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Fokker-Planck description of the inverse cascade in two-dimensional turbulence

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In many approaches the mathematical description of fully developed turbulence relies on the statistical properties of the longitudinal velocity increments ξ(r) = U(x + r) − U(x). The increment statistics can be described as a Markov process in scale, leading to a Fokker-Planck description of the probability density functions (PDFs) for the velocity increments. Here we want to extend this description to the inverse energy cascade in two-dimensional turbulence. The central question is whether the velocity field of the inverse cascade can be modeled as a Markov process in scale similar to the three-dimensional case. By estimating the coefficients of the Fokker-Planck equation we are able to discuss the role of intermittency and differences to three-dimensional flows

Author(s):

Oliver Kamps    
Center for Nonlinear Science, University of Münster
Germany

Michel Voßkuhle    
Laboratoire de Physique,, École normale supérieure de Lyon
France