Statistical Properties of Velocity Increments in Two-Dimensional Turbulence

Voßkuhle M, Kamps O, Wilczek M, & Friedrich R

In: Progress in Turbulence III ed. by Peinke J, Oberlack M, Talamelli A. Springer Proceedings in Physics, vol. 131. Springer Berlin Heidelberg, 2010, pp. 37–40. DOI: 10.1007/978-3-642-02225-8_8.

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The multiple-point probability density f(v₁, r₁; v₂, r₂; …v_N, r_N) of velocity increments v_i at different length scales r_i is investigated in a direct numerical simulation of two-dimensional turbulence. It has been shown for experimental data of three-dimensional turbulence, that this probability density can be represented by conditional probability densities in form of a Markov chain [Friedrich R & Peinke J, Phys. Rev. Lett. 78, 863 (1997)]. We have extended this analysis to the case of two-dimensional forced turbulence in the inverse cascade regime.