The prevalent understanding of fully developed turbulence is that of a cascade in which vortices ... more The prevalent understanding of fully developed turbulence is that of a cascade in which vortices successively break up into smaller ones. Based on this idea, theoretical developments were often concerned with multiplicative random cascade processes. We focus on the velocity fluctuations and derive a closed as well as complete statistical description of the underlying velocity multipliers using a Fokker-Planck equation, which is estimated directly from experimental data. This shed new light on the statistics of multipliers and their often assumed independence. For the heavy-tailed statistical features of the multipliers, close to a Cauchy distribution, no intermittency of turbulence is needed.
We present quantitative measurements of the scenario leading to chevrons in the dielectric range ... more We present quantitative measurements of the scenario leading to chevrons in the dielectric range of ac driven electroconvection in a planarly aligned layer of the nematic liquid crystal Merck Phase 5. First, we demonstrate that the threshold of electroconvection is described correctly by the standard theory. Second, we characterize above threshold the appearance of chevrons out of the defect chaotic state by a rather sudden increase of the density of defects. Furthermore, we show that the spatial correlations between defects characterizing the chevrons set in simultaneously. Finally, we give the onset curve of chevrons ͑voltage versus frequency͒ and also discuss briefly their further development. ͓S1063-651X͑98͒09608-1͔
It is a big challenge in the analysis of experimental data to disentangle the unavoidable measure... more It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time series, even in the case when the amplitudes of measurement noise and uncontaminated signal are of the same order of magnitude. Our approach is based on a recently developed method for a nonparametric reconstruction of Langevin processes. Minimizing a proper non-negative function the procedure is able to correctly extract strong measurement noise and to estimate drift and diffusion coefficients in the Langevin equation describing the evolution of the original uncorrupted signal. As input, the algorithm uses only the two first conditional moments extracted directly from the stochastic series and is therefore suitable for a broad panoply of different signals. To demonstrate the power of the method we apply the algorithm to synthetic as well as climatological measurement data, namely the daily North Atlantic Oscillation index, shedding new light on the discussion of the nature of its underlying physical processes.
The purpose of the work presented here is to analyze the transition of an initially laminar air-i... more The purpose of the work presented here is to analyze the transition of an initially laminar air-into-air free jet to turbulence. An holographic PIV system based on light-in-flight holography (LiFH) combined with a switched reference beam is used to measure velocity vector fields of a whole volume. The analysis of the velocity fields reveals that the transition to turbulence is marked by a separation of vorticity and shear.
A new method is proposed that allows a reconstruction of time series based on higher order multi-... more A new method is proposed that allows a reconstruction of time series based on higher order multi-scale statistics given by a hierarchical process. This method is able to model financial time series not only on a specific scale but for a range of scales. The method itself is based on the general n-scale joint probability density, which can be extracted directly from given data. It is shown how based on this n-scale statistics, general n-point probabilities can be estimated from which predictions can be achieved. Exemplary results are shown for the German DAX index. The ability to model correctly the behaviour of the original process for different scales simultaneously and in time is demonstrated. As a main result it is shown that this method is able to reproduce the known volatility cluster, although the model contains no explicit time dependence. Thus a new mechanism is shown how, in a stationary multi-scale process, volatility clustering can emerge.
A new method is proposed which allows a reconstruction of time series based on higher order multi... more A new method is proposed which allows a reconstruction of time series based on higher order multiscale statistics given by a hierarchical process. This method is able to model the time series not only on a specific scale but for a range of scales. It is possible to generate complete new time series, or to model the next steps for a given sequence of data. 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 results of this approach are shown for a real world dataset, namely for turbulence. The unconditional and conditional probability densities of the original and reconstructed time series are compared and the ability to reproduce both is demonstrated. Therefore in the case of Markov properties the method proposed here is able to generate artificial time series with correct n-point statistics.
