A Langevin Equation for the Turbulent Vorticity

  • Michael Wilczek
  • Rudolf Friedrich
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.


Direct Numerical Simulation Langevin Equation Multiplicative Noise High Order Statistic Conditional Average 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lundgren, T.S.: Distribution functions in the statistical theory of turbulence. Physics of Fluids 10(5), 969–975 (1967)CrossRefGoogle Scholar
  2. 2.
    Novikov, E.A.: A new approach to the problem of turbulence, based on the conditionally averaged Navier-Stokes equations. Fluid Dynamics Research 12(2), 969–975 (1993)CrossRefGoogle Scholar
  3. 3.
    Pope, S.B.: Turbulent Flows. Cambridge University Press, Cambridge (2000)CrossRefzbMATHGoogle Scholar
  4. 4.
    Canuto, C., Hussaini, M.Y., Quarteroni, A., Zang, T.A.: Spectral Methods in Fluid Dynamics. Springer, Berlin (1987)Google Scholar
  5. 5.
    Wilczek, M., Friedrich, R.: Dynamical Origins for Non-Gaussian Vorticity Distributions in Turbulent Flows. Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

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

Personalised recommendations