Turbulence Time Series Research Articles

Uncertainties in measurements of bubbly flows using phase-detection probes

The analysis of bubbly two-phase flows is challenging due to their turbulent nature and the need for intrusive phase-detection probes. However, accurately characterizing these flows is crucial for safely designing critical infrastructure such as dams and their appurtenant structures. The combination of dual-tip intrusive phase-detection probes with advanced signal processing algorithms enables the assessment of pseudo-instantaneous 1-D velocity time series; for which the limitations are not fully fathomed. In this investigation, we theoretically define four major sources of error, which we quantify using synthetically generated turbulent time series, coupled with the simulated response of a phase-detection probe. Based on the analysis of 1010 simulated bubble trajectories, our findings show that typical high-velocity flows in hydraulic structures hold up to 15% error in the mean velocity estimations and up to 35% error in the turbulence intensity estimations for the most critical conditions, typically occurring in the proximity of the wall. Based on thousands of simulations, our study provides a novel data-driven tool for the estimation of these baseline errors (bias and uncertainties) in real-word phase-detection probe measurements of bubbly flows (air concentrations c<40%).

Locally Stationary Wavelet Analysis of Nonstationary Turbulent Fluxes

We propose the multivariate locally stationary wavelet (mvLSW) process to analyze surface turbulent fluxes in nonstationary atmospheric conditions. Using theoretical spectral characteristics, we generated synthetic data representing stationary and nonstationary turbulence time series. This data enables us to explore the impact of mesoscale atmospheric flows on the stationary microscale turbulence field and detect the spectral gap in the time-varying cospectra. Applying this approach to experimental data collected in Fairbanks, Alaska and Bogota, Colombia, we demonstrated the ability to detect cospectral gaps and compute bandwidth-limited turbulent fluxes arising from stationary components of the atmospheric flow. These findings underscore the importance of considering scale-dependent atmospheric forcing when comparing model and experimental data.

Constrained synthetic wind fields from high-resolution 3D WindScanner measurements

The limited spatial and temporal resolution of wind measurements within the inflow of a wind turbine requires statistical modeling of synthetic wind fields, integrating actual measurements or derived statistics along with selected turbulence models. The short-range WindScanner technology enhances atmospheric wind measurements with high resolution in both spatial and temporal dimensions. This contribution utilizes 3D turbulent inflow measurements from three synchronized WindScanner to generate synthetic turbulent wind fields. Both, mean wind field parameters and turbulent time series are analyzed, and different input configurations for the constrained wind field generation are evaluated.Our findings indicate the presence of periods characterized by dominant horizontal shear and veer events, with wind speed and direction differences up to 1.53 ms−1 or 8.45° across the rotor span. Additionally, the study reveals that the optimal measurement configuration for constrained turbulence modeling varies depending on the specific evaluated location and velocity component being analyzed. Another observation is that excessive constraints, placed too closely, may lead to overfitting, thereby diminishing the representativeness of the synthetic field for the lateral velocity component.

Self-supervised transformers for turbulent flow time series

There has been a rapid advancement in deep learning models for diverse research fields and, more recently, in fluid dynamics. This study presents self-supervised transformers' deep learning for complex turbulent flow signals across various test problems. Self-supervision aims to leverage the ability to extract meaningful representations from sparse flow time-series data to improve the transformer model accuracy and computational efficiency. Two high-speed flow cases are considered: a supersonic compression ramp and shock-boundary layer interaction over a statically deformed surface. Several training scenarios are investigated across the two different supersonic configurations. The training data concern wall pressure fluctuations due to their importance in aerodynamics, aeroelasticity, noise, and acoustic fatigue. The results provide insight into transformers, self-supervision, and deep learning with application to complex time series. The architecture is extendable to other research domains where time series data are essential.