By computing the probability distributions of the velocity difference between cars a time-delay τ... more By computing the probability distributions of the velocity difference between cars a time-delay τ apart, the scaling properties of traffic flow can be analysed. These data display scaling behaviour thus confirming earlier results that have found 1/ fα -noise in traffic flow. Furthermore, the applicability of the scaling analysis for describing the two-point statistics of traffic flow is demonstrated, leading to an additional test for the dynamical properties of microscopic and macroscopic traffic flow models.
Institute for Snow and Avalanche Research (SLF)-We present measurements executed with the new las... more Institute for Snow and Avalanche Research (SLF)-We present measurements executed with the new laser-cantilever anemometer (LCA) under various flow conditions. Previously, the basic principles and characteristics of the LCA were investigated. Measurements led to results comparable to common measurement techniques for turbulent flows, such as hot-wire anemometry for air and hot-film anemometry for water. Here we present further experiments under various flow conditions. The LCA was used in a snow wind tunnel to investigate the behavior of the cantilever under particle impact. In comparison to data collected with a hot-film anemometer under same conditions the times series of the LCA showed less pronounced impact characteristics than that of the hot-film, namely a shorter and easier to identify recovery time. In addition the behavior of the LCA at low velocities in air was investigated to determine the threshold velocity for measurements.
A new application of the theory of Markov processes to the characterization of fractal scaling be... more A new application of the theory of Markov processes to the characterization of fractal scaling behavior is presented. We show under which condition distinct stochastic processes of a cascade lead to multifractal scaling behavior. We apply our method to the analysis of the statistical properties of the energy in turbulent fluid flow.
We present the second prototype of a new kind of Laser Cantilever Anemometer (LCA). Using the sam... more We present the second prototype of a new kind of Laser Cantilever Anemometer (LCA). Using the same elements as for an atomic force microscope we are able to measure highly accurately the local velocity. The spatial resolution is given by a micro-structured cantilever (at the current state 150 mu m ot 40 mu m ot 5 mu m) which can be scanned with up to 100 kHz. The LCA is constructed for any transparent fluids. In contrast to the hotwire anemometer there is no problem for measurements in flows with high thermal conductivity e.g. water. We show first measurements in turbulent flows. S. Barth, S. Schlueter, S. Lueck, J. Peinke, Advances in Turbulence IX, I.P. Castro, P.E. Hancock, T.G. Thomas (Eds.) (CIMNE Barcelona 2002), p.488 and Patent application DE 198 22 125.8-52 (Peinke et al. 1998)
In this paper changes in wind speed and wind direction from a measured wind field are being analy... more In this paper changes in wind speed and wind direction from a measured wind field are being analyzed at high frequencies. This is used to estimate changes in the angle of attack (AOA) on a blade segment over short time periods for different estimated turbine concepts. Here a statistical approach is chosen to grasp the characteristics of the probability distributions to give an over all view of the magnitude and rate of the changes. The main interest is the generation of basic distributions for the calculation of dynamic stall effects and stall flutter due to wind fluctuations.
We study the Markov property of experimental velocity data of different homogeneous isotropic tur... more We study the Markov property of experimental velocity data of different homogeneous isotropic turbulent flows. In particular, we examine the stochastic "cascade" process of nested velocity increments ξ (r) := u(x + r) − u(x) as a function of scale r for different nesting structures. It was found in previous work that, for a certain nesting structure, the stochastic process of ξ (r) has the Markov property for step sizes larger than the so-called Einstein-Markov coherence length l EM , which is of the order of magnitude of the Taylor microscale λ [Phys. Lett. A 359, 335 (2006)]. We now show that, if a reasonable definition of the effective step size of the process is applied, this result holds independently of the nesting structure. Furthermore, we analyze the stochastic process of the velocity u as a function of the spatial position x. Although this process does not have the exact Markov property, a characteristic length scale l u(x) ≈ l EM can be identified on the basis of a statistical test for the Markov property. Using a method based on the matrix of transition probabilities, we examine the significance of the non-Markovian character of the velocity u(x) for the statistical properties of turbulence.
