Dresden 2014 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 41: Poster - Pattern/ Nonlinear Dyn./ Fluids/ Granular/ Critical Phen.

DY 41.20: Poster

Donnerstag, 3. April 2014, 17:00–19:00, P3

Vorticity distributions in two dimensional forced turbulence — •Markus Blank-Burian — Institut für Physikalische Chemie, WWU Münster, Deutschland

In statistical fluid dynamics, turbulent flows can be characterized by probability density functions (PDFs). Within the framework of the Lundgren-Monin-Novikov hierarchy, one can derive time evolution equations for the PDFs as summarized in [1]. The closure problem arises herein by coupling multi-point PDFs of different order. These equations can also be rewritten using conditional averages.

Until now, the PDFs have been approximated by gaussian distributions. Looking at numerical data, one finds that the shape of the vorticity PDF and also the conditional averages over the vorticity field depend strongly on the strength of the forcing. The shape of the one-point as well as the two-point PDF can be modeled by a convolution of two multivariate stable distributions.

As a result of this, one can describe the force dependence of the one-point conditonal average of the vorticity field as an interpolation between a strongly oscillating function and a smooth function. It turns out, that the former function is associated with a gaussian distribution and can be attributed to the forcing. It dominates at small vorticity strength around ω < 2σ. The other function is associated with a lorentz distribution and dominates clearly at large vortices ω > 5σ.

[1] Friedrich,Daitche,Kamps,Lülff,Voßkuhle,Wilczek: The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence, C. R. Acad. Sci