Global time evolution of viscous vortex rings

IR (HANDLE) Open Access

Description

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 short-cut to manipulate the translation speed at both small and large Reynolds numbers, 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.

Journal

  • MI Preprint Series

    MI Preprint Series 2009-1 2009-01-16

    Faculty of Mathematics, Kyushu University

Keywords

Details 詳細情報について

  • CRID
    1050861482659342464
  • HANDLE
    2324/13203
  • Text Lang
    en
  • Article Type
    journal article
  • Data Source
    • IRDB

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