Quantum Temporal Winds: Turbulence in Financial Markets

This paper leverages turbulence theory from physics to examine the similarities and differences between financial market volatility and turbulent phenomena on a statistical physics level. By drawing analogies between the dynamics of financial markets and fluid turbulence, an innovative analytical framework has been developed to enhance our understanding of the complexity inherent in financial markets. The research methodology involves a comparative analysis of several national stock market indices and simulated turbulent velocity time series, with a particular focus on key statistical properties such as probability distributions, correlation structures, and power spectral densities. Furthermore, a financial market capital flow model has been established, and corresponding solutions have been proposed. Through computational simulations and data analysis, it was discovered that financial market volatility shares some statistical characteristics with turbulence, yet there are significant differences in the shape of probability distributions and the timescales of correlations. This indicates that although financial markets exhibit patterns similar to turbulence, as a multivariate-driven complex system, their behavioral patterns do not completely correspond to natural turbulence phenomena, highlighting the limitations of directly applying turbulence theory to financial market analysis. Additionally, the study explores the use of Bézier curves to simulate market volatility and, based on these analyses, formulates trading strategies that demonstrate practical applications in risk management. This research provides fresh perspectives for the fields of financial market theory and econophysics, offering new insights into the complexity of financial markets and the prevention and management of financial risks.

The deepwater oxygen deficit in stratified shallow seas is mediated by diapycnal mixing

Seasonally stratified shelf seas are amongst the most biologically productive on the planet. A consequence is that the deeper waters can become oxygen deficient in late summer. Predictions suggest global warming will accelerate this deficiency. Here we integrate turbulence timeseries with vertical profiles of water column properties from a seasonal stratified shelf sea to estimate oxygen and biogeochemical fluxes. The profiles reveal a significant subsurface chlorophyll maximum and associated mid-water oxygen maximum. We show that the oxygen maximum supports both upward and downwards O2 fluxes. The upward flux is into the surface mixed layer, whilst the downward flux into the deep water will partially off-set the seasonal O2 deficit. The results indicate the fluxes are sensitive to both the water column structure and mixing rates implying the development of the seasonal O2 deficit is mediated by diapcynal mixing. Analysis of current shear indicate that the downward flux is supported by tidal mixing, whilst the upwards flux is dominated by wind driven near-inertial shear. Summer storminess therefore plays an important role in the development of the seasonal deep water O2 deficit.

Generalizability of transformer-based deep learning for multidimensional turbulent flow data

Deep learning has been going through rapid advancement and becoming useful in scientific computation, with many opportunities to be applied to various fields, including but not limited to fluid flows and fluid–structure interactions. High-resolution numerical simulations are computationally expensive, while experiments are equally demanding and encompass instrumentation constraints for obtaining flow, acoustics and structural data, particularly at high flow speeds. This paper presents a Transformer-based deep learning method for turbulent flow time series data. Turbulent signals across spatiotemporal and geometrical variations are investigated. The pressure signals are coarsely-grained, and the Transformer creates a fine-grained pressure signal. The training includes data across spatial locations of compliant panels with static deformations arising from the aeroelastic effects of shock-boundary layer interaction. Different training approaches using the Transformer were investigated. Evaluations were carried out using the predicted pressure signal and their power spectra. The Transformer's predicted signals show promising performance. The proposed method is not limited to pressure fluctuations and can be extended to other turbulent or turbulent-like signals.

Level crossings reveal organized coherent structures in a turbulent time series

Level crossings reveal organized coherent structures in a turbulent time series

Application of the visual boundary recurrence plots to magnetohydrodynamic turbulence channel flow

The visual boundary recurrence plot (VBRP) method is used in this analysis to study time series of fluctuating velocities in turbulent magnetohydrodynamic channel flow that were studied in our previous study using the theory of the recurrence plots. The VBRP is a new graphical tool, which visualizes each point of the recurrence plot with colors depending on whether the neighboring points are recurrent or not and enhances, thus, the study of the stability of the textures of the recurrence plots, viewing them as geometrical shapes. We calculate the VBRPs of the turbulent velocity time series of a simulated channel flow monitored at constant streamwise and spanwise positions and at a number of positions along the wall-normal direction. We further estimate the visual boundary recurrence plot rates to indicate the change of the dynamics of the flow. The results highlight the flow dynamics under the influence of the magnetic field and identify additional correlations/similarities between the flow point positions within the channel. In this study, we show that these areas correspond to perturbations due to strikes that are created close to the boundary and move toward the centerline. It also seems that we have more often creation of streaks in the case of absence of magnetic field.

