Global time evolution of viscous vortex rings

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

This article gives an overview of growing knowledge of translation speed of an axisymmetric vortex ring, with focus on the influence of viscosity. Helmholtz-Lamb's method provides a shortcut to manipulate the translation speed at both small and large Reynolds number, for a vortex ring starting from an infinitely thin core. The resulting asymptotics significantly improve Saffman's formula (1970) and give closer lower and upper bounds on translation speed in an early stage. At large Reynolds numbers, Kelvin-Benjamin's kinematic variational principle achieves a further simplification. At small Reynolds numbers, the whole life of a vortex ring is available from the vorticity obeying the Stokes equations, which is closely fitted, over a long time, by Saffman's second formula.

Original languageEnglish
Pages (from-to)335-347
Number of pages13
JournalTheoretical and Computational Fluid Dynamics
Volume24
Issue number1-4
DOIs
Publication statusPublished - Mar 1 2010

Fingerprint

vortex rings
Reynolds number
Vortex flow
variational principles
Vorticity
simplification
vorticity
Kinematics
kinematics
Viscosity
viscosity

All Science Journal Classification (ASJC) codes

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

Cite this

Global time evolution of viscous vortex rings. / Fukumoto, Yasuhide.

In: Theoretical and Computational Fluid Dynamics, Vol. 24, No. 1-4, 01.03.2010, p. 335-347.

Research output: Contribution to journalArticle

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