Hetonic quartets in a two-layer quasi-geostrophic flow: V-states and stability

Reinaud, Jean Noel; Sokolovskiy, Mikhail; Carton, Xavier

doi:10.1063/1.5027181

Cited by 3 publications

(3 citation statements)

References 35 publications

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“…Deformation flows always appear near topography boundaries, coherent vortices, jets, large-scale gyres or other non-uniform flows. More generally, an arbitrary external perturbation can be expanded into a Taylor series up to the second-order terms, which gives the following flow form [54,55,[57][58][59]61,84,89,[91][92][93][94][95][96][97][98]…”

Section: External Deformation Flowmentioning

confidence: 99%

Vortex Interactions Subjected to Deformation Flows: A Review

Koshel

Ryzhov

Carton

2019

Fluids

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Deformation flows are the flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets) and various fixed obstacles (submerged obstacles and continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.

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Section: External Deformation Flowmentioning

confidence: 99%

Vortex Interactions Subjected to Deformation Flows: A Review

Koshel

Ryzhov

Carton

2019

Fluids

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show abstract

“…Deformation flows always appear near topography boundaries, coherent vortices, jets, large-scale gyres or other non-uniform flows. More generally, an arbitrary external perturbation can be expanded into a Taylor series up to the second order terms, which gives the following flow form [54,55,57,58,61,84,89,[91][92][93][94][95][96][97][98][99]…”

Section: External Deformation Flowmentioning

confidence: 99%

Vortex Interactions Subjected to Deformation Flows: A Review

Koshel¹,

Ryzhov²,

Carton³

2018

Preprint

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Deformation flows are flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets), various fixed obstacles (submerged obstacles, continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.

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“…Since the model allows for vorticity redistribution through the deformation of the vortices and generally more complicated dynamics, many authors look for steady or periodic solutions that ensure that finite area vortices engaged into the interactions remain coherent and retain their initial shape for a reasonably long time. Approaches into finding such solutions include the ones based on contour dynamics 10,[35][36][37][38][39] or analytical ones using complex analysis 40 . In particular, recent studies 38,41 attest that finite area vortex systems can manifest dynamical regimes very similar to their analogous point-vortex counterparts.…”

Section: Introductionmentioning

confidence: 99%

Entrapping of a vortex pair interacting with a fixed point vortex revisited. I. Point vortices

et al. 2018

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The problem of a pair of point vortices impinging on a fixed point vortex of arbitrary strengths [E. Ryzhov and K. Koshel, EPL 102, 44004 (2013)] is revisited and investigated comprehensively. Although the motion of pair of point vortices is established to be regular, the model presents a plethora of possible bounded and unbounded solutions with complicated vortex trajectories. The initial classification [E. Ryzhov and K. Koshel, EPL 102, 44004 (2013)] revealed that pair could be compelled to perform bounded or unbounded motion without giving a full classification of either of those dynamical regimes. The present work capitalizes upon the previous results and introduces a finer classification with a multitude of possible regimes of motion. Regimes of bounded motion for the vortex pair entrapped near the fixed vortex or of unbounded motion, when the vortex pair moves away from the fixed vortex, can be categorized by varying the two governing parameters: (i) the ratio of the distances between pair's vortices and the fixed vortex, and (ii) the ratio of the strengths of the vortices of the pair and the strength of the fixed vortex. In particular, a bounded motion regime where one of pair's vortices does not rotate about the fixed vortex is revealed. In this case, only one of pair's vortices rotates about the fixed vortex, while the other one oscillates at a certain distance. Extending the results obtained with the point-vortex model to an equivalent model of finite size vortices is the focus of a second paper.

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Hetonic quartets in a two-layer quasi-geostrophic flow: V-states and stability

Cited by 3 publications

References 35 publications

Vortex Interactions Subjected to Deformation Flows: A Review

Vortex Interactions Subjected to Deformation Flows: A Review

Vortex Interactions Subjected to Deformation Flows: A Review

Entrapping of a vortex pair interacting with a fixed point vortex revisited. I. Point vortices

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