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

scholarly journals Dust trapping in vortex pairs

2010 ◽  
Vol 239 (18) ◽  
pp. 1789-1797 ◽  
Author(s):  
Jean-Régis Angilella
Keyword(s):  
Dust Trapping ◽  
Vortex Pairs

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.

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.

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

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 Barotropic vortex pairs on a rotating sphere

1998 ◽  
Vol 358 ◽  
pp. 107-133 ◽  
Author(s):  
MARK T. DIBATTISTA ◽  
LORENZO M. POLVANI
Keyword(s):  
Single Point ◽  
Point Vortex ◽  
Spherical Geometry ◽  
Vortex Pair ◽  
Relative Strength ◽  
Equilibrium Solutions ◽  
Finite Area ◽  
Practical Applications ◽  
Vortex Pairs ◽  
Equilibrium Configurations

Using a barotropic model in spherical geometry, we construct new solutions for steadily travelling vortex pairs and study their stability properties. We consider pairs composed of both point and finite-area vortices, and we represent the rotating background with a set of zonal strips of uniform vorticity. After constructing the solution for a single point-vortex pair, we embed it in a rotating background, and determine the equilibrium configurations that travel at constant speed without changing shape. For equilibrium solutions, we find that the stability depends on the relative strength (which may be positive or negative) of the vortex pair to the rotating background: eastward-travelling pairs are always stable, while westward-travelling pairs are unstable when their speeds approach that of the linear Rossby–Haurwitz waves. This finding also applies (with minor differences) to the case when the vortices are of finite area; in that case we find that, in addition to the point-vortex-like instabilities, the rotating background excites some finite-area instabilities for vortex pairs that would otherwise be stable. As for practical applications to blocking events, for which the slow westward pairs are relevant, our results indicate that free barotropic solutions are highly unstable, and thus suggest that forcing mechanisms must play an important role in maintaining atmospheric blocking events.

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