Quasigeostrophic Confocal Spheroidal Vortices

Miyazaki, Takeshi; Fujiwara, Takahiro; Yamamoto, Masahiro

doi:10.1143/jpsj.72.2786

Cited by 3 publications

(6 citation statements)

References 17 publications

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“…This means that each mode appears as a quartet, σ, −σ,σ, −σ. For comparison, we also plot the maximum modes γ m m /q 1 , obtained from the formula derived from Miyazaki et al (2003). We see that they coincide with the largest modes σ r .…”

Section: Formulationmentioning

confidence: 91%

“…As mentioned by Miyazaki et al (2003), and since the growth rate ω m n is proportional to m, for each value of n the maximum growth rate is obtained for m = n.…”

Section: Formulationmentioning

confidence: 99%

“…Linear stability of shielded PV spheres Miyazaki, Fujiwara and Yamamoto (2003) addressed the linear stability quasi-geostrophic confocal spheroidal vortices decomposing of the modes of instability in spherical harmonics. …”

Section: Formulationmentioning

confidence: 99%

“…In this work, we consider vortices where PV is piecewise uniform. Miyazaki, Fujiwara and Yamamoto (2003) studied the linear stability of confocal, piecewise uniform potential vorticity ellipsoidal vortices. We start by revisiting these results for our specific case.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Piecewise uniform potential vorticity pancake shielded vortices

Reinaud

2017

Geophysical & Astrophysical Fluid Dynamics

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Shielded vortices consist of a core of potential vorticity of a given sign surrounded (or shielded) by a layer of opposite-signed potential vorticity. Such vortices have specific properties and have been the focus of numerous studies, first in two dimensional geometries (where potential vorticity is just the vertical component of the vorticity vector) and in geophysical applications (mostly in layered models). The present paper focuses on three-dimensional, spheroidal shielded vortices. In particular, we focus on vortical structures whose overall volume-integrated potential vorticity is zero. We restrict attention to vortices of piecewise uniform potential vorticity in the present research. We first revisit the problem within the quasi-geostrophic model, then we extend the results to the non-hydrostatic regime. We show that the stability of the structure depends on the ratio of potential vorticity between the inner core and the outer shield. In particular it depends on the polarity of the core and of the wavenumber of the azimuthal mode perturbed.

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Section: Formulationmentioning

confidence: 91%

“…As mentioned by Miyazaki et al (2003), and since the growth rate ω m n is proportional to m, for each value of n the maximum growth rate is obtained for m = n.…”

Section: Formulationmentioning

confidence: 99%

Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Piecewise uniform potential vorticity pancake shielded vortices

Reinaud

2017

Geophysical & Astrophysical Fluid Dynamics

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“…Richardson et al 2000). The stability of various baroclinic eddies has been studied by many authors, including Nguyen et al (2012), Meunier et al (2015), Yim et al (2016), Storer et al (2018), Menesguen et al (2018), Meunier et al (2018), Carton et al (2014) for so-called Gaussian vortices, or for piecewise uniform vortices by Miyazaki et al (2003), Reinaud (2017). On the other hand, tripolar vortices where two likesigned vortices are at the same depth have been investigated by Reinaud and Carton (2015).…”

Section: Introductionmentioning

confidence: 99%

The merger of two three-dimensional quasi-geostrophic baroclinic tripolar eddies

Reinaud

Carton

2021

Geophysical & Astrophysical Fluid Dynamics

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We investigate the strong interaction between two baroclinic tripolar eddies in a three-dimensional, rapidlyrotating, continuously stratified flow under the quasi-geostrophic approximation. Each tripolar eddy consists of an anticyclonic central vortex with two oblate cyclonic vortices located above and below the anticyclone. The interaction depends on the vertical and horizontal offsets between the two tripolar eddies. For small and low PV oblate cyclones, each tripolar eddy alone is only weakly unstable to a baroclinic mode. The instability puts the three vortices out of alignment. Most of the eddy however survives the instability. When two tripolar eddies interact, their constituent vortices may merge. Merger occurs when the eddies are close enough together, and shows similarities with the merger of monopolar vortices. Vertically separated eddies do not align vertically. This suggests the importance of an external flow for the alignment, observed in the oceans, to occur. We finally show that the interaction between two tripolar eddies with intense oblate cyclones is very different and show similarities with the dynamics of dipolar baroclinic eddies known as hetons.

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A 3-D minimum-enstrophy vortex in stratified quasi-geostrophic flows

Barabinot,

Reinaud,

Carton

et al. 2024

J. Fluid Mech.

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Applying a variational analysis, a minimum-enstrophy vortex in three-dimensional (3-D) fluids with continuous stratification is found, under the quasi-geostrophic hypothesis. The buoyancy frequency is held constant. This vortex is an ideal limiting state in a flow with an enstrophy decay while energy and generalized angular momentum remain fixed. The variational method used to obtain two-dimensional (2-D) minimum-enstrophy vortices is applied here to 3-D integral quantities. The solution from the first-order variation is expanded on a basis of orthogonal spherical Bessel functions. By computing second-order variations, the solution is found to be a true minimum in enstrophy. This solution is weakly unstable when inserted in a numerical code of the quasi-geostrophic equations. After a stage of linear instability, nonlinear wave interaction leads to the reorganization of this vortex into a tripolar vortex. Further work will relate our solution with maximal entropy 3-D vortices.

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Quasigeostrophic Confocal Spheroidal Vortices

Cited by 3 publications

References 17 publications

Piecewise uniform potential vorticity pancake shielded vortices

Piecewise uniform potential vorticity pancake shielded vortices

The merger of two three-dimensional quasi-geostrophic baroclinic tripolar eddies

A 3-D minimum-enstrophy vortex in stratified quasi-geostrophic flows

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