arXiv subjects

Joachim Peinke

Publications and source records attributed to Joachim Peinke.

At least 19 recordsLinked to original sources

arXiv2025

Non-equilibrium formulation for inertial particles in turbulent swirling flows

We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at different scales, we show that their evolution is consistent with a Markov process across the inertial range. This Markovian character enables a coarse-grained description of particle dynamics through a Fokker-Planck equation, from which we can extract drift and diffusion coefficients directly from the data. The inferred coefficients reveal scale-dependent relaxation and noise amplitudes, indicative of inertial filtering and intermittency effects. Beyond the kinematic description, we analyze the thermodynamic properties of particle trajectories by computing the trajectory-dependent entropy production. We show that the statistics of entropy fluctuations satisfy both the Integral Fluctuation Theorem and, under certain conditions, the Detailed Fluctuation Theorem. These results establish a quantitative bridge between stochastic thermodynamics and particle-laden flows, and open the door to modeling turbulent transport using effective stochastic theories constrained by data and physical consistency.

physics.flu-dyn↗

arXiv2025

Asymmetric behaviour of turbulence in the wake of wind farms caused by the Coriolis force

Large offshore wind farm wakes in shallow atmospheric boundary layers (ABL) exhibit often an asymmetric behaviour when observed through Synthetic-Aperture-Radar or simulated through Large-Eddy Simulations (LES). In previous LES of wind farms in the northern hemisphere, the asymmetry manifests as a streak at the left side of the wake, looking downstream, where the turbulence kinetic energy (TKE) is greater than the surrounding flow. This work aims at clarifying the physical mechanism that leads to the formation of such a phenomenon. Identifying the Coriolis force as one possible source of asymmetry in the resolved physics, we simulate a real wind farm located in the German Bight operating under different ABLs: one representative of the northern hemisphere; one of the southern hemisphere; and three fictitious ABLs where the Coriolis effects on the inflow and wake, i.e. veer and the wake deflecting force, are removed individually or altogether. Our results show that the TKE streak appears on the opposite side of the wake, i.e. the right one, in the southern hemisphere, and it is primarily caused by veer in the incoming flow, a result of the Coriolis force in a marine ABL. The process involves a larger TKE production which originates from a larger vertical shear promoted where the undisturbed veer profile converges towards the wake in the top part of the ABL. We find that the TKE streak improves the farm wake recovery modestly. Finally, we compare the asymmetry modelled by LES with those observed in several on-field measurements, finding striking similarities.

physics.flu-dyn↗

arXiv2024

Extension of the Langevin power curve analysis by separation per operational state

In the last few years, the dynamical characterization of the power output of a wind turbine by means of a Langevin equation has been well established. For this approach, temporally highly resolved measurements of wind speed and power output are used to obtain the drift and diffusion coefficients of the energy conversion process. These coefficients fully determine a Langevin stochastic differential equation with Gaussian white noise. The drift term specifies the deterministic behavior of the system whereas the diffusion term describes the stochastic behavior of the system. A precise estimation of these coefficients is essential to understand the dynamics of the power conversion process of the wind turbine. We show that the dynamics of the power output of a wind turbine have a hidden dependency on turbine's different operational states. Here, we use an approach based on clustering Pearson correlation matrices for different observables on a moving time window to identify different operational states. We have identified five operational states in total, for example the state of rated power. Those different operational states distinguish non-stationary behavior in the mutual dependencies and represent different turbine control settings. As a next step, we condition our Langevin analysis on these different states to reveal distinctly different behaviors of the power conversion process for each operational state. Moreover, in our new representation hysteresis effects which have typically appeared in the Langevin dynamics of wind turbines seem to be resolved. We assign these typically observed hysteresis effects clearly to the change of the wind energy system between our estimated different operational states. In this contribution, we discuss further consequences for the meaning of hysteric switching and detection of malbehaviors in wind turbines.

physics.data-an↗

arXiv2024

Local statistical moments to capture Kramers-Moyal coefficients

This study introduces an innovative local statistical moment approach for estimating Kramers-Moyal coefficients, effectively bridging the gap between nonparametric and parametric methodologies. These coefficients play a crucial role in characterizing stochastic processes. Our proposed approach provides a versatile framework for localized coefficient estimation, combining the flexibility of nonparametric methods with the interpretability of global parametric approaches. We showcase the efficacy of our approach through use cases involving both stationary and non-stationary time series analysis. Additionally, we demonstrate its applicability to real-world complex systems, specifically in the energy conversion process analysis of a wind turbine.

