Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 32: Focus Session: Statistics of fully developed turbulence

DY 32.3: Vortrag

Mittwoch, 18. März 2015, 15:45–16:00, BH-N 243

Markov closure for the Lundgren-Monin-Novikov hierarchy in turbulence — •Jan Friedrich and Rainer Grauer — Institut für theoretische Physik I, Ruhr-Universität Bochum, Deutschland

A central, yet unsolved problem of hydrodynamic turbulence is the closure problem, which is due to the nonlinear character of the Navier-Stokes equation. We formulate the closure problem for the many-increment probability distributions and introduce a new method for closing the hierarchy. Here we use the experimental and numerically verified assumption that the turbulent cascade possesses a Markov property in scale [1] down to the so-called Einstein-Markov length. This approximation is far beyond a Gaussian approximation and allows a full description of intermittency effects. The procedure is explained on the example of the simpler Burgers equation corresponding to a fluid without pressure contributions whose singular structures are determined by so-called shocks. The proposed closure also opens up the way to a perturbative treatment of the Navier-Stokes equation beyond the Einstein-Markov length in successively taking into account a larger and larger scale "history" of the system.

[1] R. Friedrich, J. Peinke, Phys. Rev. Lett. 78 (5) (1997) 863-866