Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 58: Poster - Fluids

DY 58.2: Poster

Donnerstag, 19. März 2015, 16:00–18:00, Poster A

Markov processes linking stochastic thermodynamics and turbulent cascades — •Daniel Nickelsen — Institut für Physik, Carl-von-Ossietzky Universität Oldenburg, Germany

An elementary example of a Markov process (MP) is Brownian motion. The work done and the entropy produced for single trajectories of the Brownian particles are random quantities. Statistical properties of such fluctuating quantities are central in the field of stochastic thermodynamics. Prominent results of stochastic thermodynamics are so-called fluctuation theorems (FTs). FTs express the balance between production and consumption of entropy.

Turbulent cascades of eddies are assumed to be the predominant mechanism of turbulence generation fixing the statistical properties of developed turbulent flows. An intriguing phenomenon of developed turbulence, known as small-scale intermittency, are violent small-scale fluctuations in flow velocity that exceed any Gaussian prediction.

In analogy to Brownian motion, we show how the assumption of the Markov property leads to a MP for the turbulent cascade that is equivalent to the seminal K62 model. In addition to the K62 model, we demonstrate how many other models of turbulence can be written as a MP, including scaling laws, multiplicative cascades, multifractal models and field-theoretic approaches. Based on the various MPs, we discuss the production of entropy and the corresponding FTs. In particular, an experimental analysis indicates that entropy consumption is linked to small-scale intermittency, and a connection between entropy consumption and inverse cascades is suggestive.