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

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

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

Periodic motions of vortices on surfaces with symmetry

2002 ◽  
Vol 460 ◽  
pp. 83-92 ◽  
Author(s):  
ANIK SOULIÈRE ◽  
TADASHI TOKIEDA
Keyword(s):  
Ideal Fluid ◽  
Relative Equilibria ◽  
Point Vortices ◽  
Two Dimensional ◽  
Periodic Motions

The theory of point vortices in a two-dimensional ideal fluid has a long history, but on surfaces other than the plane no method of finding periodic motions (except relative equilibria) of N vortices is known. We present one such method and find infinite families of periodic motions on surfaces possessing certain symmetries, including spheres, ellipsoids of revolution and cylinders. Our families exhibit bifurcations. N can be made arbitrarily large. Numerical plots of bifurcations are given.

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
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