Scaling Analysis of Time-Reversal Asymmetries in Fully Developed Turbulence

In fully developed turbulence, there is a flux of energy from large to small scales in the inertial range until the dissipation at small scales. It is associated with irreversibility, i.e., a breaking of the time reversal symmetry. Such turbulent flows are characterized by scaling properties, and we consider here how irreversibility depends on the scale. Indicators of time-reversal symmetry for time series are tested involving triple correlations in a non-symmetric way. These indicators are built so that they are zero for a time-reversal symmetric time series, and a departure from zero is an indicator of irreversibility. We study these indicators applied to two fully developed turbulence time series, from flume tank and wind tunnel databases. It is found that irreversibility occurs in the inertial range and has scaling properties with slopes close to one. A maximum value is found around the injection scale. This confirms that the irreversibility is associated with the turbulent cascade in the inertial range and shows that the irreversibility is maximal at the injection scale, the largest scale of the turbulent cascade.

Lidar measurements of wake around a bridge deck

Remote wind sensing technologies allow for measurements in a spatial domain beyond the one accessible by anemometers fixed to a mast. Remote optical wind sensors installed at an existing bridge site can both provide new information on the wind flow upstream of the bridge and capture the disturbed flow around the structure. These possibilities are explored in the presented measurement campaign with three synchronised continuous-wave Doppler lidars at the Lysefjord bridge in Norway. In particular, the interaction between the oncoming wind flow and the bridge deck is studied in terms of the mean velocity deficit wake profile as well as the spectral turbulence characteristics. The lidar measurements are validated by comparing the lidar observations at locations undisturbed by the structure with corresponding sonic anemometer data recorded 6 m and 10 m above the deck. The consistency between the two sets of data is tested in terms of the turbulence time series, their spectral content and the statistical moments. Within the wake of the bridge, significant values of vertical velocity and inclination angles, as well as turbulence intensities are seen. Moreover, the wake region can be distinguished by its singular spectral content, cross-correlation coefficient, and coherence. The results show that the tailored configuration of the lidars succeeded in providing information on 3D turbulence around the bridge, thereby capturing the bridge aerodynamic characteristics in full-scale.

Transient numerical approximation of hyperbolic diffusions and beyond

In this paper different types of hyperbolic diffusions and their corresponding transient Fokker–Planck equation are described and numerical solutions are presented. Diffusion models were developed that can fit both the marginal distribution and correlation structure and they have found a wide application in finance, turbulence and environmental time series. Hyperbolic diffusions have a complicated structure and variety of parameters and are extremely difficult to study and to model. We propose a numerical technique that solves the one-dimensional hyperbolic Fokker–Planck equation in the time dependent case. Note that this is the first study where transient hyperbolic diffusions are considered. The numerical technique is based on an adaptive reduced basis method using a spectral element discretization. It involves enrichment and projection stages where an optimal basis is found in a dynamic way using the singular value decomposition (SVD). The approach dramatically reduces the number of degrees of freedom required to solve the problem. The numerical simulations of the Fokker–Planck equation are verified with available stationary solutions.

Exploring the Potential of Neural Networks to Predict Statistics of Solar Wind Turbulence

AbstractTime series data sets often have missing or corrupted entries, which need to be handled in subsequent data analysis. For example, in the context of space physics, calibration issues, satellite telemetry issues, and unexpected events can make parts of a time series unusable. This causes problems for understanding the dynamics of the heliosphere and space weather environment. Various approaches exist to tackle this problem, including mean/median imputation, linear interpolation, and autoregressive modeling. Here, we study the utility of artificial neural networks (ANNs) to predict statistics of sparse time series. Our focus is not on time series prediction but on gleaning the best possible information about the statistical behavior of the system. As an example application, we focus on the structure functions of turbulent time series measured in the solar wind. Using a data set with artificial gaps, a neural network is trained to predict second‐order structure functions and then tested on an unseen data set to quantify its performance. A small feedforward ANN, with only 20 hidden neurons, can predict the large‐scale fluctuation amplitudes better than mean imputation or linear interpolation when the percentage of missing data is high. Although they perform worse than the other methods when it comes to capturing both the shape and fluctuation amplitude together, their performance is better in a statistical sense for large fractions of missing data. Caveats regarding their utility, the optimization procedure, and potential future improvements are discussed.

