A Langevin Equation for the Turbulent Vorticity

  • Michael Wilczek
  • Rudolf Friedrich
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 131)


The vorticity field of fully developed turbulence displays a complex spatial structure consisting of a large number of entangled filamentary vortices (see illustration). As a consequence, the PDF of the vorticity shows a highly non-Gaussian shape with pronounced tails. In the present work a kinetic theory for the turbulent vorticity is presented. Under certain conditions the arising equation may be interpreted as a Fokker- Planck equation giving rise to a Langevin model. The appearing unknown conditional averages are estimated from direct numerical simulations. The Langevin model is shown to reproduce the single point vorticity PDF.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Michael Wilczek
    • 1
  • Rudolf Friedrich
    • 1
  1. 1.Institute for Theoretical PhysicsMünsterGermany

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