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New insights into turbulence

Peinke, J (Oldenburg)
Tuesday 30 September 2008, 10:30-11:00

Seminar Room 1, Newton Institute


We present a more complete analysis of measurement data of fully developed, local isotropic turbulence by means of the estimations of Kramers- Moyal coefficients, which provide access to the joint probability density function of increments for n- scales \cite{JFM}. In this contribution we report on new findings based on this technique and based on the investigation of many different flow data over a big range of Re numbers.

In particular we show:

- An improved method to reconstruct from given data the underlying stochastic process in form of a Fokker-Planck equation, which includes intermittency effects, will be shown.

- It is shown that a new length scale, for turbulence can be defined, which corresponds to a memory effect in the cascade dynamics. This coherence length can be seen as analogue to the mean free path length of a Brownian Motion. For length scales larger than this coherence length the complexity of turbulence can be treated as a Markov process. We show that this Einstein- Markovian coherence length is closely related to the Taylor micro-scale.

- It is shown that the stochastic process of a cascade will change with the Re-number and its universal or non-universal behavior with changing large scale boundary conditions will be discussed.

- 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 for these two components can explain the reported difference for these components. The rescaling symmetry is compatible with the Kolmogorov constants and the Karman equation and give new insight into the use of extended self similarity (ESS) for transverse increments.

- A method is presented which allows to reconstruct time series from a estimated stochastic process evolving in scale. The method itself is based on the joint probability density which can be extracted directly from given data, thus no estimation of parameters is necessary. The original and reconstructed time series coincide with respect to the unconditional and conditional probability densities. Therefore the method proposed here is able to generate artificial time series with correct n-point statistics.


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