Instability of Equivalent-Barotropic Riders

Swenson, Mark

doi:10.1175/1520-0485(1987)017<0492:ioebr>2.0.co;2

Cited by 41 publications

(23 citation statements)

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“…2,6,[7][8][9][10] Our full nonlinear simulations of distorted axisymmetric monopoles suggest that sheardiffusion mixing governs the relaxation toward the tripole attractor for a moderate perturbation just as it would toward the monopole attractor for slight perturbations. In the case of the tripole, the positive portion of the quadrupolar disturbance is thoroughly mixed, while the negative portion persists to form a quasi-steady rotating tripole.…”

Section: Introductionmentioning

confidence: 79%

Quasi-steady monopole and tripole attractors for relaxing vortices

1997

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Using fully nonlinear simulations of the two-dimensional Navier-Stokes equations at large Reynolds number ͑Re͒, we bracket a threshold amplitude above which a perturbed Gaussian monopole will relax to a quasi-steady, rotating tripole, and below which will relax to an axisymmetric monopole. The resulting quasi-steady structures are robust to small perturbations. We propose a means of measuring the decay rate of disturbances to asymptotic vortical structures wherein streamlines and lines of constant vorticity correspond in some rotating or translating frame. These experiments support the hypothesis that small or moderate deviations from asymptotic structures decay through inviscid and viscous mixing.

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Section: Introductionmentioning

confidence: 79%

Quasi-steady monopole and tripole attractors for relaxing vortices

1997

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“…However, numerical experiments showed that barotropic and baroclinic solutions with such a discontinuity are strongly unstable. [9][10][11] A heton is essentially baroclinic. It is comprised of two discrete vortices of equal strength but opposite signs confined to different layers of a two-layer fluid, and typically separated by a certain distance.…”

Section: A Baroclinic Modons and Hetonsmentioning

confidence: 99%

Stability and transitions of hetonic quartets and baroclinic modons

Kizner

2006

Physics of Fluids

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A new concept, a hetonic quartet, is presented. A hetonic quartet is a two-layer ensemble of four synchronously translating quasigeostrophic discrete vortices aligned perpendicularly to the axis of their translation. On the f-plane, a hetonic quartet is made up of conventional point vortices ͑confined to either the upper or the lower layer͒ with specially fitted circulations and distances between each other, the upper-and lower-layer vortices being opposite in sign and located symmetrically about the translation axis. On the ␤-plane, a two-layer version of the modulated point vortex model ͓Phys. Fluids 25, 2175 ͑1982͔͒ is applied. A necessary and sufficient condition for the stability of f-plane hetonic quartets to perturbations that do not violate the above-mentioned symmetry is established using the analytical methods of Hamiltonian dynamics, whereas on the ␤-plane, a necessary ͑linear͒ stability condition is determined. As distinct from hetons, a stable hetonic quartet is not rigid: when slightly moved off equilibrium it undergoes elastic oscillations. Periodically or continuously acting small perturbations force a stable hetonic quartet to split up into two pairs of hetons, each traveling at different speeds along the same axis. The separation in the faster heton is generally greater than that between the "centers of mass" of the upper-and lower-layer vortices of the original hetonic quartet. The similarity between baroclinic modons and hetonic quartets is traced, and a plausible scenario of the transitions observed in smooth circular baroclinic modons with moderate riders ͓J. Fluid Mech. 468, 239 ͑2002͔͒ is suggested, with the substantial stability of the ultimate elliptical modon state being attributed to the lack of overlap of the main upper and lower vorticity chunks in the modon. The splitting of finite-core hetons ͑two-layer f-plane vortical pairs composed of two circular patches of constant vorticity͒ ͓J. Fluid Mech. 423, 127 ͑2000͔͒ is linked with the transitions in baroclinic modons and hetonic quartets.

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“…Ikeda found that perturbed, slightly elliptical vortices would evolve toward tripolar vortices under certain conditions [15]. Similarly, Swenson came to the same conclusions while studying modon-with-rider solutions to barotropic equations [34]. Van Heijst and various collaborators have performed detailed experiments of tripolar vortices in stratified tanks in stationary and rotating frames [12,18,19,39].…”

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confidence: 76%

“…The term coherent structure refers to a localized region of vorticity that retains its properties, such as physical appearance or certain integral quantities, for an extended or an infinite period of time. It has long been observed that the vorticity fields of initially energetic disorganized two-dimensional flows rapidly relax into a collection of isolated coherent vortical objects in a process known as the "inverse cascade" [13,23,24,25,34]. In this paper, we study the mathematics underlying the inverse cascade by searching for self-similar attractors to a broad category of coherent objects.…”

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confidence: 99%

“…Vorticity in the form of monopoles, dipoles and other multipoles commonly form in the oceans near coastlines through boundary interactions and jet instabilities. Once created, vortical structures in the oceans, sometimes referred to as "gyres," can survive in the mostly irrotational ocean for years before interacting with a coastline or another structure [24,34]. In impulsively started free jets and wall jets, transient monopoles form above the outlet and remain as coherent structures for extensive time periods [33,41].…”

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confidence: 99%

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On the Existence of Two-Dimensional, Localized, Rotating, Self-Similar Vortical Structures

Graham‐Eagle¹,

Rossi²

2002

SIAM J. Appl. Math.

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Abstract. We prove that a Gaussian monopole, also known as the Lamb-Oseen vortex, is the only localized, rotating, self-similar solution to the two-dimensional, incompressible Navier-Stokes equations where level sets of vorticity and corotating streamfunction coincide. Our definition of self-similarity is restricted to the natural linear combination of space, time and viscous diffusion. We arrive at this conclusion by analytically determining the azimuthal Fourier modes for all possible solutions to this problem and then proving that the amplitude of all but the first (axisymmetric) is zero. Since coherent vortex multipoles are observed to be in a state where lines of vorticity and corotating streamfunction correspond, this casts doubt on the existence of any self-similar asymptotic structure other than the monopole.

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Instability of Equivalent-Barotropic Riders

Cited by 41 publications

References 0 publications

Quasi-steady monopole and tripole attractors for relaxing vortices

Quasi-steady monopole and tripole attractors for relaxing vortices

Stability and transitions of hetonic quartets and baroclinic modons

On the Existence of Two-Dimensional, Localized, Rotating, Self-Similar Vortical Structures

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