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J. Peinke

Publications and source records attributed to J. Peinke.

At least 37 records · Page 2Linked to original sources
arXiv2005

Small and Large Scale Fluctuations in Atmospheric Wind Speeds

Atmospheric wind speeds and their fluctuations at different locations (onshore and offshore) are examined. One of the most striking features is the marked intermittency of probability density functions (PDF) of velocity differences -- no matter what location is considered. The shape of these PDFs is found to be robust over a wide range of scales which seems to contradict the mathematical concept of stability where a Gaussian distribution should be the limiting one. Motivated by the instationarity of atmospheric winds it is shown that the intermittent distributions can be understood as a superposition of different subsets of isotropic turbulence. Thus we suggest a simple stochastic model to reproduce the measured statistics of wind speed fluctuations.

nlin.AO↗
arXiv2004

Stochastic analysis of different rough surfaces

This paper shows in detail the application of a new stochastic approach for the characterization of surface height profiles, which is based on the theory of Markov processes. With this analysis we achieve a characterization of the scale dependent complexity of surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method is applied to several surfaces with different properties, for the purpose of showing the utility of this method in more details. In particular we show the evidence of Markov properties, and we estimate the parameters of the Fokker-Planck equation by pure, parameter-free data analysis. The resulting Fokker-Planck equations are verified by numerical reconstruction of conditional probability density functions. The results are compared with those from the analysis of multi-affine and extended multi-affine scaling properties which is often used for surface topographies. The different surface structures analysed here show in details advantages and disadvantages of these methods.

physics.data-an↗
arXiv2004

On a multi-scale approach to analyze the joint statistics of longitudinal and transverse increments experimentally in small scale turbulence

We analyze the relationship of longitudinal and transverse increment statistics measured in isotropic small-scale turbulence. This is done by means of the theory of Markov processes leading to a phenomenological Fokker-Planck equation for the two increments from which a generalized Karman equation is derived. We discuss in detail the analysis and show that the estimated equation can describe the statistics of the turbulent cascade. A remarkably result is that the main differences between longitudinal and transverse increments can be explained by a simple rescaling-symmetry, namely the cascade speed of the transverse increments is 1.5 times faster than that of the longitudinal increments. Small differences can be found in the skewness and in a higher order intermittency term. 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. Based on the results we propose an extended self similarity for the transverse increments (ESST).

physics.flu-dyn↗
arXiv2004

Yakhot's model of strong turbulence: A generalization of scaling models of turbulence

We report on some implications of the theory of turbulence developed by V. Yakhot [V. Yakhot, Phys. Rev. E {\bf 57}(2) (1998)]. In particular we focus on the expression for the scaling exponents $ζ_{n}$. We show that Yakhot's result contains three well known scaling models as special cases, namely K41, K62 and the theory by V. L'vov and I. Procaccia [V. L'vov & I. Procaccia, Phys. Rev. E {\bf 62}(6) (2000)]. The model furthermore yields a theoretical justification for the method of extended self--similarity (ESS).

cond-mat.soft↗
arXiv2003

On a quantitative method to analyse dynamical and measurement noise

This letter reports on a new method of analysing experimentally gained time series with respect to different types of noise involved, namely, we show that it is possible to differentiate between dynamical and measurement noise. This method does not depend on previous knowledge of model equations. For the complicated case of a chaotic dynamics spoiled at the same time by dynamical and measurement noise, we even show how to extract from data the magnitude of both types of noise. As a further result, we present a new criterion to verify the correct embedding for chaotic dynamics with dynamical noise.

physics.data-an↗
arXiv2003

Stochastic analysis of surface roughness

For the characterization of surface height profiles we present a new stochastic approach which is based on the theory of Markov processes. With this analysis we achieve a characterization of the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation, providing the complete stochastic information of multiscale joint probabilities. The method was applied to different road surface profiles which were measured with high resolution. Evidence of Markov properties is shown. Estimations for the parameters of the Fokker-Planck equation are based on pure, parameter free data analysis.

physics.data-an↗
arXiv2003

On different cascade-speeds for longitudinal and transverse velocity increments

We address the problem of differences between longitudinal and transverse velocity increments in isotropic small scale turbulence. The relationship of these two quantities is analyzed experimentally by means of stochastic Markovian processes leading to a phenomenological Fokker- Planck equation from which a generalization of the Karman equation is derived. From these results, a simple relationship between longitudinal and transverse structure functions is found which explains the difference in the scaling properties of these two structure functions.

physics.flu-dyn↗
arXiv2002

On the interaction between velocity increment and energy dissipation in the turbulent cascade

We adress the problem of interactions between the longitudinal velocity increment and the energy dissipation rate in fully developed turbulence. The coupling between these two quantities is experimentally investigated by the theory of stochastic Markovian processes. The so-called Markov analysis allows for a precise characterization of the joint statistical properties of velocity increment and energy dissipation. In particular, it is possible to determine the differential equation that governs the evolution along scales of the joint probability density of these two quantities. The properties of this equation provide interesting new insights into the coupling between energy dissipation and velocity incrementas leading to small scale intermittency.

