Slow quasigeostrophic unstable modes of a lens vortex in a continuously stratified flow

Nguyen, Hai Yen; Hua, Bach Lien; Schopp, Richard; Carton, Xavier

doi:10.1080/03091929.2011.620568

Cited by 26 publications

(59 citation statements)

References 24 publications

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“…Finally, it should be mentioned that for the cases examined here (Ro = 0.05, 0.1 Bu 1.6), the peripheral location of critical layers is found to be generic (figures 3, 5, 7, and 14(f)), which is consistent with the QG analysis of Nguyen et al (2012). …”

Section: Critical Layerssupporting

confidence: 74%

“…A comparison of our results with those of many previous studies is not straightforward because various different vortex models and flow models have been used. Below we compare our parameter map of stability with the results of the most relevant study in the QG limit (Nguyen et al 2012) and with the results of several relevant studies using multi-layer models. We also discuss the results of Yim et al (2016), who used the full Boussinesq equations but studied a different family of vortices.…”

Section: Comparison With Previous Studiesmentioning

confidence: 97%

“…In the limit of vanishing Ro, the most relevant study to ours is that of Nguyen et al (2012), who numerically calculated the unstable modes of a Gaussian vortex using the QG equations. They found that the fastest-growing mode changes from S2 to A1 around Bu = 1, which along with the general dependence of the growth rate of the fastest- Figure 9.…”

Section: Comparison With Previous Studiesmentioning

confidence: 99%

“…It should be noted that despite the peculiar nature of critical layers, it is not difficult to accurately compute them using high-resolution numerical simulations. For example, Nguyen et al (2012) and Yim et al (2016) have simulated critical layers in 3D QG and Boussinesq vortices, respectively. Recently, we have numerically computed critical layers, with and without dissipation, in stratified, rotating, unidirectional flows and found that with sufficient spatial resolution the locations, widths and other analytically-known properties of the critical layers can be quantitatively reproduced (Marcus et al 2013(Marcus et al , 2015.…”

Section: Critical Layersmentioning

confidence: 99%

“…However, the majority of those studies have used idealized models for the vortices or for the governing equations. For example, Ikeda (1981), Helfrich & Send (1988), and Benilov (2005b) studied quasigeostrophic (QG) vortices in discrete two-layer flows; Gent & McWilliams (1986) studied columnar (i.e., with no variation in the vertical direction) QG vortices; Flierl (1988) examined columnar and 3D QG vortices; Nguyen et al (2012) studied 3D QG vortices; Carton & McWilliams (1989) investigated one and two-layer QG vortices; Dewar & Killworth (1995), Killworth et al (1997), Dewar et al (1999), Baey & Carton (2002), Benilov (2004), Benilov (2005a), Benilov & Flanagan (2008), Lahaye & Zeitlin (2015), and Benilov et al (1998) examined two-layer ageostrophic vortices (the latter also studied geostrophic vortices); Katsman et al (2003) examined multi-layer ageostrophic vortices; Smyth & McWilliams (1998), Billant et al (2006), and Yim & Billant (2015) studied columnar ageostrophic vortices; Stegner & Dritschel (2000) examined shallow-water ageostrophic vortices; Lazar et al (2013a,b) studied shallow-water inertially-unstable vortices; Sutyrin (2015) examined two and three-layer ageostrophic vortices; BrunnerSuzuki et al (2012) investigated the evolution of 3D ageostrophic vortices (but this was not technically a stability study because the initial vortices were created through geostrophic adjustment and thus out-of-equilibrium); and Tsang & Dritschel (2015) also studied the evolution, rather than the stability, of 3D ageostrophic vortices made from piecewise-constant elements of potential vorticity that were not exact equilibrium solutions of their equations of motion. One study focused on 3D equilibrium vortices using the full 3D Boussinesq equation is that of Yim et al (2016) who examined the linear stability of a specific family of vortices with Gaussian angular velocity.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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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Section: Critical Layerssupporting

confidence: 74%

Section: Comparison With Previous Studiesmentioning

confidence: 97%

Section: Comparison With Previous Studiesmentioning

confidence: 99%

Section: Critical Layersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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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Why compensated cold‐core rings look stable

Sutyrin

2015

Geophysical Research Letters

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In contrast to many real‐ocean rings and eddies, circular vortices in idealized two‐layer models tend to be highly unstable, unless their radius is made small or their baroclinicity is made artificially weak. The addition of a middle layer with uniform potential vorticity weakens vertical coupling between the upper and lower layers that enhances vortex stability and makes the vortex lifespan more realistic. It is demonstrated here that such a three‐layer vortex model in so‐called compensated state (without rotation in the deep layer) possesses smaller lower interface slope than the two‐layer model that reduces the potential vorticity gradient in the lower layer and provides less unstable configurations. Numerical simulations of an unstable cyclone with parameters typical for cold‐core ring Bob reveal strong deformations and pulsations of the vortex core in the two‐layer setup, while the ring becomes only slightly deformed and looks stable when the middle layer with uniform potential vorticity is added to be consistent with observations. Enhanced vortex stability in such three‐layer setup has important implications for further studies of real‐ocean eddies.

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Can Large Oceanic Vortices Be Stable?

Benilov

2018

Geophysical Research Letters

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Observations show that radii of oceanic eddies often exceed the Rossby radius of deformation, whereas theoretical studies suggest that such vortices should be unstable. The present paper resolves this paradox by presenting a wide class of large geostrophic vortices with a sign‐definite gradient of potential vorticity (which makes them stable), in an ocean where the density gradient is mostly confined to a thin near‐surface layer (which is indeed the case in the real ocean). The condition of a thin “active” layer is what makes the present work different from the previous theoretical studies and is of utmost importance. It turns out that without it, the joint requirement that a vortex be large and have a sign‐definite potential vorticity gradient trivializes the problem by eliminating all vortices except nearly barotropic ones.

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Slow quasigeostrophic unstable modes of a lens vortex in a continuously stratified flow

Cited by 26 publications

References 24 publications

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

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

Why compensated cold‐core rings look stable

Can Large Oceanic Vortices Be Stable?

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