Rotation, collapse, and scattering of point vortices

Demina, Maria V.; Kudryashov, Nikolay A.

doi:10.1007/s00162-014-0319-4

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Cited by 9 publications

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“…The phenomenon of self-similar collapse or expansion (when the initial geometrical form is preserved and only the size of the configuration decreases or increases) was discovered by Gröbli (1877) for three vortices and then it was studied in detail (see e.g. Synge 1949; Novikov & Sedov 1979; Kimura 1990; Borisov & Lebedev 1998; Newton 2001), including cases with a large number of vortices (Demina & Kudryashov 2014; Kudela 2014). It is known (Synge 1949) that intervortical distances are bounded if the strengths of all the vortices have the same sign.…”

Section: Introductionmentioning

confidence: 99%

Group scattering of point vortices on an unbounded plane

Makarov

2021

J. Fluid Mech.

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Section: Introductionmentioning

confidence: 99%

Group scattering of point vortices on an unbounded plane

Makarov

2021

J. Fluid Mech.

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Zero-noise dynamics after collapse for three point vortices

Grotto,

Romito,

Viviani

2024

Physica D: Nonlinear Phenomena

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Point vortices in the plane: positive-dimensional configurations

Demina

Kudryashov

Semenova

2017

J. Phys.: Conf. Ser.

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Abstract. The problem of constructing and classifying stationary equilibria of point vortices in the plane is studied. An ordinary differential equation that enables one to find positions of point vortices with circulations Γ1, Γ2, and Γ3 in stationary equilibrium is obtained. A necessary condition of an equilibrium existing is derived. The case of point vortex systems consisting of n + 2 point vortices with n vortices of circulation Γ 1 and two vortices of circulations Γ2 = aΓ1 and Γ3 = bΓ1, where a and b are integers, is considered in detail. The properties of polynomial solutions of the corresponding ordinary differential equation are investigated. A set of positivedimensional equilibrium configurations is found. A continuous free parameter is presented in the coefficients of corresponding polynomial solutions. These free parameters affect the positions of the roots and hence the vortex positions. Stationary equilibrium that could be derived from each other by rotation, extension, parallel translation is considered as equivalent. All found configurations seem to be new.

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Rotation, collapse, and scattering of point vortices

Cited by 9 publications

References 22 publications

Group scattering of point vortices on an unbounded plane

Group scattering of point vortices on an unbounded plane

Zero-noise dynamics after collapse for three point vortices

Point vortices in the plane: positive-dimensional configurations

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