Vortex stability in a multi-layer quasi-geostrophic model: application to Mediterranean Water eddies

Abstract

The stability of circular vortices to normal mode perturbations is studied in a multi-layer quasigeostrophic model. The stratification is fitted on the Gulf of Cadiz where many Mediterranean Water (MW) eddies are generated. Observations of MW eddies are used to determine the parameters of the reference experiment; sensitivity tests are conducted around this basic case. The objective of the study is twofold: (a) determine the growth rates and nonlinear evolutions of unstable perturbations for different three-dimensional (3D) velocity structures of the vortices, (b) check if the different structure of our idealized vortices, mimicking MW cyclones and anticyclones, can induce different stability properties in a model that conserves parity symmetry, and apply these results to observed MW eddies. The linear stability analysis reveals that, among many 3D distributions of velocity, the observed eddies are close to maximal stability, with instability time scales longer than 100 days (these time scales would be less than 10 days for vertically more sheared eddies). The elliptical deformation is most unstable for realistic eddies (the antisymmetric one dominates for small eddies and the triangular one for large eddies); the antisymmetric mode is stronger for cyclones than for anticyclones. Nonlinear evolutions of eddies with radii of about 30 km, and elliptically perturbed, lead to their reorganization into 3D tripoles; smaller eddies are stable and larger eddies break into 3D dipoles. Horizontally more sheared eddies are more unstable and sustain more asymmetric instabilities. In summary, few differences were found between cyclone and anticyclone stability, except for strong horizontal velocity shears.

On the stability of outcropping eddies in a constant‐PV ocean

“…The term motionless ocean is used here to denote the ocean layer around and below the eddy that has no mean flow but its perturbations can interact with those in the eddy. Such unstable eddies include an eddy in solid body rotation (Paldor and Nof, 1990;Ripa, 1992), a constant potential vorticity (PV) eddy (Cohen et al, 2015a(Cohen et al, , 2015b, denoted hereafter as CDP15a and CDP15b), an eddy of exponentially decaying profile (Carton et al, 2014;Lahaye and Zeitlin, 2015) and the Gaussian eddy (Dewar and Killworth, 1995;Benilov, 2004). The instability of eddies in a continuously stratified fluid was studied by Tsang and Dritschel (2015).…”

Optimal Perturbations of an Oceanic Vortex Lens

“…Baroclinic instability of meddies was studied by [21,25] and was shown to be a source of azimuthal variability by breaking the vortex symmetry and might therefore play a primary role in the formation of layering, hence the diffusion of the vortex's thermohaline properties. Baroclinic instability was also shown to be able to split and trigger filamentation of vortex lenses [21,26] and could thus drive the production of small horizontal scales, which would in turn feed the vertical scale cascade through differential advection [24,27,28]. The stability properties of vortex lenses is thus an important topic as they strongly influences the production of small scale variance and possibly favour the mixing of a climatically important water mass.…”

Evidence of Mediterranean Water dipole collision in the Gulf of Cadiz

“…The coupling coefficients are The stratification of this model is fitted to the region: the reduced gravities g 0 j21=2 are calculated such that the external deformation radius is infinite and the first two internal deformation radii are 30 and 15 km, respectively [see Carton et al, 2014]. We have The model performs spatial derivatives via a Galerkin projection on Fourier modes with truncation and a mixed Euler-leapfrog time stepping scheme is used.…”

“…The Gaussian velocity profile is commonly used for MW eddies [see Carton et al, 2014]. Therefore, each eddy is characterized by four parameters V 0 , R, x 0 , y 0 .…”