stat.ME↗

arXiv2024

Dynamics of wind turbine operational states

Modern wind turbines gather a wealth of data with Supervisory Control And Data Acquisition (SCADA) systems. We study the short-term mutual dependencies of a variety of observables by evaluating Pearson correlation matrices on a moving time window. Using clustering on these matrices, we identify multiple stable operational states, which characterize the non-stationarity of mutual dependencies at a single turbine. They represent different turbine operational settings. Moreover, we combine the clustering analysis with a construction of a stochastic process to study the switching dynamics of those states in more detail. Calculating the distances between correlation matrices we obtain a time series that describes the behavior of the complex system in a collective way. Assuming this time series to be governed by a Langevin equation, we estimate the deterministic (drift) and stochastic (diffusion) components of the dynamics to understand the underlying non-stationarity. After adapting our method to specific features of our data, we are able to study the dynamics of operational states and their transitions as well as to resolve hysteresis effects.

physics.flu-dyn↗

arXiv2023

Assessing the Suitability of the Langevin Equation for Analyzing Measured Data Through Downsampling

The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms, ranging from continuous trajectories reminiscent of Brownian motion to noncontinuous trajectories featuring jump events. The Langevin equation serves as a powerful tool for generating stochasticity and capturing the complex behavior of measured data with continuous stochastic characteristics. However, the traditional modeling framework of the Langevin equation falls short when it comes to capturing the presence of abrupt changes, particularly jumps, in trajectories that exhibit non-continuity. Such non-continuous changes pose a significant challenge for general processes and have profound implications for risk management. Moreover, the discrete nature of observed physical phenomena, measured with a finite sample rate, adds another layer of complexity. In such cases, data points often appear as a series of discontinuous jumps, even when the underlying trajectory is continuous. In this study, we present an analytical framework that goes beyond the limitations of the Langevin equation. Our approach effectively distinguishes between diffusive or Brownian-type trajectories and trajectories with jumps. By employing downsampling techniques, where we artificially lower the sample rate, we derive a set of measures and criteria to analyze the data and differentiate between diffusive and non-diffusive behaviors. To further demonstrate its versatility and practical applicability, we have applied our proposed method to real-world data in various scientific fields, turbulence, optical tweezers for trapped particles, neuroscience, renewable energy, and market price analysis.

cond-mat.stat-mech↗

arXiv2023

Description of laminar-turbulent transition of an airfoil boundary layer measured by differential image thermography using directed percolation theory

The study presented here addresses the challenging problem of laminar-turbulent flow transition in boundary layers. Directed percolation theory has emerged as a promising approach to understand and describe this transition in different scenarios. This study utilizes differential image thermography (DIT) to investigate the boundary layer transition on the suction side of a heated airfoil, presenting new experimental findings. First, the DIT results underline the ability of capturing the near surface transition for the airfoil boundary layer with a high temporal and spatial resolution. Second, the evaluation reveals the effectiveness of directed percolation theory in describing the onset of the transition, showing agreement with all three universal exponents of (1+1)D directed percolation theory. Third, the study shows the applicability of this theory to a wide range of flow situations beyond the parameter space covered in previous examinations. These findings underscore the possible application of directed percolation models in fluid mechanics and suggest that the theory could serve as a high precision tool for describing the transition to turbulence.

physics.flu-dyn↗

arXiv2023

Signatures of geostrophic turbulence in power spectra and third-order-structure function of offshore wind speed fluctuation

