# Motion of three vortices near collapse

@article{Leoncini2000MotionOT, title={Motion of three vortices near collapse}, author={Xavier Leoncini and Leonid V. Kuznetsov and George Zaslavsky}, journal={Physics of Fluids}, year={2000}, volume={12}, pages={1911-1927} }

A system of three point vortices in an unbounded plane has a special family of self-similarly contracting or expanding solutions: during the motion, the vortex triangle remains similar to the original one, while its area decreases (grows) at a constant rate. A contracting configuration brings three vortices to a single point in a finite time; this phenomenon known as vortex collapse is of principal importance for many-vortex systems. Dynamics of close-to-collapse vortex configurations depends…

## 30 Citations

### Group scattering of point vortices on an unbounded plane

- Physics, MathematicsJournal of Fluid Mechanics
- 2021

Abstract Group scattering of an initially compact two-dimensional configuration of N point vortices with strengths of different signs in an unbounded ideal fluid is investigated. This phenomenon…

### Self-Similar Collapse of n Point Vortices

- Physics, MathematicsJ. Nonlinear Sci.
- 2014

It is shown how the initial positions that lead to the collapse can be found numerically and an explicit solution for the self-similar collapse of the trajectories is derived.

### Point-vortex approach in two-dimensional turbulence

- Physics
- 2016

The properties of two-dimensional turbulence in a circular domain are investigated within the framework of the punctuated point-vortex model. Vortex dynamics is governed by Hamiltonian equations, and…

### Finite-time Collapse of Three Point Vortices in the Plane

- PhysicsRegular and Chaotic Dynamics
- 2018

We investigate the finite-time collapse of three point vortices in the plane utilizing the geometric formulation of three-vortexmotion from Krishnamurthy, Aref and Stremler (2018) Phys. Rev. Fluids…

### Collapse of n Point Vortices, Formation of the Vortex Sheets and Transport of Passive Markers

- PhysicsEnergies
- 2021

In this paper, the motion of the n-vortex system as it collapses to a point in finite time is studied. The motion of vortices is described by the set of ordinary differential equations that we are…

### Self-similar Motions and Related Relative Equilibria in the N-point Vortex System

- Physics, MathematicsJournal of Dynamics and Differential Equations
- 2020

We study self-similar solutions of the point-vortex system. The explicit formula for self-similar solutions has been obtained for the three point-vortex problem and for a specific example of the four…

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

- PhysicsPhysics of Fluids
- 2018

The problem of a pair of point vortices impinging on a fixed point vortex of arbitrary strengths [E. Ryzhov and K. Koshel, “Dynamics of a vortex pair interacting with a fixed point vortex,” Europhys.…

### Collapse of generalized Euler and surface quasigeostrophic point vortices.

- PhysicsPhysical review. E
- 2018

Point-vortex models are presented for the generalized Euler equations, which are characterized by a fractional Laplacian relation between the active scalar and the stream function, and it is shown that for SQG the collapse can be either self-similar or non-self-similar.

### Hamiltonian Chaos and Anomalous Transport in Two Dimensional Flows

- Physics
- 2010

In this chapter we discuss the dynamics of particles advected in regular and chaotic flows. We first address the dynamics of point vortices and show the great variety of the dynamics of three point…

### Nonlinear dynamics of an elliptic vortex embedded in an oscillatory shear flow.

- PhysicsChaos
- 2017

The nonlinear dynamics of an elliptic vortex subjected to a time-periodic linear external shear flow is studied numerically and the appearance of chaotic regimes in the ellipse dynamics is focused on.

## References

SHOWING 1-10 OF 36 REFERENCES

### Collapse interactions of finite-sized two-dimensional vortices

- Physics
- 1997

The point vortex model predicts that a certain configuration of three point vortices leads to a collapse of these vortices to one point. Numerical simulations have been performed to investigate the…

### Regular and chaotic advection in the flow field of a three-vortex system

- Physics
- 1998

The dynamics of a passive particle in a two-dimensional incompressible flow generated by three point vortices advected by their mutual interaction is considered as a periodically forced Hamiltonian…

### Motion of three vortices

- Physics
- 1979

A qualitative analysis of the motion of three point vortices with arbitrary strengths is given. This simplifies and extends recent work by Novikov on the motion of three identical vortices. Using a…

### The dynamics of three vortices revisited

- Physics
- 1988

The dynamics of three vortices was studied by Synge using the length of the sides of the triangle formed by three vortices as prime variables. The critical states at which the lengths of the sides…

### Advection of a vortex pair atmosphere in a velocity field of point vortices

- Physics, Environmental Science
- 1992

Two‐dimensional inviscid flows governed by a vortex pair in the presence of another point vortex or vortex pair on an unbounded plane are considered analytically and via numerical simulations. For…

### Chaotic advection in point vortex models and two-dimensional turbulence

- Physics, Environmental Science
- 1994

The dynamics of passively advected particles in either integrable or chaotic point vortex systems and in two‐dimensional (2‐D) turbulence is studied. For point vortices, it is shown that the regular…

### Passive particle transport in three-vortex flow

- Physics, Environmental SciencePhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

Analysis of long recurrences proves, that they are caused by tracer trappings inside boundary layers of islands of regular motion, which always exist inside the mixing region.

### Lagrangian dynamics in high-dimensional point-vortex systems

- Physics
- 1998

We study the Lagrangian dynamics of systems of N point vortices and passive particles in a two-dimensional, doubly periodic domain. The probability distribution function of vortex velocity, pN, has a…