Simulation of vortex sheet roll-up: chaos, azimuthal waves, ring merger

  • Robert Krasny
  • Keith Lindsay
  • Monika Nitsche
Conference paper
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 71)


This article reviews some recent simulations of vortex sheet roll-up using the vortex blob method. In planar and axisymmetric flow, the roll-up is initially smooth but irregular small-scale features develop later in time due to the onset of chaos. A numerically generated Poincaré section shows that the vortex sheet flow resembles a chaotic Hamiltonian system with resonance bands and a heteroclinic tangle. The chaos is induced by a self-sustained oscillation in the vortex core rather than external forcing. In three-dimensional flow, an adaptive treecode algorithm is applied to reduce the CPU time from O(N 2) to O(N log N), where N is the number of particles representing the sheet. Results are presented showing the growth of azimuthal waves on a vortex ring and the merger of two vortex rings.


Vortex Ring Vortex Core Vortex Sheet Resonance Band Axisymmetric Flow 
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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Robert Krasny
    • 1
  • Keith Lindsay
    • 2
  • Monika Nitsche
    • 3
  1. 1.Department of MathematicsUniversity of MichiganAnn ArborUSA
  2. 2.Climate and Global Dynamics BoulderNational Center for Atmospheric ResearchUSA
  3. 3.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA

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