physics.flu-dyn↗
arXiv2001

On the statistics of wind gusts

Velocity measurements of wind blowing near the North Sea border of Northern Germany and velocity measurements under local isotropic conditions of a turbulent wake behind a cylinder are compared. It is shown that wind gusts - measured by means of velocity increments - do show similar statistics to the laboratory data, if they are conditioned on an averaged wind speed value. Clear differences between the laboratory data and the atmospheric wind velocity measurement are found for the waiting time statistics between successive gusts above a certain threshold of interest.

physics.ao-ph↗
arXiv2001

Reconstruction of dynamical equations for traffic flow

Traffic flow data collected by an induction loop detector on the highway close to Koeln-Nord are investigated with respect to their dynamics including the stochastic content. In particular we present a new method, with which the flow dynamics can be extracted directly from the measured data. As a result a Langevin equation for the traffic flow is obtained. From the deterministic part of the flow dynamics, stable fixed points are extracted and set into relation with common features of the fundamental diagram.

physics.data-an↗
arXiv2001

On the universality of small scale turbulence

The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from 8500 to 10^6. The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of stochastic Markovian processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more precise method our results call in question the concept of universality.

physics.flu-dyn↗
arXiv2001

Markov properties of high frequency exchange rate data

We present a stochastic analysis of a data set consisiting of 10^6 quotes of the US Doller - German Mark exchange rate. Evidence is given that the price changes x(tau) upon different delay times tau can be described as a Markov process evolving in tau. Thus, the tau-dependence of the probability density function (pdf) p(x) on the delay time tau can be described by a Fokker-Planck equation, a gerneralized diffusion equation for p(x,tau). This equation is completely determined by two coefficients D_{1}(x,tau) and D_{2}(x,tau) (drift- and diffusion coefficient, respectively). We demonstrate how these coefficients can be estimated directly from the data without using any assumptions or models for the underlying stochastic process. Furthermore, it is shown that the solutions of the resulting Fokker-Planck equation describe the empirical pdfs correctly, including the pronounced tails.

cond-mat.stat-mech↗
arXiv2000

Universal Multifractal Properties of the Small Scale Intermittency in Anisotropic and Inhomogeneous Turbulence

The notion of self-similar energy cascades and multifractality has long since been connected with fully developed, homogeneous and isotropic turbulence. We introduce a number of amendments to the standard methods for analysing the multifractal properties of the energy dissipation field of a turbulent flow. We conjecture that the scaling assumption for the moments of the energy dissipation rate is valid within the transition range to dissipation introduced by Castaing et al.(Physica D (46), 177 (1990)). The multifractal spectral functions appear to be universal well within the error margins and exhibit some as yet undiscussed features. Furthermore, this universality is also present in the neither homogeneous nor isotropic flows in the wake very close to a cylinder or the off-centre region of a free jet.

nlin.CD↗
arXiv1999

Orientational transition in nematic liquid crystals under oscillatory Poiseuille flow

We investigate the orientational behaviour of a homeotropically aligned nematic liquid crystal subjected to an oscillatory plane Poiseuille flow produced by an alternating pressure gradient. For small pressure amplitudes the director oscillates within the flow plane around the initial homeotropic position, whereas for higher amplitudes a spatially homogeneous transition to out-of-plane director motion was observed for the first time. The orientational transition was found to be supercritical and the measured frequency dependence of the critical pressure amplitude in the range between 2 and 20 Hz was in quantitative agreement with a recent theory.

cond-mat.soft↗
arXiv1999

Experimental evidence of a phase transition to fully developed turbulence in a wake flow

The transition to fully developed turbulence of a wake behind a circular cylinder is investigated with respect to its statistics. In particular, we evaluated the probability density functions of velocity increments on different length scales $r$. Evidence is presented that the $r$-dependence of the velocity increments can be taken as Markov processes in the far field, as well as, in the near field of the cylinder wake. With the estimation of the deterministic part of these Markov processes, as a function of the distance from the cylinder, we are able to set the transition to fully developed turbulence in analogy with a phase transition. We propose that the appearing order parameter corresponds to the presence of large scale coherent structures close to the cylinder.

physics.data-an↗
arXiv1998

On the Statistics of Small Scale Turbulence and its Universality

We present a method how to estimate from experimental data of a turbulent velocity field the drift and the diffusion coefficient of a Fokker-Planck equation. It is shown that solutions of this Fokker-Planck equation reproduce with high accuracy the statistics of velocity increments in the inertial range. Using solutions with different initial conditions at large scales we show that they converge. This can be interpreted as a signature of the universality of small scale turbulence in the limit of large inertial ranges.

chao-dyn↗