scholarly journals Stationary configurations for the system of three point vortices in circular domain and their stability

2010 ◽  
pp. 61-70
Author(s):  
A.V. Vaskina ◽  
Keyword(s):  
Circular Domain ◽  
Point Vortices

scholarly journals Stability of new relative equilibria of the system of three point vortices in a circular domain

2011 ◽  
pp. 119-138
Author(s):  
A. V. Borisov ◽  
◽  
I. S. Mamaev ◽  
A. V. Vaskina ◽  
◽  
...  
Keyword(s):  
Relative Equilibria ◽  
Circular Domain ◽  
Point Vortices

On the Stability of Stationary Rotation of a Point Vortices System in a Circular Domain

2015 ◽  
pp. 68-73
Author(s):  
Leonid Gennadievich Kurakin ◽  
◽  
Andrei Petrovich Melekhov ◽  
Irina Vladimirovna Ostrovskaya ◽  
◽  
...  
Keyword(s):  
Circular Domain ◽  
Point Vortices ◽  
Stationary Rotation ◽  
The Stability

scholarly journals Equation of motion for point vortices in multiply connected circular domains

2009 ◽  
Vol 465 (2108) ◽  
pp. 2589-2611 ◽  
Author(s):  
Takashi Sakajo
Keyword(s):  
Connected Domain ◽  
Single Point ◽  
Point Vortex ◽  
Equation Of Motion ◽  
Circular Domain ◽  
Point Vortices ◽  
Multiply Connected Domain ◽  
Multiply Connected ◽  
Circular Domains ◽  
Prime Function

The paper gives the equation of motion for N point vortices in a bounded planar multiply connected domain inside the unit circle that contains many circular obstacles, called the circular domain. The velocity field induced by the point vortices is described in terms of the Schottky–Klein prime function associated with the circular domain. The explicit representation of the equation enables us not only to solve the Euler equations through the point-vortex approximation numerically, but also to investigate the interactions between localized vortex structures in the circular domain. As an application of the equation, we consider the motion of two point vortices with unit strength and of opposite signs. When the multiply connected domain is symmetric with respect to the real axis, the motion of the two point vortices is reduced to that of a single point vortex in a multiply connected semicircle, which we investigate in detail.

Two Dimensional Bright and Dark Magnetoexcitons Interacting with Quantum Point Vortices

2019 ◽  
Vol 53 (16) ◽  
pp. 2055-2059
Author(s):  
S. A. Moskalenko ◽  
V. A. Moskalenko ◽  
I. V. Podlesny ◽  
I. A. Zubac
Keyword(s):  
Point Vortices ◽  
Two Dimensional ◽  
Quantum Point

scholarly journals Collapse of n Point Vortices, Formation of the Vortex Sheets and Transport of Passive Markers

Energies ◽  
2021 ◽  
Vol 14 (4) ◽  
pp. 943
Author(s):  
Henryk Kudela
Keyword(s):  
Differential Equations ◽  
Point Vortex ◽  
Optimization Procedure ◽  
Vortex Sheet ◽  
Point Vortices ◽  
Vortex Sheets ◽  
Impermeable Barrier ◽  
Initial Location ◽  
Passive Tracers ◽  
Initial Iterate

In this paper, the motion of the n-vortex system as it collapses to a point in finite time is studied. The motion of vortices is described by the set of ordinary differential equations that we are able to solve analytically. The explicit formula for the solution demands the initial location of collapsing vortices. To find the collapsing locations of vortices, the algebraic, nonlinear system of equations was built. The solution of that algebraic system was obtained using Newton’s procedure. A good initial iterate needs to be provided to succeed in the application of Newton’s procedure. An unconstrained Leverber–Marquart optimization procedure was used to find such a good initial iterate. The numerical studies were conducted, and numerical evidence was presented that if in a collapsing system n=50 point vortices include a few vortices with much greater intensities than the others in the set, the vortices with weaker intensities organize themselves onto the vortex sheet. The collapsing locations depend on the value of the Hamiltonian. By changing the Hamiltonian values in a specific interval, the collapsing curves can be obtained. All points on the collapse curves with the same Hamiltonian value represent one collapsing system of vortices. To show the properties of vortex sheets created by vortices, the passive tracers were used. Advection of tracers by the velocity induced by vortices was calculated by solving the proper differential equations. The vortex sheets are an impermeable barrier to inward and outward fluxes of tracers. Arising vortex structures are able to transport the passive tracers. In this paper, several examples showing the diversity of collapsing structures with the vortex sheet are presented. The collapsing phenomenon of many vortices, their ability to self organize and the transportation of the passive tracers are novelties in the context of point vortex dynamics.

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