%0 Book Section %1 statphys23_0923 %A Stresing, R. %A Peinke, J. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K equation fokker-planck markov processes properties statphys23 stochastic topic-5 turbulence %T Stochastic analysis of turbulence %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=923 %X We present a more complete analysis of measurement data of fully developed, locally isotropic turbulence by means of the estimation of Kramers-Moyal coefficients, which provide access to the joint probabiltiy density function of increments for n-scales 1. In this contribution we report on new findings based on this technique and based on the investigation of many different flow data over a large range of Re numbers.\\ In particular, our contribution includes the following aspects: 1. A method to reconstruct from given data the underlying stochastic process in form of a Fokker-Planck equation, which includes intermittency effects, will be presented. 2. It is shown that a new length scale, $l_mar$, for turbulence can be defined, which corresponds to a memory effect in the cascade dynamics, and which is closely related to the Taylor micro-scale, $łambda$. For length scales larger than $l_mar$, the complexity of turbulence can be treated as a Markov process 2. 3. For longitudinal and transversal velocity increments we present the reconstruction of the two dimensional stochastic process equations, which shows that the cascade evolves differently for the longitudinal and transversal increments. A different ``speed'' of the cascade can explain the reported difference for these two components. The rescaling symmetry is compatible with the Kolmogorov constants and the von Karman equation and gives new insight into the use of extended self similarity (ESS) for transverse increments 3. 4. We present first results from the analysis of data from non-isotropic flow situations and show how the cascade process and Markov properties for both longitudinal and transversal velocity increments change in these cases.\\ Literature: 1) Ch. Renner, J. Peinke, and R. Friedrich: Markov properties of small scale turbulence, J. Fluid Mech. 433, 383 (2001)\\ 2) St. Lueck, Ch. Renner, J. Peinke, and R. Friedrich: The Markov coherence length -- a new meaning for the Taylor length in turbulence, Phys. Lett., in press\\ 3) M. Siefert and J. Peinke: On a multi-scale approach to analyze the joint statistics of longitudinal and transverse increments experimentally in small scale turbulence, J. of Turbulence 7, (No 50) 1-35 (2006)

@incollection{statphys23_0923, abstract = {We present a more complete analysis of measurement data of fully developed, locally isotropic turbulence by means of the estimation of Kramers-Moyal coefficients, which provide access to the joint probabiltiy density function of increments for n-scales [1]. In this contribution we report on new findings based on this technique and based on the investigation of many different flow data over a large range of Re numbers.\\ In particular, our contribution includes the following aspects: 1. A method to reconstruct from given data the underlying stochastic process in form of a Fokker-Planck equation, which includes intermittency effects, will be presented. 2. It is shown that a new length scale, $l_{mar}$, for turbulence can be defined, which corresponds to a memory effect in the cascade dynamics, and which is closely related to the Taylor micro-scale, $\lambda$. For length scales larger than $l_{mar}$, the complexity of turbulence can be treated as a Markov process [2]. 3. For longitudinal and transversal velocity increments we present the reconstruction of the two dimensional stochastic process equations, which shows that the cascade evolves differently for the longitudinal and transversal increments. A different ``speed'' of the cascade can explain the reported difference for these two components. The rescaling symmetry is compatible with the Kolmogorov constants and the von Karman equation and gives new insight into the use of extended self similarity (ESS) for transverse increments [3]. 4. We present first results from the analysis of data from non-isotropic flow situations and show how the cascade process and Markov properties for both longitudinal and transversal velocity increments change in these cases.\\ Literature: 1) Ch. Renner, J. Peinke, and R. Friedrich: Markov properties of small scale turbulence, J. Fluid Mech. 433, 383 (2001)\\ 2) St. Lueck, Ch. Renner, J. Peinke, and R. Friedrich: The Markov coherence length -- a new meaning for the Taylor length in turbulence, Phys. Lett., in press\\ 3) M. Siefert and J. Peinke: On a multi-scale approach to analyze the joint statistics of longitudinal and transverse increments experimentally in small scale turbulence, J. of Turbulence 7, (No 50) 1-35 (2006)}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Stresing, R. and Peinke, J.}, biburl = {https://www.bibsonomy.org/bibtex/2b849bae458e0c31eacf3defa5eddf2b1/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {0c9d3519c8709788db8880807a6883a2}, intrahash = {b849bae458e0c31eacf3defa5eddf2b1}, keywords = {equation fokker-planck markov processes properties statphys23 stochastic topic-5 turbulence}, month = {9-13 July}, timestamp = {2007-06-20T10:16:34.000+0200}, title = {Stochastic analysis of turbulence}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=923}, year = 2007 }