The Role of Curvature in Modifying Frontal Instabilities. Part II: Application of the Criterion to Curved Density Fronts at Low Richardson Numbers

Type Article
Date 2021-02
Language English
Author(s) Buckingham Christian1, 2, Gula Jonathan1, Carton Xavier1
Affiliation(s) 1 : Université de Bretagne Occidentale, CNRS, IRD, Ifremer, Laboratoire d’Océanographie Physique et Spatiale, IUEM, Plouzané, France
2 : British Antarctic Survey, Cambridge, United Kingdom
Source Journal of Physical Oceanography (0022-3670) (American Meteorological Society), 2021-02 , Vol. 51 , N. 2 , P. 317-341
DOI 10.1175/JPO-D-20-0258.1
Keyword(s) Eddies, Fronts, Instability, Ocean circulation, Potential vorticity, Frontogenesis/frontolysis, Vortices, Angular momentum

We continue our study of the role of curvature in modifying frontal stability. In Part I, we obtained an instability criterion valid for curved fronts and vortices in gradient wind balance (GWB): Φ′ = L′q′ < 0, where L′ and q′ are the nondimensional absolute angular momentum and Ertel potential vorticity (PV), respectively. In Part II, we investigate this criterion in a parameter space representative of low-Richardson-number fronts and vortices in GWB. An interesting outcome is that, for Richardson numbers near 1, anticyclonic flows increase in q′, while cyclonic flows decrease in q′, tending to stabilize anticyclonic and destabilize cyclonic flow. Although stability is marginal or weak for anticyclonic flow (owing to multiplication by L′), the destabilization of cyclonic flow is pronounced, and may help to explain an observed asymmetry in the distribution of small-scale, coherent vortices in the ocean interior. We are referring to midlatitude submesoscale and polar mesoscale vortices that are generated by friction and/or buoyancy forcing within boundary layers but that are often documented outside these layers. A comparison is made between several documented vortices and predicted stability maps, providing support for the proposed mechanism. A simple expression, which is a root of the stability discriminant Φ′, explains the observed asymmetry in the distribution of vorticity. In conclusion, the generalized criterion is consistent with theory, observations, and recent modeling studies and demonstrates that curvature in low-stratified environments can destabilize cyclonic and stabilize anticyclonic fronts and vortices to symmetric instability. The results may have implications for Earth system models.


Considerable progress has been made by considering ocean fronts to be in geostrophic balance. By this, we mean that fluid parcels accelerate as a result of horizontal pressure gradients and Earth’s rotation. A good example of this is in our efforts to understand symmetric instability, a process thought to impact energy, buoyancy, and tracer budgets in the ocean. However, we wanted to know how the physics might change if we accounted for centrifugal forces, or curvature. It turns out that this same question had been asked and answered nearly 100 years ago. However, the new criteria that we introduce in Part I yield (in Part II) one result that is new: in low-stratified waters, curved cyclonic fronts become strongly unstable and curved anticyclonic fronts become marginally stable. This suggests that highly curved cyclonic fronts and vortices are symmetrically unstable, with potential implications for the aforementioned budgets.

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