Chaotic scattering of two identical point vortex pairs

1993 ◽  
Vol 5 (10) ◽  
pp. 2479-2483 ◽  
Author(s):  
Tim Price
Keyword(s):  
Point Vortex ◽  
Chaotic Scattering ◽  
Vortex Pairs ◽  
Identical Point

scholarly journals Chaotic scattering of two identical point vortex pairs revisited

2008 ◽  
Vol 20 (9) ◽  
pp. 093605 ◽  
Author(s):  
Laust Tophøj ◽  
Hassan Aref
Keyword(s):  
Point Vortex ◽  
Chaotic Scattering ◽  
Vortex Pairs ◽  
Identical Point

Visualizing Coherent and Fractal Structures in Numerical Experiments on Chaotic Advection in Fluids

2005 ◽  
Author(s):  
M. V. Budyansky ◽  
S. V. Prants
Keyword(s):  
Numerical Experiments ◽  
Fractal Structure ◽  
Point Vortex ◽  
Chaotic Advection ◽  
Mixing Zone ◽  
Background Current ◽  
Fractal Structures ◽  
Chaotic Scattering ◽  
And Topology ◽  
Fractal Properties

We investigate typical mixing and fractal properties of chaotic scattering of passive particles in open hydrodynamic flows taking as an example a model two-dimensional incompressible flow composed of a fixed point vortex and a background current with a periodic component, the model inspired by the phenomenon of topographic eddies over mountains in the ocean and atmosphere. We have found, described and visualized a non-attracting invariant chaotic set defining chaotic scattering, fractality, and trapping of incoming particles. Geometry and topology of chaotic scattering have been studied and visualized. Scattering functions in the mixing zone have been found to have a fractal structure with a complicated hierarchy that has been described in terms of strophes and epistrophes. Mixing, trapping, and fractal properties of passive particles have been studied under the influence of a white noise with different amplitudes and frequency ranges. A new effect of clustering the particles in a noised flow has been demonstrated in numerical experiments.

scholarly journals Some estimates on the space scales of vortex pairs emitted from river mouths

2001 ◽  
Vol 8 (1/2) ◽  
pp. 1-7 ◽  
Author(s):  
V. P. Goncharov ◽  
V. I. Pavlov
Keyword(s):  
Point Vortex ◽  
Vortex Pair ◽  
Vortex Structures ◽  
Shelf Zone ◽  
Vortex Pairs ◽  
Polygonal Boundary ◽  
Dipole Vortex ◽  
Qualitative Classification ◽  
River Mouths

Abstract. Two-dimensional vortex pairs are frequently observed in geophysical conditions, for example, in a shelf zone of the ocean near river mouths. The main aims of the work are to estimate the space scales of such vortex structures, to analyze possible scenarios of vortex pair motion and to give the qualitative classification of their trajectories. We discuss some features of the motion of strong localized vorticity concentrations in a given flow in the presence of boundaries. The analyses are made in the framework of a 2D point vortex mo-del with an open polygonal boundary. Estimations are made for the characteristic parameters of dipole vortex structures emitted from river mouths into the open ocean.

scholarly journals Note on dust trapping in point vortex pairs with unequal strengths

2010 ◽  
Vol 22 (11) ◽  
pp. 113301 ◽  
Author(s):  
Tatiana Nizkaya ◽  
Jean-Régis Angilella ◽  
Michel Buès
Keyword(s):  
Point Vortex ◽  
Dust Trapping ◽  
Vortex Pairs

On the Validity of the β-Plane Approximation in the Dynamics and the Chaotic Advection of a Point Vortex Pair Model on a Rotating Sphere

2015 ◽  
Vol 72 (1) ◽  
pp. 415-429 ◽  
Author(s):  
Gábor Drótos ◽  
Tamás Tél
Keyword(s):  
Equations Of Motion ◽  
Qualitative Difference ◽  
Point Vortex ◽  
Vortex Pair ◽  
Chaotic Advection ◽  
Strong Indication ◽  
Rotating Sphere ◽  
Vortex Pairs ◽  
Pair Model ◽  
The One

