Ertel Potential Vorticity versus Bernoulli Potential on Approximately Neutral Surfaces in the Antarctic Circumpolar Current

Geoffrey J Stanley,Mary E Bradley,David P Marshall,Timothy E Dowling

doi:10.1175/jpo-d-19-0140.1

Abstract

AbstractWe 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.

Highlights

Denotes content that is immediately available upon publication as open access
For each 5-day archived state of Southern Ocean State Estimate (SOSE)’s 6-yr run, we compute the pressure, layer thickness, potential vorticity (PV), and Bernoulli potential on nine orthobaric density surfaces: sn 5 27.1, 27.2, 27.3, 27.4, 27.5, 27.6, 27.7, 27.75, and 27.8. (Surfaces that are much shallower or deeper are not circumpolar, year-round.) Figure 1 shows the depths of these surfaces at 2408E on 22–26 March 2006, a representative time step in late summer when orthobaric surfaces are shallowest
We predefine a region of interest (ROI) for the Antarctic Circumpolar Current (ACC) by combining two regions

Summary

Methods

Motivated by Arnol’d’s nonlinear stability theorems in quasigeostrophy, we leap to the primitive equations, studying the relationship between the Ertel PV Q and the Bernoulli potential B and their nondimensionalized relationship expressed using ‘‘Ma.’’ This is a leap because no analog for Arnol’d’s second stability theorem has been found for the 3D primitive equations. It is not unreasonable to suspect Arnol’d’s stability theorems are relevant to the ACC governed by the primitive equations. We will not attempt to apply Arnol’d’s theorems: the stability criteria will undoubtedly be met in some places and violated elsewhere. ‘‘Ma’’ is an interesting diagnostic to study, since practical evidence in the QG setting suggests instability often occurs near to where the stability criteria are violated (Waterman and Jayne 2012; Waterman and Lilly 2015). If b is monotonic with depth, it can serve as the vertical coordinate, and the hydrostatic Boussinesq equations become (Young 2012)

Results

Discussion

Conclusion