A Langevin equation for the turbulent vorticity

Wilczek, Michael; Friedrich, Rudolf

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A Langevin equation for the turbulent vorticity

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Wilczek, Michael
Max Planck Research Group Theory of Turbulent Flows, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Wilczek, M., & Friedrich, R. (2010). A Langevin equation for the turbulent vorticity. In J. Peinke, M. Oberlack, & A. Talamelli (Eds.), Progress in Turbulence III. Berlin: Springer-Verlag.

Cite as: https://hdl.handle.net/21.11116/0000-0003-E0AA-0

Abstract

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.