The role of curvature in modifying frontal instabilities. Part II: Application of the criterion to curved density fronts at low Richardson numbers

We continue our study of the role of curvature in modifying frontal stability. In Part 1, 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 non-dimensional absolute angular momentum and Ertel potential vorticity (PV), respectively. In Part 2, 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 one, anticyclonic flows increase in q′, while cyclonic flows decrease in q′, tending to stabilize anticyclonic and de-stabilize cyclonic flow. Although stability is marginal or weak for anticyclonic flow (owing to multiplication by L′), the de-stabilization 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 mid-latitude 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. Finally, 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 de-stabilize cyclonic and stabilize anticyclonic fronts and vortices to symmetric instability. The results may have implications for Earth system models.

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