A Langevin Equation for the Turbulent Vorticity
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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