Oscillations and rotations of elliptical warm‐core rings

Cushman-Roisin, Benoı̂t; Heil, Wolfgang; Nof, Doron

doi:10.1029/jc090ic06p11756

Cited by 96 publications

(70 citation statements)

References 26 publications

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“…In the more general geophysical context, isolated vortices called 'rodons' (Cushman-Roisin et al 1985;Young 1986) have been found as exact solutions to the single-layer shallow-water equations (having a variable fluid depth), a model of warm-core rings shed by the Gulf stream. Płotka & Dritschel (2012) examined a wide class of vortex patch equilibria with uniform potential vorticity (PV) in the quasi-geostrophic (QG) shallow-water equations, determining both their equilibrium shapes and stability numerically.…”

Section: Introductionmentioning

confidence: 99%

Ellipsoidal vortices in rotating stratified fluids: beyond the quasi-geostrophic approximation

Tsang

Dritschel

2014

J. Fluid Mech.

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We examine the basic properties and stability of isolated vortices having uniform potential vorticity in a non-hydrostatic rotating stratified fluid, under the Boussinesq approximation. For simplicity, we consider a uniform background rotation and a linear basic-state stratification for which both the Coriolis and buoyancy frequencies, f and N , are constant. Moreover, we take f /N ≪ 1, as typically observed in the Earth's atmosphere and oceans. In the small Rossby number 'quasigeostrophic' limit, when the flow is weak compared to the background rotation, there exists exact solutions for steadily-rotating ellipsoidal volumes of uniform potential vorticity in an unbounded flow (Zhmur & Shchepetkin 1991;Meacham 1992). Furthermore, a wide range of these solutions are stable so long as the horizontal and vertical aspect ratios λ and µ do not depart greatly from unity (Dritschel et al. 2005). In the present study, we examine the behaviour of ellipsoidal vortices at Rossby numbers up to near unity in magnitude. We find that there is a monotonic increase in stability as one varies the Rossby number from nearly −1 (anticyclone) to nearly +1 (cyclone). That is, quasi-geostrophic vortices are more stable than anticyclones at finite (negative) Rossby number, and generally less stable than cyclones at finite (positive) Rossby number. Ageostrophic effects strengthen both the rotation and the stratification within a cyclone, enhancing its stability. The converse is true for an anticyclone. For all Rossby numbers, stability is reinforced by increasing λ towards unity or decreasing µ. An unstable vortex often restabilises by developing a near-circular cross section, typically resulting in a roughly ellipsoidal vortex, but occasionally a binary system is formed. Throughout the nonlinear evolution of a vortex, the emission of inertiagravity waves is negligible across the entire parameter space investigated. Thus, vortices at small to moderate Rossby numbers, and any associated instabilities are (ageostrophically) balanced. A manifestation of this balance is that, at finite Rossby number, an anticyclone rotates faster than a cyclone.

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Section: Introductionmentioning

confidence: 99%

Ellipsoidal vortices in rotating stratified fluids: beyond the quasi-geostrophic approximation

Tsang

Dritschel

2014

J. Fluid Mech.

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“…The relation (5.35) in the above is readily validated by symbolic computation and has an analog in the theory of the evolution of elliptical ocean warm-core eddies ( [8,14,32]). On elimination of θ − ϕ in (5.22) via the relation (5.32) and use of (5.37) is seen that,B is given by the elliptic integral relation…”

Section: An Elliptic Vortex Reduction To An Integrable Ermakov-ray-rementioning

confidence: 99%

“…On introduction of the Madelung transformation [25] 8) it is seen that the capillarity system (2.6)−(2.7) may be embodied in the NLS-type equation…”

Section: Introductionmentioning

confidence: 99%

Integrable Substructure in a Korteweg Capillarity Model. A Karman-Tsien Type Constitutive Relation

Rogers

2021

JNMP

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“…Another approach is related to when the vorticity is concentrated into elliptical form. While such a vortex can be deformed (stretch-shrink and rotate), the suggestion is that the elliptical shape should be maintained [6] [7] [8] [9].…”

Section: Introductionmentioning

confidence: 99%

Blocking Anticyclone in the Atlantic Sector of the Arctic as an Example of an Individual Atmospheric Vortex

Kislov¹,

Sokolikhina²,

Semenov³

et al. 2017

ACS

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The task of vortex boundaries setting is one of the most complexes in examination of factors influencing on the vortex (circulation system) development and destruction. In this study a new approach of vortex analysis as a whole system is proposed. It is based on vorticity equation where vorticity (left part of the equation) is defined as time coefficients of EOF-decomposition, which is integrated indexes characterizing individual vortex dynamics. Right part of the vorticity equation depicts internal and external factors influencing on the vortex. It's approbation is done on the example of an arctic-subarctic circulation system including blocking anticyclone in winter 2012 which persisted for a long time over the Atlantic sector of the Arctic and led to the formation of the largest positive air temperature anomalies and the minimum ice cover area in the Barents and Kara seas in the entire history of regular observations. It is shown that the main factor in long-term maintenance of the blocking anticyclone over the Arctic was vorticity advection, which was stabilized by horizontal heat advection.

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Oscillations and rotations of elliptical warm‐core rings

Cited by 96 publications

References 26 publications

Ellipsoidal vortices in rotating stratified fluids: beyond the quasi-geostrophic approximation

Ellipsoidal vortices in rotating stratified fluids: beyond the quasi-geostrophic approximation

Integrable Substructure in a Korteweg Capillarity Model. A Karman-Tsien Type Constitutive Relation

Blocking Anticyclone in the Atlantic Sector of the Arctic as an Example of an Individual Atmospheric Vortex

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