How Large-Scale and Cyclogeostrophic Barotropic Instabilities Favor the Formation of Anticyclonic Vortices in the Ocean

Perret, Gaële; Dubos, Thomas; Stegner, Alexandre

doi:10.1175/2010jpo4362.1

Cited by 16 publications

(17 citation statements)

References 38 publications

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“…Hence, it may contribute to the cyclonic-anticyclonic asymmetry of the vortices resulting from the saturation of the baroclinic instability (see e.g. Perret, Dubos & Stegner 2011, for the cyclone-anticyclone asymmetry of the vortices resulting from the instability of the jet).…”

Section: Nonlinear Evolution Of Inertially Unstable Jet In the Symmetmentioning

confidence: 99%

Inertial versus baroclinic instability of the Bickley jet in continuously stratified rotating fluid

2014

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International audienceThe paper contains a detailed study of the inertial instability of a barotropic Bickley jet on the f-plane in the continuously stratified primitive equations model, and a comparison of this essentially ageostrophic instability with the classical baroclinic one. Analytical and numerical investigation of the linear stability of the jet in the long-wave sector is performed for a range of Rossby and Burger numbers. The major results are that: (1) the standard symmetric inertial instability, appearing at high enough Rossby numbers, turns out to be the infinite-wavelength limit of an asymmetric inertial instability, this latter having the highest growth rate for a large range of vertical wavenumbers; (2) inertial instability coexists with the standard baroclinic instability, which becomes dominant at small Rossby numbers. Nonlinear saturation of the inertial instability of the jet with a superimposed random small-amplitude perturbation is then studied, using the Weather Research and Forecast model. It is shown that at first stages the inertial instability dominates. It is localized near the maximum of the anticyclonic shear and is associated with the highest attainable value of the vertical wavenumber. The saturation of the inertial instability leads to the homogenization of the geostrophic momentum in the unstable region. At later stages, another baroclinic instability develops, characterized by lower values of the vertical wavenumber. This instability saturates by forming large-scale vortices downstream. It is identified as the leading instability of a marginally inertially stable jet resulting from the initial one through homogenization of the geostrophic momentum. The rough scenario of the evolution of essentially ageostrophic jets is, thus, as follows: the inertial instability rapidly saturates and baroclinic instability takes over. It is shown that reorganization of the flow due to developing instabilities is an efficient source of inertia-gravity waves

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Section: Nonlinear Evolution Of Inertially Unstable Jet In the Symmetmentioning

confidence: 99%

Inertial versus baroclinic instability of the Bickley jet in continuously stratified rotating fluid

2014

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“…Whether this asymmetry is due to differences between the stability (linear or nonlinear) properties of cyclones and anticyclones requires a better understanding of how stability changes with the Rossby number. It should be noted that factors other than stability can be responsible for, or at least contribute to, the observed cyclone-anticyclone asymmetry; for example the creation mechanisms might favor anticyclones (Perret et al 2011), anticyclones might decay slower than cyclones (Hoskins et al 1985, section 7;Graves et al 2006), or coherent cyclones might be harder to observe in planetary atmospheres than anticyclones (Marcus 2004).…”

Section: Introductionmentioning

confidence: 99%

Stability of three-dimensional Gaussian vortices in an unbounded, rotating, vertically stratified, Boussinesq flow: linear analysis

Mahdinia

Hassanzadeh²,

Marcus

et al. 2017

J. Fluid Mech.

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The linear stability of three-dimensional (3D) vortices in rotating, stratified flows has been studied by analyzing the non-hydrostatic inviscid Boussinesq equations. We have focused on a widely-used model of geophysical and astrophysical vortices, which assumes an axisymmetric Gaussian structure for pressure anomalies in the horizontal and vertical directions. For a range of Rossby number (−0.5 < Ro < 0.5) and Burger number (0.02 < Bu < 2.3) relevant to observed long-lived vortices, the growth rate and spatial structure of the most unstable eigenmodes have been numerically calculated and presented as a function of Ro − Bu. We have found neutrally-stable vortices only over a small region of the Ro − Bu parameter space: cyclones with Ro ∼ 0.02 − 0.05 and Bu ∼ 0.85 − 0.95. However, we have also found that anticyclones in general have slower growth rates compared to cyclones. In particular, the growth rate of the most unstable eigenmode for anticyclones in a large region of the parameter space (e.g., Ro < 0 and 0.5 Bu 1.3) is slower than 50 turn-around times of the vortex (which often corresponds to several years for ocean eddies). For cyclones, the region with such slow growth rates is confined to 0 < Ro < 0.1 and 0.5 Bu 1.3. While most calculations have been done for f /N = 0.1 (where f andN are the Coriolis and background Brunt-Väisälä frequencies), we have numerically verified and explained analytically, using non-dimensionalized equations, the insensitivity of the results to reducing f /N to the more ocean-relevant value of 0.01. The results of our stability analysis of Gaussian vortices both support and contradict findings of earlier studies with QG or multi-layer models or with other families of vortices. The results of this paper provide a steppingstone to study the more complicated problems of the stability of geophysical (e.g., those in the atmospheres of giant planets) and astrophysical vortices (in accretion disks).

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“…Therefore for moderate Ro and Fr, the B-B mode in j = 3 occurs only in the anticyclonic shear. The study of Perret et al (2011) also shows that B-B instability favours the anticyclonic shear. The B-B instability is mostly balanced, even for an intermediate Ro and Fr.…”

Section: B-b Instabilitymentioning

confidence: 84%

Ageostrophic instability in rotating shallow water

2012

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Linear instabilities, both momentum-balanced and unbalanced, in several different u(y) shear profiles are investigated in the rotating shallow water equations. The unbalanced instabilities are strongly ageostrophic and involve inertia-gravity wave motions, occurring only for finite Rossby (Ro) and Froude (Fr) numbers. They serve as a possible route for the breakdown of balance in a rotating shallow water system, which leads the energy to cascade towards small scales. Unlike previous work, this paper focuses on general shear flows with non-uniform potential vorticity, and without side or equatorial boundaries or vanishing layer depth (frontal outcropping). As well as classical shear instability among balanced shear wave modes (i.e. B-B type), two types of ageostrophic instability (B-G and G-G) are found. The B-G instability has attributes of both a balanced shear wave mode and an inertia-gravity wave mode. The G-G instability occurs as a sharp resonance between two inertia-gravity wave modes. The criterion for the occurrence of the ageostrophic instability is associated with the second stability condition of Ripa (1983), which requires a sufficiently large local Froude number. When Ro and especially Fr increase, the balanced instability is suppressed, while the ageostrophic instabilities are enhanced. The profile of the mean flow also affects the strength of the balanced and ageostrophic instabilities.

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How Large-Scale and Cyclogeostrophic Barotropic Instabilities Favor the Formation of Anticyclonic Vortices in the Ocean

Cited by 16 publications

References 38 publications

Inertial versus baroclinic instability of the Bickley jet in continuously stratified rotating fluid

Inertial versus baroclinic instability of the Bickley jet in continuously stratified rotating fluid

Stability of three-dimensional Gaussian vortices in an unbounded, rotating, vertically stratified, Boussinesq flow: linear analysis

Ageostrophic instability in rotating shallow water

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