We analyze offshore wind speeds with a time resolution of one second over a long period of 20 months for different heights above the sea level. Energy spectra extending over more than seven decades give a comprehensive picture of wind fluctuations, including intermittency effects at small length scales and synoptic weather phenomena at large scales. The spectra $S(f)$ show a scaling behavior consistent with three-dimensional turbulence at high frequencies $f$, followed by a regime at lower frequencies, where $fS(f)$ varies weakly. Lowering the frequency below a crossover frequency $f_{\rm\scriptscriptstyle 2D}$, a rapid rise of $fS(f)$ occurs. An analysis of the third-order structure function $D_3(τ)$ of wind speed differences for a given time lag $τ$ shows a rapid change from negative to positive values of $D_3(τ)$ at $τ\simeq 1/f_{\rm\scriptscriptstyle 2D}$. Remarkably, after applying Taylor's hypothesis locally, we find the third-order structure function to exhibit a behavior very similar to that obtained previously from aircraft measurements at much higher altitudes in the atmosphere. In particular, the third-order structure function grows linearly with the separation distance for negative $D_3$, and with the third power for positive $D_3$. This allows us to estimate energy and enstrophy dissipation rates for offshore wind. The crossover from negative to positive values occurs at about the same separation distance of 400 km as found from the aircraft measurements, suggesting that this length is independent of the altitude in the atmosphere.

physics.flu-dyn↗

arXiv2023

Enhanced recovery and non-linear dynamics in the wake of a model floating offshore wind turbine submitted to side-to-side and fore-aft motion

An experimental study in a wind tunnel is presented to explore the wake of a floating wind turbine subjected to harmonic side-to-side and fore-aft motions under laminar inflow conditions. The wake recovery is analysed as a function of the frequency of motion, measured by the Strouhal number, St. Our findings indicate that both directions of motion accelerate the transition to the far-wake compared to the fixed turbine. The experimental outcomes confirm the CFD results of Li et al. (2022) showing that sideways motions lead to faster wake recovery, especially for St in [0.3, 0.6]. Additionally, we find that fore-aft motions also lead to better recovery for St in [0.3, 0.9]. Moreover, we see that the recovery is closely linked to non-linear spatio-temporal dynamics. Special nonlinear dynamical effects are found in the shear layer region of the wake (y = R). For both directions of motion and St in [0.25, 0.55], the noisy wake dynamics synchronise to the frequency of the motion. For fore-aft motions and St in [0.55, 0.9], the wake shows more complex quasi-periodic phenomena. In fact, the driven frequency and a selfgenerated meandering mode emerge and interact non-linearly, as proved by occurring mixing components. Sideways motions result in large spatial structures of meandering. Fore-aft motions induce pulsing of the wake. Both modes are linked to the synchronisation effect. The quasi-periodic phenomena of fore-aft motions are connected to meandering mode. Overall, the spatio-temporal phenomena lead to faster recovery likely due to an increase of momentum transport towards wake centre.

physics.flu-dyn↗

arXiv2023

Discontinuous Jump Behavior of the Energy Conversion in Wind Energy Systems

The power conversion process of a wind turbine can be characterized by a stochastic differential equation (SDE) of the power output conditioned to certain fixed wind speeds. An analogous approach can also be applied to the mechanical loads on a wind turbine, such as generator torque. The constructed SDE consists of the deterministic and stochastic terms, the latter corresponding to the highly fluctuating behavior of the wind turbine. Here we show how advanced stochastic analysis of the noise contribution can be used to show different operating modes of the conversion process of a wind turbine. The parameters of the SDE, known as Kramers-Moyal (KM) coefficients, are estimated directly from the measurement data. Clear evidence is found that both, continuous diffusion noise and discontinuous jump noise are present. The difference in the noise contributions indicates different operational regions. In particular, we observe that the jump character or discontinuity in power production has a significant contribution in the regions where the control system switches strategies. We find that there is a high increase in jump amplitude near the transition to the rated region, and the switching strategies cannot result in a smooth transition. The proposed analysis provides new insights to the control strategies of the wind turbine.

eess.SY↗

arXiv2022

Experimental and Computational Investigation of a Fractal Grid Wake

Fractal grids generate turbulence by exciting many length scales of different sizes simultaneously rather than using the nonlinear cascade mechanism to obtain multi-scale structures, as it is the case for regular grids. The interest in these grids has been further building up since the surprising findings stemming from the experimental and computational studies conducted on these grids. This work presents experimental wind tunnel and computational fluid dynamics (CFD) studies of the turbulent flow generated by a space-filling fractal square grid. The experimental work includes Particle Image Velocimetry (PIV) and hot-wire measurements. In addition, Delayed Detached Eddy Simulations (DDES) with a Spalart-Allmaras background turbulence model are conducted using the open-source package OpenFOAM. This is the first time DDES simulations are used to simulate and characterize the turbulent flow generated by a fractal grid. Finally, this article reports on the extensive statistical study and the direct comparison between the experimentally and numerically acquired time series to investigate and compare one-point- and two-point statistics. Our goal is to validate our computational results and provide enhanced insight into the complexity of the multi-scale generation of turbulence using a fractal grid with a low number of fractal iterations. In particular, we investigate the different turbulent structures and their complex interaction in the near-grid region or the production regime of the fractal grid flow.

