Parametric resonance with a point-vortex pair in a nonstationary deformation flow

2012 ◽  
Vol 376 (5) ◽  
pp. 744-747 ◽  
Author(s):  
K.V. Koshel ◽  
E.A. Ryzhov
Keyword(s):  
Parametric Resonance ◽  
Point Vortex ◽  
Vortex Pair ◽  
Nonstationary Deformation

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

2018 ◽  
Vol 30 (9) ◽  
pp. 096603 ◽  
Author(s):  
Konstantin V. Koshel ◽  
Jean N. Reinaud ◽  
Giorgio Riccardi ◽  
Eugene A. Ryzhov
Keyword(s):  
Fixed Point ◽  
Point Vortex ◽  
Vortex Pair ◽  
Point Vortices

scholarly journals Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation

2018 ◽  
Vol 30 (9) ◽  
pp. 096604 ◽  
Author(s):  
Jean N. Reinaud ◽  
Konstantin V. Koshel ◽  
Eugene A. Ryzhov
Keyword(s):  
Fixed Point ◽  
Point Vortex ◽  
Finite Size ◽  
Vortex Pair

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.

Steady point vortex pair in a field of Stuart-type vorticity

2019 ◽  
Vol 874 ◽  
Author(s):  
Vikas S. Krishnamurthy ◽  
Miles H. Wheeler ◽  
Darren G. Crowdy ◽  
Adrian Constantin
Keyword(s):  
Point Vortex ◽  
Vortex Pair ◽  
Point Vortices ◽  
Incompressible Euler Equation ◽  
New Class ◽  
New Family ◽  
Point Vortex Equilibria ◽  
Similar Class ◽  
Incompressible Euler ◽  
Additional Point

A new family of exact solutions to the two-dimensional steady incompressible Euler equation is presented. The solutions provide a class of hybrid equilibria comprising two point vortices of unit circulation – a point vortex pair – embedded in a smooth sea of non-zero vorticity of ‘Stuart-type’ so that the vorticity $\unicode[STIX]{x1D714}$ and the stream function $\unicode[STIX]{x1D713}$ are related by $\unicode[STIX]{x1D714}=a\text{e}^{b\unicode[STIX]{x1D713}}-\unicode[STIX]{x1D6FF}(\boldsymbol{x}-\boldsymbol{x}_{0})-\unicode[STIX]{x1D6FF}(\boldsymbol{x}+\boldsymbol{x}_{0})$, where $a$ and $b$ are constants. We also examine limits of these new Stuart-embedded point vortex equilibria where the Stuart-type vorticity becomes localized into additional point vortices. One such limit results in a two-real-parameter family of smoothly deformable point vortex equilibria in an otherwise irrotational flow. The new class of hybrid equilibria can be viewed as continuously interpolating between the limiting pure point vortex equilibria. At the same time the new solutions continuously extrapolate a similar class of hybrid equilibria identified by Crowdy (Phys. Fluids, vol. 15, 2003, pp. 3710–3717).

Theoretical predictions for the elliptical instability in a two-vortex flow

2002 ◽  
Vol 471 ◽  
pp. 169-201 ◽  
Author(s):  
STÉPHANE LE DIZÈS ◽  
FLORENT LAPORTE
Keyword(s):  
Growth Rate ◽  
Inclination Angle ◽  
Asymptotic Expression ◽  
Point Vortex ◽  
Normal Modes ◽  
Vortex Pair ◽  
Local Perturbation ◽  
Global Mode ◽  
Elliptical Instability ◽  
Elliptical Flow

Two parallel Gaussian vortices of circulations Γ1 and Γ2 radii a1 and a2, separated by a distance b may become unstable by the elliptical instability due the elliptic deformation of their cores. The goal of the paper is to analyse this occurrence theoretically in a general framework. An explicit formula for the temporal growth rate of the elliptical instability in each vortex is obtained as a function of the above global parameters of the system, the Reynolds number Γ1/v and the non-dimensionalized axial wavenumber kzb of the perturbation. This formula is based on a known asymptotic expression for the local instability growth rate at an elliptical stagnation point which depends on the local characteristics of the elliptical flow and the inclination angle of the local perturbation wavevector at this point. The elliptical flow characteristics are estimated by considering each Gaussian vortex alone in a weak uniform external strain field whose properties are provided by a point vortex modelling of the vortex pair. The inclination angle is obtained from the dispersion relation for the Gaussian vortex normal modes and the local expression near each vortex centre for the two helical modes of azimuthal wavenumber m = 1 and m = −1 which constitute the elliptical instability global mode. Both the final formula and the hypotheses made for its derivation are tested and validated by direct numerical simulations and large-eddy simulations.

Dynamics of a vortex pair interacting with a fixed point vortex

2013 ◽  
Vol 102 (4) ◽  
pp. 44004 ◽  
Author(s):  
E. A. Ryzhov ◽  
K. V. Koshel
Keyword(s):  
Fixed Point ◽  
Point Vortex ◽  
Vortex Pair

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.

Instability of secondary vortices generated by a vortex pair in ground effect

2012 ◽  
Vol 700 ◽  
pp. 148-186 ◽  
Author(s):  
D. M. Harris ◽  
C. H. K. Williamson
Keyword(s):  
Ground Plane ◽  
Point Vortex ◽  
Vortex Pair ◽  
Ground Effect ◽  
Secondary Vortex ◽  
Primary Vortex ◽  
Single Vortex ◽  
Displacement Mode ◽  
Instability Modes ◽  
Secondary Vortices

AbstractIn this work, we investigate the approach of a descending vortex pair to a horizontal ground plane. As in previous studies, the primary vortices exhibit a ‘rebound’, due to the separation of secondary opposite-sign vortices underneath each primary vortex. On each side of the flow, the weaker secondary vortex can become three-dimensionally unstable, as it advects around the stronger primary vortex. It has been suggested in several recent numerical simulations that elliptic instability is the origin of such waviness in the secondary vortices. In the present research, we employ a technique whereby the primary vortices are visualized separately from the secondary vortices; in fact, we are able to mark the secondary vortex separation, often leaving the primary vortices invisible. We find that the vortices are bent as a whole in a Crow-type ‘displacement’ mode, and, by keeping the primary vortices invisible, we are able to see both sides of the flow simultaneously, showing that the instability perturbations on the secondary vortices are antisymmetric. Triggered by previous research on four-vortex aircraft wake flows, we analyse one half of the flow as an unequal-strength counter-rotating pair, noting that it is essential to take into account the angular velocity of the weak vortex around the stronger primary vortex in the analysis. In contrast with previous results for the vortex–ground interaction, we find that the measured secondary vortex wavelength corresponds well with the displacement bending mode, similar to the Crow-type instability. We have analysed the elliptic instability modes, by employing the approximate dispersion relation of Le Dizés & Laporte (J. Fluid Mech., vol. 471, 2002, p. 169) in our problem, finding that the experimental wavelength is distinctly longer than predicted for the higher-order elliptic modes. Finally, we observe that the secondary vortices deform into a distinct waviness along their lengths, and this places two rows of highly stretched vertical segments of the vortices in between the horizontal primary vortices. The two rows of alternating-sign vortices translate towards each other and ultimately merge into a single vortex row. A simple point vortex row model is able to predict trajectories of such vortex rows, and the net result of the model’s ‘orbital’ or ‘passing’ modes is to bring like-sign vortices, from each secondary vortex row, close to each other, such that merging may ensue in the experiments.

Sign in / Sign up

Export Citation Format

Share Document