The prevalent understanding of fully developed turbulence is that of a cascade in which vortices ... more The prevalent understanding of fully developed turbulence is that of a cascade in which vortices successively break up into smaller ones. Based on this idea, theoretical developments were often concerned with multiplicative random cascade processes. We focus on the velocity fluctuations and derive a closed as well as complete statistical description of the underlying velocity multipliers using a Fokker-Planck equation, which is estimated directly from experimental data. This shed new light on the statistics of multipliers and their often assumed independence. For the heavy-tailed statistical features of the multipliers, close to a Cauchy distribution, no intermittency of turbulence is needed.
We present quantitative measurements of the scenario leading to chevrons in the dielectric range ... more We present quantitative measurements of the scenario leading to chevrons in the dielectric range of ac driven electroconvection in a planarly aligned layer of the nematic liquid crystal Merck Phase 5. First, we demonstrate that the threshold of electroconvection is described correctly by the standard theory. Second, we characterize above threshold the appearance of chevrons out of the defect chaotic state by a rather sudden increase of the density of defects. Furthermore, we show that the spatial correlations between defects characterizing the chevrons set in simultaneously. Finally, we give the onset curve of chevrons ͑voltage versus frequency͒ and also discuss briefly their further development. ͓S1063-651X͑98͒09608-1͔
It is a big challenge in the analysis of experimental data to disentangle the unavoidable measure... more It is a big challenge in the analysis of experimental data to disentangle the unavoidable measurement noise from the intrinsic dynamical noise. Here we present a general operational method to extract measurement noise from stochastic time series, even in the case when the amplitudes of measurement noise and uncontaminated signal are of the same order of magnitude. Our approach is based on a recently developed method for a nonparametric reconstruction of Langevin processes. Minimizing a proper non-negative function the procedure is able to correctly extract strong measurement noise and to estimate drift and diffusion coefficients in the Langevin equation describing the evolution of the original uncorrupted signal. As input, the algorithm uses only the two first conditional moments extracted directly from the stochastic series and is therefore suitable for a broad panoply of different signals. To demonstrate the power of the method we apply the algorithm to synthetic as well as climatological measurement data, namely the daily North Atlantic Oscillation index, shedding new light on the discussion of the nature of its underlying physical processes.
The purpose of the work presented here is to analyze the transition of an initially laminar air-i... more The purpose of the work presented here is to analyze the transition of an initially laminar air-into-air free jet to turbulence. An holographic PIV system based on light-in-flight holography (LiFH) combined with a switched reference beam is used to measure velocity vector fields of a whole volume. The analysis of the velocity fields reveals that the transition to turbulence is marked by a separation of vorticity and shear.
A new method is proposed that allows a reconstruction of time series based on higher order multi-... more A new method is proposed that allows a reconstruction of time series based on higher order multi-scale statistics given by a hierarchical process. This method is able to model financial time series not only on a specific scale but for a range of scales. The method itself is based on the general n-scale joint probability density, which can be extracted directly from given data. It is shown how based on this n-scale statistics, general n-point probabilities can be estimated from which predictions can be achieved. Exemplary results are shown for the German DAX index. The ability to model correctly the behaviour of the original process for different scales simultaneously and in time is demonstrated. As a main result it is shown that this method is able to reproduce the known volatility cluster, although the model contains no explicit time dependence. Thus a new mechanism is shown how, in a stationary multi-scale process, volatility clustering can emerge.
A new method is proposed which allows a reconstruction of time series based on higher order multi... more A new method is proposed which allows a reconstruction of time series based on higher order multiscale statistics given by a hierarchical process. This method is able to model the time series not only on a specific scale but for a range of scales. It is possible to generate complete new time series, or to model the next steps for a given sequence of data. 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 results of this approach are shown for a real world dataset, namely for turbulence. The unconditional and conditional probability densities of the original and reconstructed time series are compared and the ability to reproduce both is demonstrated. Therefore in the case of Markov properties the method proposed here is able to generate artificial time series with correct n-point statistics.
