Dynamics of vortex line in presence of stationary vortex

Vladimir E. Zakharov

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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 languageEnglish (US)
Pages (from-to)377-382
Number of pages6
JournalTheoretical and Computational Fluid Dynamics
Issue number1-4
StatePublished - Mar 2010


  • Helix
  • Instability
  • Soliton
  • Vortex

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Engineering(all)
  • Fluid Flow and Transfer Processes


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