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Christian E. Buckingham, Jonathan Gula, and Xavier Carton

Abstract

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′ = Lq′ < 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.

Open access
Christian E. Buckingham, Jonathan Gula, and Xavier Carton

Abstract

In this study, we examine the role of curvature in modifying frontal stability. We first evaluate the classical criterion that the Coriolis parameter f multiplied by the Ertel potential vorticity (PV) q is positive for stable flow and that instability is possible when this quantity is negative. The first portion of this statement can be deduced from Ertel’s PV theorem, assuming an initially positive fq. Moreover, the full statement is implicit in the governing equation for the mean geostrophic flow, as the discriminant, fq, changes sign. However, for curved fronts in cyclogeostrophic or gradient wind balance (GWB), an additional term enters the discriminant owing to conservation of absolute angular momentum L. The resulting expression, (1 + Cu)fq < 0 or Lq < 0, where Cu is a nondimensional number quantifying the curvature of the flow, simultaneously generalizes Rayleigh’s criterion by accounting for baroclinicity and Hoskins’s criterion by accounting for centrifugal effects. In particular, changes in the front’s vertical shear and stratification owing to curvature tilt the absolute vorticity vector away from its thermal wind state; in an effort to conserve the product of absolute angular momentum and Ertel PV, this modifies gradient Rossby and Richardson numbers permitted for stable flow. This forms the basis of a nondimensional expression that is valid for inviscid, curved fronts on the f plane, which can be used to classify frontal instabilities. In conclusion, the classical criterion fq < 0 should be replaced by the more general criterion for studies involving gravitational, centrifugal, and symmetric instabilities at curved density fronts. In Part II of the study, we examine interesting outcomes of the criterion applied to low-Richardson-number fronts and vortices in GWB.

Open access
Xiaolong Yu, Alberto C. Naveira Garabato, Adrian P. Martin, Christian E. Buckingham, Liam Brannigan, and Zhan Su

Abstract

Numerical simulations suggest that submesoscale turbulence may transform lateral buoyancy gradients into vertical stratification and thus restratify the upper ocean via vertical flow. However, the observational evidence for this restratifying process has been lacking due to the difficulty in measuring such ephemeral phenomena, particularly over periods of months to years. This study presents an annual cycle of the vertical velocity and associated restratification estimated from two nested clusters of meso- and submesoscale-resolving moorings, deployed in a typical midocean area of the northeast Atlantic. Vertical velocities inferred using the nondiffusive density equation are substantially stronger at submesoscales (horizontal scales of 1–10 km) than at mesoscales (horizontal scales of 10–100 km), with respective root-mean-square values of 38.0 ± 6.9 and 22.5 ± 3.3 m day−1. The largest submesoscale vertical velocities and rates of restratification occur in events of a few days’ duration in winter and spring, and extend down to at least 200 m below the mixed layer base. These events commonly coincide with the enhancement of submesoscale lateral buoyancy gradients, which is itself associated with persistent mesoscale frontogenesis. This suggests that mesoscale frontogenesis is a regular precursor of the submesoscale turbulence that restratifies the upper ocean. The upper-ocean restratification induced by submesoscale motions integrated over the annual cycle is comparable in magnitude to the net destratification driven by local atmospheric cooling, indicating that submesoscale flows play a significant role in determining the climatological upper-ocean stratification in the study area.

Open access
Carl P. Spingys, Alberto C. Naveira Garabato, Sonya Legg, Kurt L. Polzin, E. Povl Abrahamsen, Christian E. Buckingham, Alexander Forryan, and Eleanor E. Frajka-Williams

Abstract

Water-mass transformation by turbulent mixing is a key part of the deep-ocean overturning, as it drives the upwelling of dense waters formed at high latitudes. Here, we quantify this transformation and its underpinning processes in a small Southern Ocean basin: the Orkney Deep. Observations reveal a focussing of the transport in density space as a deep western boundary current (DWBC) flows through the region, associated with lightening and densification of the current’s denser and lighter layers, respectively. These transformations are driven by vigorous turbulent mixing. Comparing this transformation with measurements of the rate of turbulent kinetic energy dissipation indicates that, within the DWBC, turbulence operates with a high mixing efficiency, characterized by a dissipation ratio of 0.6 to 1 that exceeds the common value of 0.2. This result is corroborated by estimates of the dissipation ratio from microstructure observations. The causes of the transformation are unravelled through a decomposition into contributions dependent on the gradients in density space of the: dianeutral mixing rate, isoneutral area, and stratification. The transformation is found to be primarily driven by strong turbulence acting on an abrupt transition from the weakly-stratified bottom boundary layer to well-stratified off-boundary waters. The reduced boundary-layer stratification is generated by a downslope Ekman flow associated with the DWBC’s flow along sloping topography, and is further regulated by submesoscale instabilities acting to re-stratify near-boundary waters. Our results provide observational evidence endorsing the importance of near-boundary mixing processes to deep-ocean overturning, and highlight the role of DWBCs as hot spots of dianeutral upwelling.

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