Abstract The dynamics of modulated point vortex pairs is investigated on a rotating sphere, where modulation is chosen to reflect the conservation of angular momentum (potential vorticity). In this setting the authors point out a qualitative difference between the full spherical dynamics and the one obtained in a β-plane approximation. In particular, dipole trajectories starting at the same location evolve to completely different directions under these two treatments, despite the fact that the deviations from the initial latitude remain small. This is a strong indication for the mathematical inconsistency of the traditional β-plane approximation. At the same time, a consistently linearized set of equations of motion leads to trajectories agreeing with those obtained under the full spherical treatment. The β-plane advection patterns due to chaotic advection in the velocity field of finite-sized vortex pairs are also found to considerably deviate from those of the full spherical treatment, and quantities characterizing transport properties (e.g., the escape rate from a given region) strongly differ.

Two-layer quasi-geostrophic singular vortices embedded in a regular flow. Part 1. Invariants of motion and stability of vortex pairs

2007 ◽  
Vol 584 ◽  
pp. 185-202 ◽  
Author(s):  
GREGORY REZNIK ◽  
ZIV KIZNER
Keyword(s):  
Free Surface ◽  
Point Vortex ◽  
Delta Function ◽  
Passive Layer ◽  
Layer Model ◽  
Flow Energy ◽  
Vortex Pairs ◽  
Two Layer Model ◽  
Regular Flow ◽  
Singular Vortex

The concept of a quasi-geostrophic singular vortex is extended to several types of two-layer model: a rigid-lid two-layer, a free-surface two-layer and a $2{\textstyle{1 \over 2}}$-layer model with two active and one passive layer. Generally, a singular vortex differs from a conventional point vortex in that the intrinsic vorticity of a singular vortex, in addition to delta-function, contains an exponentially decaying term. The theory developed herein occupies an intermediate position between discrete and fully continuous multilayer models, since the regular flow and its interaction with the singular vortices are also taken into account. A system of equations describing the joint evolution of the vortices and the regular field is presented, and integrals expressing the conservation of enstrophy, energy, momentum and mass are derived. Using these integrals, the initial phases of evolution of an individual singular vortex confined to one layer and of a coaxial pair of vortices positioned in different layers of a two-layer fluid on a beta-plane are described. A valuable application of the conservation integrals is related to the stability analysis of point-vortex pairs within the $1{\textstyle{1 \over 2}}$-layer model, $2{\textstyle{1 \over 2}}$-layer model, and free-surface two-layer model on the f-plane. Such vortex pairs are shown to be nonlinearly stable with respect to any small perturbation provided its regular-flow energy and enstrophy are finite.

scholarly journals Stationary states of identical point vortices and vortex foam on the sphere

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120622 ◽  
Author(s):  
Kevin A. O'Neil
Keyword(s):  
Initial Conditions ◽  
Point Vortex ◽  
Intermediate Energy ◽  
Point Vortices ◽  
Stationary States ◽  
Vortex Sheets ◽  
Identical Point ◽  
Equilibrium Configurations ◽  
Stationary Vortex ◽  
Point Vortex Equilibria

Stationary configurations of identical point vortices on the sphere are investigated using a simple numerical scheme. Configurations in which the vortices are arrayed along curves on the sphere are exhibited, which approximate equilibrium configurations of vortex sheets on the sphere. Other configurations (found after starting from random initial conditions) exhibit net-like distributions of vorticity, dividing the sphere into many cells that contain no vorticity or diffuse vorticity and forming a stationary ‘vortex foam’ on the sphere. They may be viewed as intermediate-energy elements in the set of all identical point vortex equilibria on the sphere. In the continuum limit, these foam states may correspond to stationary states of multiple intersecting vortex sheets. Stationary configurations of point vortices are not found to have this character when vortices of opposite circulations are included.

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