| Summary: | We investigate the relationship between Ertel potential vorticity Q and Bernoulli potential B on orthobaric density surfaces in the Antarctic Circumpolar Current (ACC), using the Southern Ocean State Estimate. Similar to the extratropical atmospheres of Earth and Mars, Q and B correlate in the ACC in a function-like manner with modest scatter. Below the near-surface, the underlying function relating Q and B appears to be nearly linear. Nondimensionalizing its slope yields “Ma,” a “Mach” number for long Rossby waves, the ratio of the local flow speed to the intrinsic long Rossby wave speed. We empirically estimate the latter using established and novel techniques that yield qualitatively consistent results. Previous work related “Ma” to the degree of homogeneity of Q and to Arnol’d’s shear stability criteria. Estimates of “Ma” for the whole ACC are notably positive, implying inhomogeneous Q, on all circumpolar buoyancy surfaces studied. Upper layers generally exhibit “Ma” slightly less than unity, suggesting that shear instability may operate within these layers. Deep layers exhibit “Ma” greater than unity, implying stability. On surfaces shallower than 1000 m just north of the ACC, the Q versus B slope varies strongly on subannual and interannual time scales, but “Ma” hovers near unity. We also study spatial variability: the ACC is speckled with hundreds of small-scale features with “Ma” near unity, whereas away from the ACC “Ma” is more commonly negative or above unity, both corresponding to stability. Maps of the time-mean “Ma” show stable regions occupy most of the Southern Ocean, except for several topographically controlled hotspots where “Ma” is always near unity.
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