Microbarometer measurements to probe turbulent kinetic energy in the atmospheric boundary layer

Microbarometer networks are typically in place for the detection of atmospheric infrasound waves. The monitoring of such waves can be of interest for source characterization, which include a wide array of geophysical and man-made sources, as well as atmospheric infrasound propagation studies. In such studies, the presence of turbulence and other wind-induced effects are considered a nuisance. For this reason, wind noise filters are typically in place for suppression. As Cuxart et al. [BLM (2013)] pointed out, microbarometer measurements indeed have a value for detection of local and remote turbulence and measurements can be used to estimate turbulent kinetic energy (TKE). In this study, we compare microbarometer observations at the Cabauw atmospheric research site to co-located in-situ TKE measurements. Moreover, we compare turbulence timeseries to predictions from the high-resolution HARMONIE weather model in which this quantity is parameterized. This approach has two foreseen applications: (1) modeled TKE fields could possibly help in identifying regions that are most appropriate for infrasound monitoring due to low TKE values and (2) microbarometer observations could possibly be of use in the further refining of the modeled TKE parameter.

A tutorial on reproducing a predefined autocovariance function through AR models: application to stationary homogeneous isotropic turbulence

Sequential methods for synthetic realisation of random processes have a number of advantages compared with spectral methods. In this article, the determination of optimal autoregressive (AR) models for reproducing a predefined target autocovariance function of a random process is addressed. To this end, a novel formulation of the problem is developed. This formulation is linear and generalises the well-known Yule-Walker (Y-W) equations and a recent approach based on restricted AR models (Krenk-Møller approach, K-M). Two main features characterise the introduced formulation: (i) flexibility in the choice for the autocovariance equations employed in the model determination, and (ii) flexibility in the definition of the AR model scheme. Both features were exploited by a genetic algorithm to obtain optimal AR models for the particular case of synthetic generation of homogeneous stationary isotropic turbulence time series. The obtained models improved those obtained with the Y-W and K-M approaches for the same model parsimony in terms of the global fitting of the target autocovariance function. Implications for the reproduced spectra are also discussed. The formulation for the multivariate case is also presented, highlighting the causes behind some computational bottlenecks.

Estimation of Aircraft-Dependent Bumpiness Severity in Turbulent Flight

Atmospheric turbulence threatens flight safety of civil aviation aircraft by inducing aircraft bumpiness. A severity estimation method of aircraft bumpiness in turbulent flight is explored according to in-situ Eddy Dissipation Rate (EDR) indicator. With the turbulence intensity derived from EDR value, a time series of longitudinal and vertical turbulence was generated according to von Karman turbulence model. In order to obtain the vertical acceleration response of aircraft, the continuous change of aerodynamic force on the assembly of wing and horizontal tail was computed by Unsteady Vortex Lattice Method (UVLM). The computing accuracy was improved by using semi-circle division and assigning the vortex rings on the mean camber surface. Furthermore, the adverse effects of control surface deflections on bumpiness severity estimation can be effectively removed by separating turbulence-induced and aircraft maneuvers-induced aerodynamic force change. After that, the variance of vertical acceleration, as the severity indicator of aircraft bumpiness, was obtained by Welch spectrum estimation. With the refined grid level, the pitching moment change due to control surface deflections can be solved accurately by UVLM. The instantaneous acceleration change obtained by UVLM approximates recorded acceleration data with better accuracy than linear transfer function model. A further test with a set of flight data on the same airway shows that compared with in-situ EDR indicator, the proposed method gives an aircraft-dependent estimation of bumpiness severity, which can not only be used to estimate in-situ bumpiness but also be applied to forecast the bumpiness severity of other different aircrafts.

