Turbulence Hypothesis Research Articles

Resistively controlled primordial magnetic turbulence decay

Context. Magnetic fields generated in the early Universe undergo turbulent decay during the radiation-dominated era. The decay is governed by a decay exponent and a decay time. It has been argued that the latter is prolonged by magnetic reconnection, which depends on the microphysical resistivity and viscosity. Turbulence, on the other hand, is not usually expected to be sensitive to microphysical dissipation, which affects only very small scales. Aims. We want to test and quantify the reconnection hypothesis in decaying hydromagnetic turbulence. Methods. We performed high-resolution numerical simulations with zero net magnetic helicity using the PENCIL CODE with up to 20483 mesh points and relate the decay time to the Alfvén time for different resistivities and viscosities. Results. The decay time is found to be longer than the Alfvén time by a factor that increases with increasing Lundquist number to the 1/4 power. The decay exponent is as expected from the conservation of the Hosking integral, but a timescale dependence on resistivity is unusual for developed turbulence and not found for hydrodynamic turbulence. In two dimensions, the Lundquist number dependence is shown to be leveling off above values of ≈25 000, independently of the value of the viscosity. Conclusions. Our numerical results suggest that resistivity effects have been overestimated in earlier work. Instead of reconnection, it may be the magnetic helicity density in smaller patches that is responsible for the resistively slow decay. The leveling off at large Lundquist number cannot currently be confirmed in three dimensions.

Simulating low-frequency wind fluctuations

Abstract. Large-scale flow structures are vital in influencing the dynamic response of floating wind turbines and wake meandering behind large offshore wind turbines. It is imperative that we develop an inflow wind turbulence model capable of replicating the large-scale and low-frequency wind fluctuations occurring in the marine atmosphere since the current turbulence models do not account well for this phenomenon. Here, we present a method to simulate low-frequency wind fluctuations. This method employs the two-dimensional (2D) spectral tensor for low-frequency, anisotropic wind fluctuations presented by Syed and Mann (2024) to generate stochastic wind fields. The simulation method generates large-scale 2D spatial wind fields for the longitudinal u and lateral v wind components, which can be converted into a frequency domain using Taylor's frozen turbulence hypothesis. The low-frequency wind turbulence is assumed to be independent of the high-frequency turbulence; thus, a broad spectral representation can be obtained just by superposing the two turbulent wind fields. The method is tested by comparing the simulated and theoretical spectra and co-coherences of the combined low- and high-frequency fluctuations. Furthermore, the low-frequency wind fluctuations can also be subjected to anisotropy. The resulting wind fields from this method can be used to analyze the impact of low-frequency wind fluctuations on wind turbine loads and dynamic response and to study the wake meandering behind large offshore wind farms.

Spatiotemporal statistics of optical turbulence beyond Taylor’s frozen turbulence hypothesis

Currently, limitations in modeling the temporal behavior of light propagating through atmospheric turbulence stem from the Taylor’s frozen turbulence hypothesis (TFTH). Indeed, under certain conditions it has been reported to be unreliable, often leading to inaccurate predictions. On the other hand, in fluid dynamics an alternative has been validated: the random sweeping hypothesis. Nevertheless, its applicability to optical turbulence has remained unexplored. This work introduces the first, to the best of our knowledge, controlled experiment testing this hypothesis on the spatiotemporal properties from image wander. The existence of two characteristic times is observed, one associated with TFTH decorrelation and a second potentially linked to the sweeping hypothesis.

A Systematic Investigation of the Applicability of Taylor’s Hypothesis in an Idealized Surface Layer

Taylor’s Frozen Turbulence Hypothesis (TH) is a critical assumption in turbulent theory and practice which allows time series of point measurements of turbulent variables to be translated to the spatial domain via the mean wind. Using a 3D array of fibre-optic distributed temperature sensing in the atmospheric surface layer over an idealized desert site we present a systematic investigation of the applicability of Taylor’s Hypothesis to atmospheric surface layer flows over a variety of conditions: unstable, near-neutral, and stable atmospheric stabilities; and multiple measurement heights between the surface and 3 m above ground level. Both spatially integrated and spatially scale-dependent eddy velocities are investigated by means of time-lagged streamwise two-point correlations and compared to the mean Eulerian wind. We find that eddies travel slower than predicted by TH at small spatial separations, as predicted by TH at separations typically between 5 and 16 m, and faster than predicted by TH at larger spatial separations. In unstable atmospheric conditions the spatial separation at which eddy velocity is larger than Eulerian velocity decreases with height.

