scholarly journals Close pairs of relative equilibria for identical point vortices

2011 ◽  
Vol 23 (5) ◽  
pp. 051706 ◽  
Author(s):  
Tobias Dirksen ◽  
Hassan Aref
Keyword(s):  
Relative Equilibria ◽  
Point Vortices ◽  
Identical Point ◽  
Close Pairs

Bilinear Relative Equilibria of Identical Point Vortices

2012 ◽  
Vol 22 (5) ◽  
pp. 849-885 ◽  
Author(s):  
H. Aref ◽  
P. Beelen ◽  
M. Brøns
Keyword(s):  
Relative Equilibria ◽  
Point Vortices ◽  
Identical Point

scholarly journals Point vortices on the sphere: Stability of symmetric relative equilibria

2011 ◽  
Vol 3 (4) ◽  
pp. 439-486 ◽  
Author(s):  
Frederic Laurent-Polz ◽  
◽  
James Montaldi ◽  
Mark Roberts ◽  
◽  
...  
Keyword(s):  
Relative Equilibria ◽  
Point Vortices

scholarly journals Evolution of localized vortices in the presence of stochastic perturbations

2006 ◽  
Vol 13 (1) ◽  
pp. 41-51 ◽  
Author(s):  
E. Bécu ◽  
V. Pavlov
Keyword(s):  
Initial Distribution ◽  
Point Vortices ◽  
Symmetric Distribution ◽  
Axially Symmetric ◽  
Stochastic Perturbations ◽  
Integral Invariants ◽  
Identical Point ◽  
Runge Kutta

Abstract. We consider the evolution of a distribution of N identical point vortices when stochastic perturbations in the Hamiltonian are present. It is shown that different initial configurations of vorticity with identical integral invariants may exist. Using the Runge-Kutta scheme of order 4, it is also demonstrated that different initial configurations with the same invariants may evolve without having any tendency to approach to a unique final, axially symmetric, distribution. In the presence of stochastic perturbations, if the initial distribution of vortices is not axially symmetric, vortices can be trapped in certain domains whose location is correlated with the configuration of the initial vortex distribution.

Relative equilibria of point vortices on the hyperbolic sphere

2013 ◽  
Vol 54 (6) ◽  
pp. 063101 ◽  
Author(s):  
Seungsu Hwang ◽  
Sun-Chul Kim
Keyword(s):  
Relative Equilibria ◽  
Point Vortices

Point vortices on a sphere: Stability of relative equilibria

1998 ◽  
Vol 39 (11) ◽  
pp. 5894-5907 ◽  
Author(s):  
Sergey Pekarsky ◽  
Jerrold E. Marsden
Keyword(s):  
Relative Equilibria ◽  
Point Vortices

scholarly journals Recent Progress in the Relative Equilibria of Point Vortices — In Memoriam Hassan Aref

2013 ◽  
Vol 7 ◽  
pp. 3-12 ◽  
Author(s):  
Peter Beelen ◽  
Morten Brøns ◽  
Vikas S. Krishnamurthy ◽  
Mark A. Stremler
Keyword(s):  
Recent Progress ◽  
Relative Equilibria ◽  
Point Vortices ◽  
In Memoriam
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