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- Title
Dynamics of vortex line in presence of stationary vortex.
- Authors
Zakharov, Vladimir E.
- Abstract
The motion of a thin vortex with infinitesimally small vorticity in the velocity field created by a steady straight vortex is studied. The motion is governed by non-integrable PDE generalizing the Nonlinear Schrodinger equation (NLSE). Situation is essentially different in a co-rotating case, which is analog of the defocusing NLSE and a counter-rotating case, which can be compared with the focusing NLSE. The governing equation has special solutions shaped as rotating helixes. In the counter-rotating case all helixes are unstable, while in the co-rotating case they could be both stable and unstable. Growth of instability of counter-rotating helix ends up with formation of singularity and merging of vortices. The process of merging goes in a self-similar regime. The basic equation has a rich family of solitonic solutions. Analytic calculations are supported by numerical experiment.
- Subjects
VORTEX motion; SCHRODINGER equation; PARTIAL differential equations; SOLITONS; NONLINEAR theories
- Publication
Theoretical & Computational Fluid Dynamics, 2010, Vol 24, Issue 1-4, p377
- ISSN
0935-4964
- Publication type
Article
- DOI
10.1007/s00162-009-0164-z