Dynamics of vortex line in presence of stationary vortex

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 languageEnglish (US)
Pages (from-to)377-382
Number of pages6
JournalTheoretical and Computational Fluid Dynamics
Volume24
Issue number1-4
DOIs
StatePublished - Mar 2010

Fingerprint

Schrodinger equation
Vortex flow
vortices
Merging
helices
nonlinear equations
counters
Vorticity
pulse detonation engines
defocusing
vorticity
velocity distribution
Experiments
analogs

Keywords

  • Helix
  • Instability
  • Soliton
  • Vortex

ASJC Scopus subject areas

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

Cite this

Dynamics of vortex line in presence of stationary vortex. / Zakharov, Vladimir E.

In: Theoretical and Computational Fluid Dynamics, Vol. 24, No. 1-4, 03.2010, p. 377-382.

Research output: Contribution to journalArticle

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