By computing the probability distributions of the velocity difference between cars a time-delay τ... more By computing the probability distributions of the velocity difference between cars a time-delay τ apart, the scaling properties of traffic flow can be analysed. These data display scaling behaviour thus confirming earlier results that have found 1/ fα -noise in traffic flow. Furthermore, the applicability of the scaling analysis for describing the two-point statistics of traffic flow is demonstrated, leading to an additional test for the dynamical properties of microscopic and macroscopic traffic flow models.
Institute for Snow and Avalanche Research (SLF)-We present measurements executed with the new las... more Institute for Snow and Avalanche Research (SLF)-We present measurements executed with the new laser-cantilever anemometer (LCA) under various flow conditions. Previously, the basic principles and characteristics of the LCA were investigated. Measurements led to results comparable to common measurement techniques for turbulent flows, such as hot-wire anemometry for air and hot-film anemometry for water. Here we present further experiments under various flow conditions. The LCA was used in a snow wind tunnel to investigate the behavior of the cantilever under particle impact. In comparison to data collected with a hot-film anemometer under same conditions the times series of the LCA showed less pronounced impact characteristics than that of the hot-film, namely a shorter and easier to identify recovery time. In addition the behavior of the LCA at low velocities in air was investigated to determine the threshold velocity for measurements.
A new application of the theory of Markov processes to the characterization of fractal scaling be... more A new application of the theory of Markov processes to the characterization of fractal scaling behavior is presented. We show under which condition distinct stochastic processes of a cascade lead to multifractal scaling behavior. We apply our method to the analysis of the statistical properties of the energy in turbulent fluid flow.
We present the second prototype of a new kind of Laser Cantilever Anemometer (LCA). Using the sam... more We present the second prototype of a new kind of Laser Cantilever Anemometer (LCA). Using the same elements as for an atomic force microscope we are able to measure highly accurately the local velocity. The spatial resolution is given by a micro-structured cantilever (at the current state 150 mu m ot 40 mu m ot 5 mu m) which can be scanned with up to 100 kHz. The LCA is constructed for any transparent fluids. In contrast to the hotwire anemometer there is no problem for measurements in flows with high thermal conductivity e.g. water. We show first measurements in turbulent flows. S. Barth, S. Schlueter, S. Lueck, J. Peinke, Advances in Turbulence IX, I.P. Castro, P.E. Hancock, T.G. Thomas (Eds.) (CIMNE Barcelona 2002), p.488 and Patent application DE 198 22 125.8-52 (Peinke et al. 1998)
In this paper changes in wind speed and wind direction from a measured wind field are being analy... more In this paper changes in wind speed and wind direction from a measured wind field are being analyzed at high frequencies. This is used to estimate changes in the angle of attack (AOA) on a blade segment over short time periods for different estimated turbine concepts. Here a statistical approach is chosen to grasp the characteristics of the probability distributions to give an over all view of the magnitude and rate of the changes. The main interest is the generation of basic distributions for the calculation of dynamic stall effects and stall flutter due to wind fluctuations.
We study the Markov property of experimental velocity data of different homogeneous isotropic tur... more We study the Markov property of experimental velocity data of different homogeneous isotropic turbulent flows. In particular, we examine the stochastic "cascade" process of nested velocity increments ξ (r) := u(x + r) − u(x) as a function of scale r for different nesting structures. It was found in previous work that, for a certain nesting structure, the stochastic process of ξ (r) has the Markov property for step sizes larger than the so-called Einstein-Markov coherence length l EM , which is of the order of magnitude of the Taylor microscale λ [Phys. Lett. A 359, 335 (2006)]. We now show that, if a reasonable definition of the effective step size of the process is applied, this result holds independently of the nesting structure. Furthermore, we analyze the stochastic process of the velocity u as a function of the spatial position x. Although this process does not have the exact Markov property, a characteristic length scale l u(x) ≈ l EM can be identified on the basis of a statistical test for the Markov property. Using a method based on the matrix of transition probabilities, we examine the significance of the non-Markovian character of the velocity u(x) for the statistical properties of turbulence.
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Papers by J. Peinke