physics.flu-dyn↗

arXiv2022

Superstatistical wind fields from point-wise atmospheric turbulence measurements

Accurate models of turbulent wind fields have become increasingly important in the atmospheric sciences, e.g., for the determination of spatiotemporal correlations in wind parks, the estimation of individual loads on turbine rotor and blades, or for the modeling of particle-turbulence interaction in atmospheric clouds or pollutant distributions in urban settings. Due to the prohibitive task of resolving the fields across a broad range of scales, one oftentimes has to resort to stochastic wind field models that fulfill specific, empirically observed, properties. Here, we present a new model for the generation of synthetic wind fields that can be apprehended as an extension of the well-known Mann model for inflow turbulence in the wind energy sciences. Whereas such Gaussian random field models solely control second-order statistics (i.e., velocity correlation tensors or kinetic energy spectra), we explicitly show that our extended model emulates the effects of higher-order statistics as well. Most importantly, the empirically observed phenomenon of small-scale intermittency, which can be regarded as one of the key features of atmospheric turbulent flows, is reproduced with high accuracy and at considerably low computational cost. Our method is based on a recently developed multipoint statistical description of turbulent velocity fields [J. Friedrich et al., J. Phys. Complex. 2 045006 (2021)] and consists of a superposition of multivariate Gaussian statistics with fluctuating covariances. We demonstrate exemplarily how such "superstatistical" wind fields can be constrained on a certain number of point-wise measurement data from a meteorological mast array.

physics.flu-dyn↗

arXiv2022

An open source MATLAB package to perform basic and advanced statistical analysis of turbulence data and other complex systems

We present a user-friendly open-source MATLAB\textsuperscript{\textregistered} package developed by the research group Turbulence, Wind energy and Stochastics (TWiSt) at the Carl von Ossietzky University of Oldenburg. Firstly, this package helps the user to perform a very basic statistical analysis of a given turbulent data set which we believe to be useful to the entire turbulence community. It can be used to estimate the statistical quantities of turbulence such as the spectrum density, turbulent intensity, integral length scale, Taylor microscale, Kolmogorov scale and dissipation rate. Different well-known methods available in the literature were selected so that they can be compared. Secondly, this package also performs an advanced analysis which includes the scale-dependent statistical description of turbulent cascade using the Fokker-Planck equation which consequently leads to the assessment of integral fluctuation theorem. This is utilized to estimate velocity increments, structure functions and their scaling exponents, drift and diffusion coefficients of the Fokker-Planck equation and consequently the total entropy production of the turbulent cascade. As a precondition for the stochastic process approach, Markovian properties of the turbulent cascade in scale are tested. The knowledge of a Fokker-Planck equation allows to determine for each independent cascade trajectories a total entropy production. The estimation of total entropy production allows to verify a rigorous law of non-equilibrium stochastic thermodynamics, namely the integral fluctuation theorem, which must be valid if Markov properties hold and the Fokker-Planck equation is correct. This approach to the turbulent cascade process has the potential for a new way to link the statistical description of turbulence, non-equilibrium stochastic thermodynamics and local turbulent flow structures.

physics.flu-dyn↗

arXiv2022

Instantons and the path to intermittency in turbulent flows

Processes leading to anomalous fluctuations in turbulent flows, referred to as intermittency, are still challenging. We consider cascade trajectories through scales as realizations of a stochastic Langevin process for which multiplicative noise is an intrinsic feature of the turbulent state. The trajectories are conditioned on their entropy exchange. Such selected trajectories concentrate around an optimal path, called instanton, which is the minimum of an effective action. The action is derived from the Langevin equation, estimated from measured data. In particular instantons with negative entropy pinpoint the trajectories responsible for the emergence of non-Gaussian statistics at small-scales.