Sources and mechanisms of flow loss and hydroacoustics in a pre-swirl stator pump-jet propulsor

Accurately identifying sources of flow loss and hydroacoustics and clarifying the mechanism of their generation are crucial for directing the optimal design of efficient and quiet pump-jet propulsors (PJPs). In this paper, numerical simulations of steady and unsteady flow are performed for a PJP equipped with pre-swirl stationary vanes, based on which both sources of flow loss and hydroacoustics are investigated at multi-level granularity. Analyses of flow efficiency and entropy generation rate are performed to identify the sources of flow loss, and analyses of thrust fluctuation and wall pressure fluctuation are conduced to identify the sources of hydroacoustics. The results indicate that the pressure drag accounts for 76% of the total drag and is mainly contributed from the stator and the duct, but the flow efficiency of the rotor is much smaller than that of the stator and the sources of the flow loss are mainly located at three regions of the rotating blades: the leading edge, the tip, and the corner of the suction surface. The hydroacoustic sources are mainly located at the leading edge and the tip of the rotating blades due to stator–rotor and duct–rotor interactions, respectively, but the Taylor's frozen turbulence hypothesis is inappropriate to describe the wake evolution of the stationary vanes owing to the potential interaction caused by the blade rotation.

Hierarchical Turbulence and Geometry Modeling: Case Study for Fan Stage Flows

Flow separations occur in the tip region when the fan is operating at the approach condition. To reduce computational cost without degrading accuracy, the hierarchical modeling approach has been developed to predict such fan flow. This allows both flow and geometry to be treated with various fidelity levels in different zones. To be specific, this is achieved by zonalizing large-eddy simulation (LES) in the fan tip region and modeling downstream stators with low-order blade body forces. This approach provides an accurate and economical prediction of separated fan flows in the stage environment. The predicted fan wake profiles show a reasonably good agreement with the hot-wire measurements considering passage-to-passage variations. Finally, the simulation data are used to assess the isotropic turbulence hypothesis that is made on fan wake in low-order acoustics models.

Pseudospectrum-based methods for estimating the wind speed and direction based on closely spaced microphone signals

Acoustic array processing can be employed to measure the wind speed and direction based on microphone signals. Turbulent pressure fluctuations picked up by microphones are referred to as wind noise. According to Taylor's frozen turbulence hypothesis, turbulent eddies retain their shape while advecting at nearly the mean wind speed and in the wind direction. It follows that wind noise propagates accordingly across a microphone array when the inter-microphone distance is smaller than the turbulence wavelength. This property can be exploited to track the orientation of the turbulence advection, and hence to characterize the wind flow. We propose beamforming and signal subspace-based methods to estimate the wind speed and direction using a compact microphone array. In particular, the pseudospectrum of measured wind noise is computed against candidate pairs of wind speed and direction. The wind speed and direction estimates are then obtained as the maximizers of the pseudospectrum. In addition, we extend an existing time difference of arrival-based method originally derived for three microphones to an arbitrary number of microphones. We evaluate the estimation accuracy of the proposed methods separately for the wind speed and direction. Possible applications include highly integrable, portable, and inexpensive anemometers for smart sensors or action cameras.

