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

Abstract

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.

The Scale and Activity of Symmetric Instability Estimated from a Global Submesoscale-Permitting Ocean Model

“…If kinetic energy is increased from the wind work when there exists a down-front wind component, part of the wind work is dissipated by SI triggered by the down-front wind (Thomas and Taylor 2010). Give that the growth of SI can be described by the geostrophic shear production (GSP), the SI dissipation rate « SI is expressed as (Thomas et al 2013;Bachman et al 2017;Buckingham et al 2019) An integral of the dissipation rate within the SI layer is believed to be an upper bound of the usable wind-work reduction due to SI (an upper bound because part of the dissipation may be directly from the kinetic energy of ocean circulation due to B 0 ), namely,…”

“…Given that the scale of the fastest-growing MLI is close to the local deformation radius in the SML (i.e., L ; NH/f, N is the buoyancy frequency in the SML, H is the SML thickness, f is the local Coriolis parameter), MLI spatial scales vary from 1 to 10 km, requiring a model horizontal grid spacing of 0.55 km to capture 90% of regions globally in all seasons (Dong et al 2020b). Hence, submesoscale eddies generated by MLI can be mostly resolved by current-capability nested models, permitted in a few leading-edge global models (e.g., Capet et al 2008;Mensa et al 2013;Rocha et al 2016a,b;Sasaki et al 2017;Su et al 2018;Dong and Zhong 2018;Dong et al 2020a), and studied in specialized observations (e.g., Callies et al 2015;Buckingham et al 2016;Sarkar et al 2016;Viglione et al 2018;Little et al 2018;Yu et al 2019a;Zhang et al 2021).…”

“…(3) implies that SI is associated with stronger (i.e., larger horizontal buoyancy gradient) fronts than MLI. Many studies have shown the SML possesses SI in the presence of strong horizontal buoyancy gradients (D'Asaro et al 2011;Thomas et al 2013;Haney et al 2015;Ramachandran et al 2018;Savelyev et al 2018;Viglione et al 2018;Buckingham et al 2019;Du Plessis et al 2019;Yu et al 2019b). SI are also potentially present in the bottom boundary layer (Wenegrat and Thomas 2020;Yankovsky et al 2020) as are MLI (Wenegrat et al 2018a;Dong et al 2020b).…”

“…MLI extracts background potential energy to grow but often transfers kinetic energy toward larger scales (i.e., inverse cascade; Callies et al 2016;Dong et al 2020a;Schubert et al 2020), although it can contribute to the forward cascade of total energy (Capet et al 2008;Dong et al 2020a). By contrast, SI mainly extracts kinetic energy from geostrophic fronts and transfers kinetic energy to smaller scales, contributing to local mixing (Taylor and Ferrari 2009;Buckingham et al 2019) and effectively reducing usable wind work (i.e., the rate of kinetic energy increase in coherent motions due to down-front winds) done on fronts under forced SI (Thomas and Taylor 2010).…”

“…SI spatial scales are O(100) m in the SML, much smaller than MLI, thus SI is not resolved even in most current regional models, much less climate models. Parameterizations have been proposed to include the impacts of SI (e.g., Lindstrom and Nordeng 1992;Balasubramanian and Yau 1994;Fei et al 2011;Bachman et al 2017;Yankovsky et al 2020), although they are not commonly in use (Buckingham et al 2019).…”