WAVE-CURRENT INTERACTION AT A RIGHT ANGLE OVER ROUGH BEDS: TURBULENCE ANALYSIS

In the present work, an investigation on the hydrodynamics of wave-current orthogonal combined flow has been carried out. The work focuses on the effects of the oscillatory flow superposed on the current steady boundary layer, and on how the oscillatory flow affects the current velocity distribution. A laboratory experimental campaign of wave-current orthogonal interaction has been carried out in a shallow water basin at DHI Water and Environment (Horsholm, Denmark), in order to investigate the orthogonal combined flow in the presence of different roughness beds. Mean flow has been investigated by computing time- and space-averaged velocity profiles. Friction velocity and equivalent roughness have been inferred from the velocity profiles by best fit technique, in order to quantify the shear stress experienced by the current mean flow. Tests in the presence of only current, only waves and combined flow have been performed. Instantaneous velocities have been Reynolds-averaged in order to obtain turbulent fluctuations time series and compute turbulence related quantities, such as Reynolds stresses. The mean current velocity profiles have been also compared with a selection of analytical models in order to assess their validity for the case of wave-current orthogonal flow for the considered wave and current condition ranges. The analysis of the mean flow revealed a complex interaction of the waves and currents combined flow. Depending on the relative strength of the current with respect to the waves, the superposition of the oscillatory flow may determine an increase or a decrease of the bottom friction experienced by the current. Such a behavior is also strictly related to the bed physical roughness. Analysis of the turbulence Reynolds stresses seems to confirm the results of the mean flow investigation.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/GbtOgeLlVTU

Investigation of power quality and structural loads for two‐bladed wind turbines with rigid and teetered rotors using a wind turbine emulator

Two-bladed wind turbines (WTs) are recently discussed as a potential alternative to reduce the cost of energy in offshore wind farms which have a higher cost compared to onshore wind farms. However, the dynamic response and performance of these WTs are different from the three-bladed WTs. In this study, new and comprehensive models for rigid and teetered rotor WTs are developed in FAST and emulated with a setup of the previous simulation-based works. Then, the power quality issues are discussed and compared for two-bladed WTs with rigid and teetered rotors as the main contribution of this study. The performance of a WT with different rotors is evaluated and compared in terms of power fluctuations, voltage fluctuations, flicker emission level. In addition, the structural loads of the turbine are studied and compared with both rotor types. This was done in emulation and simulation by varying linear horizontal and logarithmic vertical wind shear as well as utilising a turbulent wind time series without shear. The study presents results obtained by simulation and by emulation, using a scaled-down WT emulator. It presents conclusions as to which type of rotor offers better performance for various operating conditions.

Robust estimators for free surface turbulence characterization: a stepped spillway application

Robust estimators are parameters insensitive to the presence of outliers. However, they presume the shape of the variables’ probability density function. This study exemplifies the sensitivity of turbulent quantities to the use of classic and robust estimators and the presence of outliers in turbulent flow depth time series. A wide range of turbulence quantities was analysed based upon a stepped spillway case study, using flow depths sampled with Acoustic Displacement Meters as the flow variable of interest. The studied parameters include: the expected free surface level, the expected fluctuation intensity, the depth skewness, the autocorrelation timescales, the vertical velocity fluctuation intensity, the perturbations celerity and the one-dimensional free surface turbulence spectrum. Three levels of filtering were utilised prior to applying classic and robust estimators, showing that comparable robustness can be obtained either using classic estimators together with an intermediate filtering technique or using robust estimators instead, without any filtering technique.

Multiresolution decomposition and wavelet analysis of urban aerosol fluxes in Italy and Austria

Observations of turbulent aerosol fluxes are fundamental to understand basic transport processes that govern changes of particle concentrations in the atmospheric boundary layer. The turbulent surface-atmosphere exchange of atmospheric particles can be quantified using several methods, including the eddy-covariance (EC) method and spectral flux estimation methods such as wavelet analysis and multiresolution decomposition. In this work, turbulent time series obtained by EC measurements in two different cities, Lecce (Italy) and Innsbruck (Austria), are spectrally analysed applying wavelet analysis and multiresolution decomposition, and the respective turbulent spectra are compared in these two European cities to quantify the contributions to turbulent fluxes in both the time and the frequency domains. As expected, particle emission is dominant in both cities following a similar diurnal cycle. Multiresolution decomposition reveals a similar cospectral peak of particle fluxes in both cities, with a median normalized frequency of n = 0.087 in Lecce and n = 0.086 in Innsbruck. Wavelet analysis shows that the 2–20 s time scales contribute very strongly to the particle flux in Lecce, while in Innsbruck the 20–200 s time scales are clearly dominant. In both cities, larger-sized eddies contribute only sporadically to turbulent aerosol fluxes. These results suggest that spectral similarity of urban particle number fluxes holds, to a large extent, even when comparing two very different urban environments and different meteorological conditions.