| 29 Sep 2026
Static stability and local stratification constrain where and when oceanic eddies can exist
Abstract. Oceanic eddies play a major role in redistributing heat, salt, and tracers. Their three-dimensional structure has historically been studied from a dynamical perspective. Here, we investigate a more fundamental constraint: whether a balanced eddy can remain statically stable when embedded in a given oceanic environment. We prescribe idealized three-dimensional eddies from their vorticity structure and derive the associated density anomaly required for gradient-wind and hydrostatic balance. We then combine these anomalies with background density profiles representative of different regions and seasons to assess the resulting static stability. Our results show that static stability strongly depends on eddy polarity, intensity, vertical extent, and, for subsurface eddies, their position relative to the background pycnocline. Thin and intense cyclonic eddies are particularly prone to gravitational instability, whereas anticyclonic and thicker eddies are generally more stable. The same eddy structure can therefore be statically stable in one region or season but unstable in another, demonstrating that background stratification can constrain where particular eddy structures can exist and propagate. This process may also provide an additional pathway for eddy-induced vertical mixing through convective adjustment. We provide an open notebook that allows users to evaluate the static stability and three-dimensional density signature of prescribed eddies in arbitrary background stratifications.
de Marez et al. start on the premise that the density profile that emerges from the lateral stirring of the density field by mesoscale eddies is not guaranteed to be statically stable. While this statement in itself is fair, I find their ensuing arguments to be flawed.
Eddies do not exist in isolation from the background density profile but rather they modify each other through mutual feed backs. Eddies never emerge spontaneously as in being “embedded” into a background flow. Namely, I am skeptical that the total density field could be considered as a linear superposition of the eddy density and background density. I think an actual reference/identification on the likelihood of gravitational instability in the real ocean is needed as a preface to this study.
Furthermore, even if the eddy is initially prone to gravitational instability, this alone is not sufficient to satisfy their claim of “the ability of a balanced eddy to exist depends not only on its dynamical properties, but also on the background stratification in which it is embedded”. An unbalanced eddy will inevitably modify the background state in order to bring its surrounding environment into balance and may survive onwards. Thus, it is unclear whether the “a priori estimate of the static compatibility of an idealized eddy structure with a given oceanic environment” is useful in any sense. The eddies will sort out the compatibility by themselves. The authors also acknowledge the caveats I raise in lines 296-301 but not enough emphasis is given to them and are left as a qualitative passing note.
Minor comments: