from planetary spacecraft.