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Xavier Carton

Abstract

The instability of circular vortices is studied numerically in the surface quasigeostrophic (SQG) model, and their evolutions are compared with those of barotropically unstable 2D vortices. The growth rates in the SQG model evidence similarity with their barotropic counterparts for moderate radial gradients of temperature (or of vorticity in the 2D model). For stronger gradients, SQG vortices are more unstable than 2D vortices. The nonlinear, finite-amplitude evolutions of perturbed vortices provide evidence that moderately unstable, elliptically perturbed vortices form tripoles. When they are more unstable, they break into two dipoles. Weakly unstable vortices with triangular perturbations form transient quadrupoles that break; they stabilize only for large gradients of mean temperature. Finally, with square perturbations, pentapoles degenerate into dipoles, at least for the range of mean temperature gradients explored here. The analysis of nonlinear stabilizations reveals that the deformation of the vortex core and the leak of its temperature anomaly to the periphery are essential ingredients to stabilize the perturbation at finite amplitude. In conclusion, SQG vortex instability exhibits considerable similarity to the barotropic instability of 2D vortices.

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Xavier J. Capet and Xavier J. Carton

Abstract

A process study is conducted on the evolution of boundary currents in a two-layer quasigeostrophic model on the f plane. These currents are composed of two strips of uniform potential vorticity (PV), one in each layer, and both hugging the coast. Coastal water separation (“detrainment”) through baroclinic instability and topographic perturbation is examined. It is shown that the key characteristics of the flow finite-amplitude destabilization can be explained with the help of a linear quantity—the critical amplitude A c—that refers to the location of the line (often called critical layer) where the phase speed of the growing perturbation is equal to the unperturbed flow velocity. Notably, prediction on PV front breaking location is made possible. Different detrainment regimes (i.e., the way fragments of the boundary current are isolated and detached from the initially rectilinear core—e.g., filament formation, eddy shedding) are also identified, related to various A c value ranges, and compared with observed oceanic events.

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Marc Pavec, Xavier Carton, and Gordon Swaters

Abstract

The Phillips problem of baroclinic instability is generalized in a frontal geostrophic model. The configuration used here is a two-layer flow (with quasigeostrophic upper-layer current) over a sloping bottom. Baroclinic instability in the frontal model has a single unstable mode, corresponding to isobaths and isopycnals sloping in the same direction, contrary to the quasigeostrophic model, which has two unstable modes. In physical terms, this is explained by the absence of relative vorticity in the lower (frontal) layer. Indeed, the frontal geostrophic model can be related to the quasigeostrophic model in the limit of very small thickness of the lower layer, implying that potential vorticity reduces to vortex stretching in this layer. This stability study is then extended to unsteady flows. In the frontal geostrophic model, a mean flow oscillation can stabilize an unstable steady flow; it can destabilize a stable steady flow only for a discrete spectrum of low frequencies. In this case, the model equations reduce to the Mathieu equation, the properties of which are well known.

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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.

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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.

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Benjamin J. Harvey, Maarten H. P. Ambaum, and Xavier J. Carton

Abstract

The stability characteristics of the surface quasigeostrophic shielded Rankine vortex are found using a linearized contour dynamics model. Both the normal modes and nonmodal evolution of the system are analyzed and the results are compared with two previous studies. One is a numerical study of the instability of smooth surface quasigeostrophic vortices with which qualitative similarities are found and the other is a corresponding study for the two-dimensional Euler system with which several notable differences are highlighted.

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Jérôme Paillet, Bernard Le Cann, Xavier Carton, Yves Morel, and Alain Serpette

Abstract

A meddy was discovered in April 1997 off the northwestern corner of Spain, near 45°N, 11°30′W. It was tracked during 18 months with Lagrangian floats and deep drogued buoys, and several cruises were set to collect further hydrological and Lowered-ADCP measurements on it. The meddy, named Ulla, was a one-core lens with maximum values of temperature and salinity of 11.5°C and 36.17 psu near 1000-m depth, yielding anomalies above 2.5°C and 0.5 psu compared to its environment. Its rotation frequency was close to 1 loop every 5 days. The maximum azimuthal velocities of 15–20 cm s−1 were reached near a 15-km radius. The meddy had a wide remote influence, notably up to the surface, and was associated with a total azimuthal volume transport of around 10 Sv, (Sv = 106 m3 s−1), of which around 2 Sv was trapped in the core. A widening of the radial structure with decreasing depth was notable in August 1997. Meddy Ulla was significantly elliptic for most of the time and, depending on the periods, the main ellipse axis either slowly rotated clockwise, or kept a constant orientation. The hydrological properties and vorticity of the core remained relatively constant during the observation period. Beyond the radius of maximum azimuthal velocity, the velocity structure was extremely variable and cannot be modeled simply. Meddy Ulla had two other characteristics that make it a particular member of the meddy family: first, it is the northernmost meddy, by around 5 latitude, that has ever been thoroughly studied. It is believed that Ulla was generated in the Cape Finisterre–Cape Ortegal area, far to the north of previously known formation sites. Second, Meddy Ulla stayed in the same area for 11 months while meddies usually drift quite rapidly, in a generally southwestward direction. Among the reasons advocated for its near stagnation are the frequent interaction with other “northern meddies” that drifted past Ulla to its south and the likely interaction with deep seamounts. After 11 months of stagnation, the meddy suddenly accelerated southwestward and lost some volume at the same time. Finally, after 18 months of observations, it was lost: at that time its net displacement was only 190 km southwestward, at a mean velocity of 4 mm s−1. Meddy Ulla is the first of a series of “northern meddies” identified during the Action de Recherche sur la Circulation en Atlantique Nord Est (ARCANE) program.

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