Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation

Reinaud, Jean Noel; Koshel, K. V.; Ryzhov, Eugene A.

doi:10.1063/1.5052202

Cited by 10 publications

(5 citation statements)

References 35 publications

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“…A number of the results we observe are similar to behavior found in point vortex models. In these models, vortices in fluids are represented as non-dissipative point particles with a logarithmic long range interaction and nondissipative dynamics that are controlled by a Coriolis or Magnus term [23][24][25][26] . A pair of point vortices with the same vorticity rotate around one another, while a pair with opposite vorticity translates.…”

Section: Discussionmentioning

confidence: 99%

“…In most of these systems, the dynamics is overdamped; however, some systems also include nondissipative effects such as inertia or Magnus forces. In particular, Magnus forces produce a velocity component that is perpendicular to the net force experienced by a particle, and such forces arise for vortices in fluids [23][24][25][26] , active spinners [27][28][29][30][31] , chiral active matter 32 , charged particles in magnetic fields 33 , and skyrmions in chiral magnets [34][35][36] . One consequence of this is that pairs or clusters of particles can undergo rotations or spiraling motion when they enter a confining potential [37][38][39][40][41] or are subjected to a quench 42 .…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of Magnus Dominated Particle Clusters, Collisions, Pinning and Ratchets

Reichhardt,

Reichhardt

2020

Preprint

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Motivated by the recent work in skyrmions and active chiral matter systems, we examine pairs and small clusters of repulsively interacting point particles in the limit where the dynamics is dominated by the Magnus force. We find that particles with the same Magnus force can form stable pairs, triples and higher ordered clusters or exhibit chaotic motion. For mixtures of particles with opposite Magnus force, particle pairs can combine to form translating dipoles. Under an applied drive, particles with the same Magnus force translate; however, particles with different or opposite Magnus force exhibit a drive-dependent decoupling transition. When the particles interact with a repulsive obstacle, they can form localized orbits with depinning or unwinding transitions under an applied drive. We examine the interaction of these particles with clusters or lines of obstacles, and find that the particles can become trapped in orbits that encircle multiple obstacles. Under an ac drive, we observe a series of ratchet effects, including ratchet reversals, for particles interacting with a line of obstacles due to the formation of commensurate orbits. Finally, in assemblies of particles with mixed Magnus forces of the same sign, we find that the particles with the largest Magnus force become localized in the center of the cluster, while for mixtures with opposite Magnus forces, the motion is dominated by transient local pairs or clusters, where the translating pairs can be regarded as a form of active matter.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics of Magnus Dominated Particle Clusters, Collisions, Pinning and Ratchets

Reichhardt,

Reichhardt

2020

Preprint

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“…where H is a some fixed value of the Hamiltonian. It is, therefore, useful to analyse, in turn, the extreme values of the Hamiltonian (see also [61][62][63]):…”

Section: Analysis Of Possible Motion Regimesmentioning

confidence: 99%

“…We next measure the vortex deformation by evaluating the semi-axis lengths a and b, with a > b without loss of generality. We perform this by fitting ellipses having the same second-order spatial moments to the actual vortex bounding contours (see, e.g., [63]). As R v is increased while keeping the other parameters fixed, as expected, the vortex deformation becomes more significant, as shown in Figure 20 for the first vortex of the upper layer.…”

Section: Finite-core Hetonsmentioning

confidence: 99%

N-Symmetric Interaction of N Hetons, II: Analysis of the Case of Arbitrary N

Koshel,

Sokolovskiy,

Dritschel

et al. 2024

Fluids

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This paper seeks and examines N-symmetric vortical solutions of the two-layer geostrophic model for the special case when the vortices (or eddies) have vanishing summed strength (circulation anomaly). This study is an extension [Sokolovskiy et al. Phys. Fluids 2020, 32, 09660], where the general formulation for arbitrary N was given, but the analysis was only carried out for N=2. Here, families of stationary solutions are obtained and their properties, including asymptotic ones, are investigated in detail. From the point of view of geophysical applications, the results may help interpret the propagation of thermal anomalies in the oceans.

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“…are performed using the contour dynamic techniques as in the work 38 . Detailed analysis of the configuration using the finite-size vortex model is reported in the accompanying paper 44 . The next section addresses the asymmetric case, i.e.…”

Section: Symmetric Casementioning

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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Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation

Cited by 10 publications

References 35 publications

Dynamics of Magnus Dominated Particle Clusters, Collisions, Pinning and Ratchets

Dynamics of Magnus Dominated Particle Clusters, Collisions, Pinning and Ratchets

N-Symmetric Interaction of N Hetons, II: Analysis of the Case of Arbitrary N

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

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