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.
Original language | English (US) |
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Pages (from-to) | 377-382 |
Number of pages | 6 |
Journal | Theoretical and Computational Fluid Dynamics |
Volume | 24 |
Issue number | 1-4 |
DOIs | |
State | Published - Mar 2010 |
Keywords
- Helix
- Instability
- Soliton
- Vortex
ASJC Scopus subject areas
- Computational Mechanics
- Condensed Matter Physics
- General Engineering
- Fluid Flow and Transfer Processes