Integrable Dynamics of Knotted Vortex Filaments

2012 ◽  
Author(s):  
Annalisa Calini
Keyword(s):  
Vortex Filaments ◽  
Integrable Dynamics

scholarly journals Cascades and reconnection in interacting vortex filaments

2021 ◽  
Vol 6 (7) ◽  
Author(s):  
Rodolfo Ostilla-Mónico ◽  
Ryan McKeown ◽  
Michael P. Brenner ◽  
Shmuel M. Rubinstein ◽  
Alain Pumir
Keyword(s):  
Vortex Filaments

scholarly journals Yang–Baxter maps and integrable dynamics

2003 ◽  
Vol 314 (3) ◽  
pp. 214-221 ◽  
Author(s):  
A.P. Veselov
Keyword(s):  
Integrable Dynamics

Numerical studies of motion and decay of vortex filaments

AIAA Journal ◽  
1986 ◽  
Vol 24 (8) ◽  
pp. 1290-1297 ◽  
Author(s):  
C. H. Liu ◽  
John Tavantzis ◽  
Lu Ting
Keyword(s):  
Vortex Filaments ◽  
Numerical Studies

Dynamics of Corotating Vortex Filaments Part 1: Analytical Model

2006 ◽  
Vol 43 (5) ◽  
pp. 1434-1439 ◽  
Author(s):  
Teresa S. Miller ◽  
Linda K. Kliment ◽  
Kamran Rokhsaz
Keyword(s):  
Analytical Model ◽  
Vortex Filaments

On the curvature and torsion of an isolated vortex filament

1965 ◽  
Vol 22 (3) ◽  
pp. 471-479 ◽  
Author(s):  
Robert Betchov
Keyword(s):  
Vortex Filament ◽  
Inviscid Fluid ◽  
Arc Length ◽  
Local Curvature ◽  
Vortex Filaments ◽  
Non Linear ◽  
Curvature And Torsion

We consider a very thin vortex filament in an unbounded, incompressible and inviscid fluid. The filament is not necessarily plane. Each portion of the filament moves with a velocity that can be approximated in terms of the local curvature of the filament. This approximation leads to a pair of intrinsic equations giving the curvature and the torsion of the filament, as functions of the time and the arc length along the filament. It is found that helicoidal vortex filaments are elementary solutions, and that they are unstable.The intrisic equations also suggest a linear mechanism that tends to produce concentrated torsion and a non-linear mechanism tending to disperse such singularities.

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