The N-Vortex Problem on a Riemann Sphere

Wang, Qun

doi:10.1007/s00220-021-04044-8

Cited by 5 publications

(2 citation statements)

References 47 publications

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“…In general, the present paper is, in addition to the papers by S. Boatto and J. Koiller already mentioned, much in spirit of papers (Smith 2011;Smith and Nagem 2013;Ragazzo 2017;Ragazzo and Viglioni 2017;Wang 2021) by S. G. Llewellyn Smith, R. J. Nagem, C. Grotta Ragazzo, H. Viglioni, and Q. Wang. The paper (Bogatskiy 2019) by A. Bogatskiy contains ideas concerning the higher genus case which are somewhat similar to those in the present paper; see in particular Section A.3 in Bogatskiy (2019).…”

Section: Introductionmentioning

confidence: 57%

Vortex Pairs and Dipoles on Closed Surfaces

Gustafsson

2022

J Nonlinear Sci

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We set up general equations of motion for point vortex systems on closed Riemannian surfaces, allowing for the case that the sum of vorticities is not zero and there hence must be counter-vorticity present. The dynamics of global circulations which is coupled to the dynamics of the vortices is carefully taken into account. Much emphasis is put to the study of vortex pairs, having the Kimura conjecture in focus. This says that vortex pairs move, in the dipole limit, along geodesic curves, and proofs for it have previously been given by S. Boatto and J. Koiller by using Gaussian geodesic coordinates. In the present paper, we reach the same conclusion by following a slightly different route, leading directly to the geodesic equation with a reparametrized time variable. In a final section, we explain how vortex motion in planar domains can be seen as a special case of vortex motion on closed surfaces.

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Section: Introductionmentioning

confidence: 57%

Vortex Pairs and Dipoles on Closed Surfaces

Gustafsson

2022

J Nonlinear Sci

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“…In general the present paper is, in addition to the papers by S. Boatto and J. Koiller already mentioned, much in spirit of papers [37,38,18,19,49] by S. G. Llewellyn Smith, R. J. Nagem, C. Grotta Ragazzo, H. Viglioni, and Q. Wang. The paper [4] by A. Bogatskiy contains ideas concerning the higher genus case which are somewhat similar to those in the present paper, see in particular Section A.3 in [4].…”

Section: Introductionmentioning

confidence: 60%

Vortex pairs and dipoles on closed surfaces

Gustafsson

2022

Preprint

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We set up general equations of motion for point vortex systems on closed Riemannian surfaces, allowing for the case that the sum of vorticities is not zero and there hence must be counter-vorticity present. The dynamics of global circulations which is coupled to the dynamics of the vortices is carefully taken into account.Much emphasis is put to the study of vortex pairs, having the Kimura conjecture in focus. This says that vortex pairs move, in the dipole limit, along geodesic curves, and proofs for it have previously been given by S. Boatto and J. Koiller by using Gaussian geodesic coordinates. In the present paper we reach the same conclusion by following a slightly different route, leading directly to the geodesic equation with a reparametrized time variable.In a final section we explain how vortex motion in planar domains can be seen as a special case of vortex motion on closed surfaces, and in two appendices we give some necessary background on affine and projective connections.

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Platonic Solids and Symmetric Solutions of the N-vortex Problem on the Sphere

García-Azpeitia

García-Naranjo

2022

J Nonlinear Sci

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The N-Vortex Problem on a Riemann Sphere

Cited by 5 publications

References 47 publications

Vortex Pairs and Dipoles on Closed Surfaces

Vortex Pairs and Dipoles on Closed Surfaces

Vortex pairs and dipoles on closed surfaces

Platonic Solids and Symmetric Solutions of the N-vortex Problem on the Sphere

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