A Practical Approach for Determining Multi-Dimensional Spatial Rainfall Scaling Relations Using High-Resolution Time–Height Doppler Data from a Single Mobile Vertical Pointing Radar

The rescaling of rainfall requires measurements of rainfall rates over many dimensions. This paper develops one approach using 10 m vertical spatial observations of the Doppler spectra of falling rain every 10 s over intervals varying from 15 up to 41 min in two different locations and in two different years using two different micro-rain radars (MRR). The transformation of the temporal domain into spatial observations uses the Taylor “frozen” turbulence hypothesis to estimate an average advection speed over an entire observation interval. Thus, when no other advection estimates are possible, this paper offers a new approach for estimating the appropriate frozen turbulence advection speed by minimizing power spectral differences between the ensemble of purely spatial radial power spectra observed at all times in the vertical and those using the ensemble of temporal spectra at all heights to yield statistically reliable scaling relations. Thus, it is likely that MRR and other vertically pointing Doppler radars may often help to obviate the need for expensive and immobile large networks of instruments in order to determine such scaling relations but not the need of those radars for surveillance.

The space-time structure of turbulence for lidar-assisted wind turbine control

Lidar-assisted wind turbine control has been proven to be beneficial for turbine load reduction. It relies on the preview of incoming turbulence provided by a nacelle lidar, which allows the turbine controller to react to the flow disturbances before their impact on the turbine. When assessing its benefits, previous studies mainly use the standard turbulence parameters suggested by the IEC 61400-1 standard and assume Taylor's frozen hypothesis. Based on atmospheric turbulence observations, the parameters of the Mann spectral turbulence model differ significantly from the values recommended in the standard, and they vary, e.g., with atmospheric stability. Also, turbulence evolution from upstream to the rotor position conflicts with the frozen turbulence hypothesis, and its effect on the preview quality by a nacelle lidar still needs quantification. This work presents a simple method to extend the Mann model to account for the temporal evolution of turbulence using a space-time spectral velocity tensor. Under various atmospheric stability conditions, we derive the space-time tensor parameters and evaluate the space-time tensor using data from a five-beam lidar and a meteorological mast, we found good agreement between the space-time tensor and the measurement data. In addition, a numerical method for simulating a four-dimensional (4D) space-time velocity field based on the space-time tensor is presented. In the end, we analyze the importance of including the temporal evolution of turbulence for assessing lidar wind preview quality.

Evaluation of Turbulent Jet Characteristic Scales Using Joint Statistical Moments and an Adaptive Time-Frequency Analysis

This paper presents an analysis of turbulence characteristic scales and eddy convection velocity of jet flows computed using joint statistical moments, digital filters, and a modified version of the empirical mode decomposition (EMD). The ongoing aim of this study is to develop semi-empirical space-time cross-correlation models based on stationary statistics and jet physical lengths. Multivariate statistics are used to correlate jet properties to one-dimensional time series. The data available to this study were recorded from single-point and two-point hot-wire anemometry experiments carried out for a range of jet Mach numbers (0.2≤M≤0.8). Firstly, the jet eddy convection velocity, turbulence length, and time scales are computed using space-time cross-correlation functions. Isotropic flow and frozen turbulence hypothesis are then used to estimate the joint moments from single-point statistics in the fully developed turbulence region. An EMD-based decomposition method is presented and assessed in both the Gaussian and non-Gaussian signal regions. It is demonstrated that the artificially filtered signal reconstructs the physical properties of single and multi-point jet statistics. The relationship between central moments and joint moments presented here focuses on the region of high turbulence levels, which generates the vast majority of jet mixing noise produced by turbofan engines. Further analysis is required to extend this investigation to intermittent zones and other jet noise sources, such as jet-surface installation noise.