physics.flu-dyn↗

arXiv2021

Hybrid time series from PIV for characterization of turbulent flow fields: ASTRA -- Approach using Spatially and Temporally Resolved Advection

Particle Image Velocimetry (PIV) has become increasingly popular to study structures in turbulent flows. PIV allows direct extraction and investigation of spatial structures in the given flow field. Increasing temporal resolution of PIV systems allows a more accurate capture of the flow evolution. Despite the very good spatial resolution of PIV, current systems can only match the multiple $kHz$ sampling rates of hot-wire or Laser Doppler Anemometer (LDA) measurements for a very short period in temporal analyses of flow. In this study, an advection-based approach is presented which uses Taylor's hypothesis of "frozen turbulence" for small scale turbulent patterns. Compared to the underlying raw data a major increase of the temporal resolution for extracted time series is shown. The quality of the presented approach is shown for two-point analyses, which would not be possible with presently known methods. To demonstrate this, different turbulent flow cases behind a fractal grid are studied. For the validation of the results corresponding hot-wire measurements at various positions along the centerline were used.

physics.flu-dyn↗

arXiv2021

How to design a 2D active grid for dynamic inflow modulation

Wind turbines operate under constantly changing turbulent inflow conditions. In the rotating system, wind gusts lead to variations in the angle of attack at local blade segments resulting in dynamic effects such as dynamic stall. Such highly non-linear effects are known to produce a significant overshoot in the lift and thus an increase in loads acting on the wind turbine, leading to long-term fatigue. To better understand these effects, it is essential to perform experiments under defined conditions on 2D airfoil segments in the wind tunnel. In this study, a so-called 2D active grid is presented which allows to generate local inflow conditions with defined fluctuations of the angle of incidence (AoI) in wind tunnel experiments. The focus of the investigations is on sinusoidal variations of AoI with high amplitudes generated by different grid configurations. By changing the AoI dynamic phenomena can be induced without the need to move the object under investigation. Inertial effects during force measurements and a changing shadow casting due to a moving airfoil in particle image velocimetry measurements do not appear. Additional variations in the longitudinal velocity component are another aspect in the presented work. Such longitudinal gusts can be combined with AoI variations in arbitrary phase. This can be used to mimic various inflow situations such as yaw or tower shadow effects on wind turbines.

physics.flu-dyn↗

arXiv2021

Detecting Hidden Units and Network Size from Perceptible Dynamics

The number of units of a network dynamical system, its size, arguably constitutes its most fundamental property. Many units of a network, however, are typically experimentally inaccessible such that the network size is often unknown. Here we introduce a \emph{detection matrix }that suitably arranges multiple transient time series from the subset of accessible units to detect network size via matching rank constraints. The proposed method is model-free, applicable across system types and interaction topologies and applies to non-stationary dynamics near fixed points, as well as periodic and chaotic collective motion. Even if only a small minority of units is perceptible and for systems simultaneously exhibiting nonlinearities, heterogeneities and noise, \emph{exact} size detection is feasible. We illustrate applicability for a paradigmatic class of biochemical reaction networks.

nlin.AO↗

arXiv2021

Correlated power time series of individual wind turbines: A data driven model approach

Wind farms can be regarded as complex systems that are, on the one hand, coupled to the nonlinear, stochastic characteristics of weather and, on the other hand, strongly influenced by supervisory control mechanisms. One crucial problem in this context today is the predictability of wind energy as an intermittent renewable resource with additional non-stationary nature. In this context, we analyze the power time series measured in an offshore wind farm for a total period of one year with a time resolution of 10 min. Applying detrended fluctuation analysis, we characterize the autocorrelation of power time series and find a Hurst exponent in the persistent regime with cross-over behavior. To enrich the modeling perspective of complex large wind energy systems, we develop a stochastic reduced-form model ofpower time series. The observed transitions between two dominating power generation phases are reflected by a bistable deterministic component, while correlated stochastic fluctuations account for the identified persistence. The model succeeds to qualitatively reproduce several empirical characteristics such as the autocorrelation function and the bimodal probability density function.

stat.AP↗