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 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.

What happens to the vortex structures when the rising bubble transits from zigzag to spiral?

2017 ◽  
Vol 828 ◽  
pp. 353-373 ◽  
Author(s):  
Jie Zhang ◽  
Ming-Jiu Ni
Keyword(s):  
Angular Velocity ◽  
Magnetic Fields ◽  
Physical Mechanism ◽  
Critical Value ◽  
Theoretical Explanation ◽  
Vortex Structures ◽  
Direct Numerical Simulations ◽  
Vortex Pairs ◽  
Spiral Path ◽  
Rising Bubble

It has been demonstrated by many experiments carried out over the last 60 years that in certain liquids a single millimetre-sized bubble will rise within an unstable path, which is sometimes observed to transit from zigzag to spiral. After performing several groups of direct numerical simulations, the present work gives a theoretical explanation to reveal the physical mechanism causing the transition, and the results are presented in two parts. In the first part, in which a freely rising bubble is simulated, equal-strength vortex pairs are observed to shed twice during a period of the pure zigzag path, and this type of motion is triggered by the amounts of streamwise vorticities accumulated on the bubble interface, when a critical value is reached. However, when the balance between the counter-rotating vortices is broken, an angular velocity is induced between the asymmetric vortex pairs, driving the bubble to rise in an opposite spiral path. Therefore, although there is no preference of the spiral direction as observed in experiments, it is actually determined by the sign of the stronger vortex thread. In the second part, external vertical magnetic fields are imposed onto the spirally rising bubble in order to further confirm the relations between the vortex structures and the unstable path patterns. As shown in our previous studies (Zhang & Ni, Phys. Fluids, vol. 26 (10), 2014, 102102), the strength of the double-threaded vortex pairs, as well as the imbalance between them, will be weakened under magnetic fields. Therefore, as the vortex pairs become more symmetric, the rotating radius of the spirally rising bubble is observed to decrease. We try to answer the question, put forward by Shew et al. (2005, Preprint, ENS, Lyon), ‘what caused the bubble to transit from zigzag to spiral naturally?’

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