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    Crowdy, Darren G. Llewellyn Smith, Stefan G. and Freilich, Daniel V. 2013. Translating hollow vortex pairs. European Journal of Mechanics - B/Fluids, Vol. 37, p. 180.

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    Stremler, Mark A. 2003. Relative equilibria of singly periodic point vortex arrays. Physics of Fluids, Vol. 15, Issue. 12, p. 3767.

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    Meiron, D. I. Saffman, P. G. and Saffman, J. C. 1984. The linear two-dimensional stability of inviscid vortex streets of finite-cored vortices. Journal of Fluid Mechanics, Vol. 147, Issue. -1, p. 187.

    Saffman, P. G. and Szeto, R. 1981. Structure of a Linear Array of Uniform Vortices. Studies in Applied Mathematics, Vol. 65, Issue. 3, p. 223.

    Saffman, P.G. 1981. Transition and Turbulence.

    Baker, Gregory R. 1980. Energetics of a linear array of hollow vortices of finite cross-section. Journal of Fluid Mechanics, Vol. 99, Issue. 01, p. 97.


Structure of a linear array of hollow vortices of finite cross-section

  • G. R. Baker (a1), P. G. Saffman (a1) and J. S. Sheffield (a1)
  • DOI:
  • Published online: 01 March 2006

Free-streamline theory is employed to construct an exact steady solution for a linear array of hollow, or stagnant cored, vortices in an inviscid incompressible fluid. If each vortex has area A and the separation is L, there are two possible shapes if A½/L is less than a critical value 0.38 and none if it is larger. The stability of the shapes to two-dimensional, periodic and symmetric disturbances is considered for hollow vortices. The more deformed of the two possible shapes is found to be unstable while the less deformed shape is stable.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
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