Modelling the spectral shape of continuous-wave lidar measurements in a turbulent wind tunnel

Abstract. This paper describes the development of a theoretical model for the turbulence spectrum measured by a short-range, continuous-wave lidar (light detection and ranging). The lidar performance was assessed by measurements conducted with two WindScanners in an open-jet wind tunnel equipped with an active grid, for a range of different turbulent wind conditions. A hot-wire anemometer is used as reference to assess the lidar's measured statistics, time series and spectra. In addition to evaluating the statistics, the correlation between the time series and the root-mean-square error (RMSE) on the wind speed, the turbulence spectrum measured by the lidar is compared with a modelled spectrum. The theoretical spectral model is applied in the frequency domain, using a Lorentzian filter in combination with Taylor's frozen turbulence hypothesis for the probe length averaging effect and an added white noise term, evaluated by qualitatively matching the lidar measurement spectrum. High goodness-of-fit coefficients and low RMSE values between the hot wire and WindScanner were observed for the measured time series. The correlation showed an inverse relationship with the prevalent turbulence intensity in the flow for cases with a comparable power spectrum shape. Larger flow structures can be captured more accurately by the lidar, whereas small-scale turbulent flow structures are partly filtered out as a result of the lidar's probe volume averaging effect. It is demonstrated that an accurate way to define the cut-off frequency at which the lidar's power spectrum starts to deviate from the hot-wire reference spectrum is the frequency at which the coherence drops below 0.5. This coherence-based cut-off frequency increases linearly with the mean wind speed and is generally an order of magnitude lower than the probe length equivalent cut-off frequency, estimated according to a simple model based on the full width at half maximum (FWHM) of the laser beam intensity along the line of sight and assuming Taylor's frozen turbulence hypothesis. A convincing match between the modelled and the measured WindScanner power spectrum was found for various different cases, which confirmed that the deviation of the lidar's measured power spectrum in the higher frequency range can be analytically explained and modelled as a combination of a Lorentzian-shaped intensity function and white noise in the lidar measurement. Although the models were developed on the basis of wind tunnel measurements, they should be applicable to atmospheric boundary layer field measurements as well.

The impact of ocean biogeochemistry on physics and its consequences for modelling shelf seas

We use modelling and assimilation tools to explore the impact of biogeochemistry on physics in the shelf sea environment, using North-West European Shelf (NWES) as a case study. We demonstrate that such impact is significant: the attenuation of light by biogeochemical substances heats up the upper 20 m of the ocean by up to 1 °C and by a similar margin cools down the ocean within the 20–200 m range of depths. We demonstrate that these changes to sea temperature influence mixing in the upper ocean and feed back into marine biology by influencing the timing of the phytoplankton bloom, as suggested by the critical turbulence hypothesis. We compare different light schemes representing the impact of biogeochemistry on physics, and show that the physics is sensitive to both the spectral resolution of radiances and the represented optically active constituents. We introduce a new development into the research version of the operational model for the NWES, in which we calculate the heat fluxes based on the spectrally resolved attenuation by the simulated biogeochemical tracers, establishing a two-way coupling between biogeochemistry and physics. We demonstrate that in the late spring–summer the two-way coupled model increases heating in the upper oceanic layer compared to the existing model and improves by 1–3 days the timing of the simulated phytoplankton bloom. This improvement is relatively small compared with the existing model bias in bloom timing, but is sufficient to have a visible impact on model skill in the free run. We also validate the skill of the two-way coupling in the context of the weakly coupled physical–biogeochemical assimilation currently used for operational forecasting of the NWES. We show that the change to the skill is negligible for analyses, but it remains to be seen how much it differs for the forecasts.

LiDAR-based detection of wind gusts: An experimental study of gust propagation speed and impact on wind power ramps

Understanding the complex behaviours inherent to the wind is a key challenge in improving the accuracy of short-term prediction models. Turbulent wind gusts are one of several factors expected to contribute to uncertainties in forecasts and can also cause turbine damage in extreme cases. This study aims to (1) evaluate how spatial gust properties map to temporal variations in power generation at the wind turbine and farm scale and (2) assess the validity of Taylor’s frozen turbulence hypothesis for gust impact prediction. First, a gust identification scheme building upon existing research is presented. Gusts are extracted from LiDAR-based near-horizontal wind fields collected throughout a year-long measurement campaign at an onshore wind farm. The tendency of gusts to induce wind power ramps is investigated, and their propagation speed is compared against the background flow. Results show that gusts are associated with increased power variability at the turbine scale and the wind farm scale, with the most noticeable effect being at the turbine level. Gusts with length scales less than one kilometre generally propagate at the rate of the background flow, whereas larger gusts travel marginally faster. The study emphasises the importance of gusts for short-term power forecasting applications and affirms the use of Taylor’s frozen turbulence hypothesis for gust impact prediction.

