On the motion of two point vortex pairs with glide-reflective symmetry in a periodic strip

2015 ◽  
Vol 27 (10) ◽  
pp. 103603 ◽  
Author(s):  
Saikat Basu ◽  
Mark A. Stremler
Keyword(s):  
Point Vortex ◽  
Vortex Pairs ◽  
Periodic Strip ◽  
Reflective Symmetry

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

scholarly journals On the motion of three point vortices in a periodic strip

1996 ◽  
Vol 314 ◽  
pp. 1-25 ◽  
Author(s):  
Hassan Aref ◽  
Mark A. Stremler
Keyword(s):  
Fixed Point ◽  
Original Problem ◽  
General Procedure ◽  
Point Vortex ◽  
Solution Space ◽  
Point Vortices ◽  
Complicated Structure ◽  
Integrable Problem ◽  
Periodic Strip ◽  
Shed Light

Motivated by observations of Williamson & Roshko of the wake of an oscillating cylinder with three vortices per cycle, and by the analyses of Rott and Aref of the motion of three vortices with vanishing net circulation on the unbounded plane, the integrable problem of three interacting, periodic vortex rows is solved. The problem is ‘mapped’ onto a problem of advection of a passive particle by a certain set of fixed point vortices. The results of this mapped problem are then re-interpreted in terms of the motion of the vortices in the original problem. A rather complicated structure of the solution space emerges with a surprisingly large number of regimes of motion, some of them somewhat counter-intuitive. Representative cases are analysed in detail, and a general procedure is indicated for all cases. We also trace the bifurcations of the solutions with changing linear momentum of the system. For rational ratios of the vortex circulations all motions are periodic. For irrational ratios this is no longer true. The point vortex results are compared to the aforementioned wake experiments and appear to shed light on the experimental observations. Many additional possibilities for the wake dynamics are suggested by the analysis.

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.

Exploring the dynamics of ‘2P’ wakes with reflective symmetry using point vortices

2017 ◽  
Vol 831 ◽  
pp. 72-100 ◽  
Author(s):  
Saikat Basu ◽  
Mark A. Stremler
Keyword(s):  
Periodic Point ◽  
Integrable Hamiltonian System ◽  
Point Vortex ◽  
The Body ◽  
Level Curves ◽  
Spatial Periodicity ◽  
Equilibrium Configurations ◽  
Spatially Periodic ◽  
Reflective Symmetry

Wakes formed behind bluff bodies frequently reveal complex patterns of coherent vortical structures, with emergence of streamwise spatial periodicity particularly in the mid-wake region. In some cases, the vortex positions also maintain symmetry about the wake centreline. For the case in which two pairs of vortices are generated per shedding cycle, thereby constituting the so-called ‘2P’ mode wake, assumptions of spatial periodicity and symmetry allow for development of a mathematically tractable model using the point-vortex approximation. Our previous work (Basu & Stremler, Phys. Fluids, vol. 27 (10), 2015, 103603) considered staggered 2P wake configurations with two glide-reflective pairs of vortices shed in each period. Here we investigate the dynamics of a spatially periodic point-vortex street consisting of two pairs of vortices arranged with reflective symmetry about the streamwise centreline. Because of the symmetry, it is possible to model the spatially periodic point-vortex dynamics as an integrable Hamiltonian system. For a particular choice of initial condition, the topological structure of the Hamiltonian level curves is determined by location in a circulation–impulse parameter space. These Hamiltonian level curves delineate multiple regimes of motion, with all vortex motions within one regime being qualitatively identical. This approach thus enables identification and a full classification of all possible vortex motions in this constrained system. There also exist a limited number of equilibrium configurations with no relative vortex motion; some of these relative equilibria are neutrally stable to (appropriate) perturbations. Only one such neutrally stable equilibrium configuration continues to preserve the distinct four-vortex array, and numerical experiments indicate that these configurations are also neutrally stable to small perturbations that break the spatial symmetry. We apply this analysis to identify the parameter values necessary for co-existence of two closely spaced, neutrally stable Kármán vortex streets that preserve the assumed symmetry. Finally, comparison of the model dynamics to a wake pattern reported in the literature suggests that the classification of exotic wakes should be based on more details than just the number of vortices periodically shed by the body.

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