Sweeping Effects Modify Taylor’s Frozen Turbulence Hypothesis for Scalars in the Roughness Sublayer

AbstractTaylor’s frozen turbulence hypothesis (FTH) is investigated in the roughness sublayer of a sloped vineyard canopy using a spatial array of fine‐wire thermocouples and ultrasonic anemometers. The Ellipse Approximation (EA) method is applied to the measured space‐time temperature correlation function to delineate sweeping effects from advection velocity. Sweeping effects are explained primarily by the turbulence kinetic energy. Upon the removal of sweeping effects, the advection velocity is found to be commensurate with the mean velocity.

Three-dimensional spatiotemporal wind field reconstruction based on physics-informed deep learning

In this work, a physics-informed deep learning model is developed to achieve the reconstruction of the three-dimensional (3-D) spatiotemporal wind field in front of a wind turbine, by combining the 3-D Navier–Stokes equations and the scanning LIDAR measurements. To the best of the authors’ knowledge, this is for the first time that the full 3-D spatiotemporal wind field reconstruction is achieved based on real-time measurements and flow physics. The proposed method is evaluated using high-fidelity large eddy simulations. The results show that the wind vector field in the whole 3-D domain is predicted very accurately based on only scalar line-of-sight LIDAR measurements at sparse locations. Specifically, at the baseline case, the prediction errors for the streamwise, spanwise and vertical velocity fields are 0.263 m/s, 0.397 m/s and 0.361 m/s, respectively. The prediction errors for the horizontal and vertical direction fields are 2.84° and 2.58° which are important in tackling yaw misalignment and turbine tilt control, respectively. Further analysis shows that the 3-D wind features are captured clearly, including the evolutions of flow structures, the wind shear in vertical direction, the blade-level speed variations due to turbine rotation, and the speed variations modulated by the turbulent wind. Also, the developed model achieves short-term wind forecasting without the commonly-used Taylor’s frozen turbulence hypothesis. Furthermore it is very useful in advancing other wind energy research fields e.g. wind turbine control & monitoring, power forecasting, and resource assessments because the 3-D spatiotemporal information is important for them but not available with current sensor and prediction technologies.

The Route to Spring Phytoplankton Blooms Simulated by a Lagrangian Plankton Model

AbstractA Lagrangian plankton model (LPM) is developed, in which the motion of a large number of Lagrangian particles, representing a parcel of plankton, is calculated under the turbulence field simulated by large‐eddy simulation. A spring phytoplankton bloom is realized using the LPM, and the mechanism for its 1 generation is investigated. The criterion based on these results is proposed as , where δ E (= u ∗/f) is the scale for the Ekman boundary layer, δ S (= ) is the scale for the depth of a seasonal thermocline, u ∗ is the wind stress, Q 0 is the surface buoyancy flux, f is the Coriolis parameter, and C 1 and C 2 are constants. The critical depth hypothesis can be applied for the onset of a spring bloom, when , using the mixing layer depth instead of the mixed layer depth, as z c > C 2 δ S , but the critical turbulence hypothesis can be applied, as z c > C 1 δ E , when . A spring bloom is more likely to occur at higher latitudes, even if the atmospheric forcing is the same. The diurnal variation of Q 0 tends to increase the strength of the spring bloom at small u ∗. Furthermore, various statistics of Lagrangian particles, such as the mixing length of plankton, the residence time of plankton within the euphotic zone, and the growth of plankton clarify the movement and growth of plankton cells.

Spatial and temporal resolution of a fast-response aerodynamic pressure probe in grid-generated turbulence

The spatial and temporal resolution of a fast-response aerodynamic pressure probe (FRAP) is investigated in a benchmark flow of grid-generated turbulence. A grid with a mesh size of M=6.4 mm is tested for two different free-stream velocities, hence, resulting in Reynolds numbers of Re_M= {4300,12800}. A thorough analysis of the applicability of the underlying assumptions with regard to turbulence isotropy and homogeneity is carried out. Taylor’s frozen turbulence hypothesis is assumed for the calculation of deducible flow quantities, like the turbulent kinetic energy or the dissipation rate. Furthermore, besides the examination of statistical quantities, velocity spectra of measurements downstream of the grid are quantified. Results of a small fast-response five-hole pressure probe equipped with piezo-resistive differential pressure sensors are compared to single-wire hot-wire constant temperature anemometry data for two different wire lengths. Estimates of temporal and spatial turbulent scales (e.g., Taylor micro scale and Kolmogorov length scale) show good agreement to data in the literature but are affected by filtering effects. Especially in the energy spectra, very high bandwidth content cannot be resolved by the FRAP, which is mainly due to bandwidth limits in the temporal calibration of the FRAP and the minimal resolution of the integrated sensors.Graphic abstract

The law of the wall: A new perspective

The law of the wall, regarded as one of the very few pieces of turbulence hypothesis, predicts the mean-velocity profile (MVP) in a wall-bound flow. For about nine decades, the underlying physics of the law is deemed to be governed by an ad hoc mixing-length hypothesis. Here, we seek the origin of the law, for the first time, with the aid of a new hypothesis, which we call the mixing-instability hypothesis. The hypothesis unveils the previously unknown universal scaling behavior for the amplitude of turbulent ripples or waves (that cause spontaneous stretching and shrinking of turbulent eddies) within the overlap layer and accurately maps the experimental data of the MVPs for moderate to extremely large Reynolds numbers. This study offers a new mechanism of the momentum transfer in a turbulent wall-bound flow, calling for a revision of the conventional mixing-length hypothesis, which has persisted in standard textbooks on turbulence for many decades.

Role of Horizontal Eddy Diffusivity within the Canopy on Fire Spread

Wind profile observations are used to estimate turbulent mixing in the atmospheric boundary layer from 1 m up to 300 m height in two locations of pine forests characteristic of the southeast US region, and to 30 m height at one location in the northeast. Basic turbulence characteristics of the boundary layers above and within the canopy were measured near prescribed fires for time periods spanning the burns. Together with theoretical models for the mean horizontal velocity and empirical relations between mean flow and variance, we derive the lateral diffusivity using Taylor’s frozen turbulence hypothesis in the thin surface-fuel layer. This parameter is used in a simple 1D model to predict the spread of surface fires in different wind conditions. Initial assessments of sensitivity of the fire spread rates to the lateral diffusivity are made. The lateral diffusivity with and without fire-induced wind is estimated and associated fire spread rates are explored. Our results support the conceptual framework that eddy dynamics in the fuel layer is set by larger eddies developed in the canopy layer aloft. The presence of fire modifies the wind, hence spread rate, depending on the fire intensity.

Large-eddy simulations of the inlet grid-generated turbulence

In this paper, a new technique of turbulence generation in large eddy simulation (LES) is studied and verified. In order to generate turbulence similar to the wind tunnel test, the proposed grid inlet technique places the grid on the Inlet boundary to achieve the following effects: changing the grid size controls the turbulence integral length scale and changing the distance from inlet controls the turbulence intensity. The purpose of this paper is to explore the domain requirements of grid-inlet technology by studying the turbulence characteristics of three different grid inlets. In particular, this paper further studies the effects of domain sizes on the lateral correlation of fluctuating wind by arranging the transverse positions of monitoring points irregularly and in equal proportion. Meanwhile, the isotropic hypothesis of gird-generated turbulence is verified by power spectrum. The results show that the turbulence intensity is unaffected by the domain sizes, the larger calculation domain corresponds to the gentler changing trend of the lateral correlation of the fluctuating wind and the flow fields under the three different domain sizes basically satisfy the isotropic hypothesis. The above results are helpful for the further application of the grid inlet technique.