Spatial Power Spectral Density Research Articles

Coherent structures of elastoinertial instabilities in Taylor–Couette flows

We combine flow visualisation techniques and particle image velocimetry to experimentally investigate the higher-order transition to elastoinertial turbulence of Boger fluids ( $El = 0.11\unicode{x2013}0.34$ ) in Taylor–Couette flows. The observed route to turbulence is associated with the appearance of chaotic inflow jets, termed flame patterns, for increasing inertia, and stable structures of solitons, known as diwhirls, for decreasing inertia. We also report for the first time spatially and temporally resolved flow fields in the meridional plane for the three characteristic viscoelastic flow regimes (diwhirls, flame patterns and elastoinertial turbulence). We observe in all cases coherent structures of dynamically independent solitary vortex pairs. The stability of these coherent structures is jet-dominated and can be mainly ascribed to the high extension of the polymer chains in the inflow boundaries in the $r$ – $z$ plane. Solitary pairs are self-sustained when created through random events and do not split; instead, they merge when moving sufficiently close and annihilate when hoop stresses are not sufficient to sustain them. The highly localised and random events result in highly fluctuating, chaotic flow states. We estimate the decay exponent of spatial power spectral density, illustrating a universal scaling of $-2.5$ for elastoinertial turbulence. Based on our observations and in an effort to unify and combine precedent theories with our results, we suggest a mechanism for the origins of elastoinertial instabilities, accounting for both the effect of elasticity on the vortex formation and the effect of increasing/decreasing inertia on the flow dynamics.

A novel vector potential random flow generation method for synthesizing divergence-free homogeneous isotropic turbulence with arbitrary spectra

A novel method, known as the vector potential random flow generation (VPRFG) method, is introduced for synthesizing divergence-free homogeneous isotropic turbulence with arbitrary spectra. First, the proposed approach employs the random-flow-generation-based method to create a vector potential field. Subsequent application of the curl operation to this field produces a turbulent flow that inherently satisfies the divergence-free condition. In the formulas of the proposed method, we explicitly impose arbitrary homogeneous isotropic three-dimensional spatial cross-spectral density (CSD) and Taylor's frozen hypothesis. This ensures that the generated turbulence conforms to prescribed statistical characteristics, including energy spectra, one-dimensional spatial power spectral density (PSD), temporal PSD, spatial coherence function, turbulent kinetic energy, and Reynolds stress. Additionally, the theoretical accuracy of the proposed method is validated through numerical examples, employing the von Kármán energy spectrum as the target value. Finally, large eddy simulations of homogeneous isotropic temporal-decaying box turbulence generated by the VPRFG method demonstrate a close alignment with the experimental results.

A data-driven network decomposition of the temporal, spatial, and spectral dynamics underpinning visual-verbal working memory processes

The brain dynamics underlying working memory (WM) unroll via transient frequency-specific large-scale brain networks. This multidimensionality (time, space, and frequency) challenges traditional analyses. Through an unsupervised technique, the time delay embedded-hidden Markov model (TDE-HMM), we pursue a functional network analysis of magnetoencephalographic data from 38 healthy subjects acquired during an n-back task. Here we show that this model inferred task-specific networks with unique temporal (activation), spectral (phase-coupling connections), and spatial (power spectral density distribution) profiles. A theta frontoparietal network exerts attentional control and encodes the stimulus, an alpha temporo-occipital network rehearses the verbal information, and a broad-band frontoparietal network with a P300-like temporal profile leads the retrieval process and motor response. Therefore, this work provides a unified and integrated description of the multidimensional working memory dynamics that can be interpreted within the neuropsychological multi-component model of WM, improving the overall neurophysiological and neuropsychological comprehension of WM functioning.

Dynamic Factor of Suburban Railway Bridge Considering Random Vibration

The focus of this paper is to examine the dynamic factor of the suburban railway by utilizing the random vibration approach. Breaking through the previous methods of relying on huge amounts of measured data, herein, the dynamic factor essentially results from two major parts: the dynamic effect caused by moving train loads and that generated by track irregularity, which has clear physical significance. As the internal excitation of the vehicle–bridge system, track irregularity has strong randomness. Based on the dimension reduction method, the spatial domain power spectral density (PSD) of the track irregularity is transformed into the time-domain PSD. Therefore, the randomness of the random process is reduced by exploiting the constraint form of a random function, and then, the typical samples of the track irregularity considering randomness are constructed. Using the vehicle–bridge coupled vibration model, the standard deviation of the dynamic factor is evaluated accounting for the random track irregularity and 99.7% guarantee rate. Finally, the impact coefficient of the track irregularity on the bridge is methodically obtained. The sensitivity of the standard deviation of the dynamic factor to vehicle speed and bridge frequency is analyzed. The given solution methodology can fully take into account the randomness of the track irregularity. Thereby, it provides the dynamic factor formulas as a reference for the dynamic performance evaluation of suburban railway bridges and possible revision of current design specifications.

Plate boundary layer transition regulation based on plasma actuation array at Mach 6

An experimental study on controlling hypersonic boundary layer transition using a surface arc plasma actuation array was conducted. First, base boundary transition characteristics were analyzed in virtue of various sensors and high-speed schlieren, and the transition criterion was established based on the critical value of schlieren spatial power spectral density resolution. Then, the influence of three different actuation frequencies (8, 34, and 55 kHz) was studied based on linear stability theory analysis. The impact of different actuation frequencies on the dominant unstable waves in the boundary layer was analyzed, and a transition criterion under the regulation of plasma actuation was proposed. Finally, the proper orthogonal decomposition method was used to analyze the influence of different actuation frequencies on the unstable characteristic structures. Based on the research, the efficacy of plasma actuation array in promoting transition is verified, the corresponding regulation mechanism is summarized, and transition regulation mechanization is refined.

The Distribution of Small‐Scale Irregularities in the E‐Region, and Its Tendency to Match the Spectrum of Field‐Aligned Current Structures in the F‐Region

AbstractWe associate new data from icebear, a coherent scatter radar located in Saskatchewan, Canada, with scale‐dependent physics in the ionosphere. We subject the large‐scale icebear 3D echo patterns (treated as 2D point clouds) to a data analysis technique hitherto never applied to the ionosphere, a technique that is widely applied in cosmological red‐shift surveys to characterize the spatial clustering of galaxies. The technique results in a novel method to calculate the spatial power spectral density of the greater ionospheric irregularity field. We compare results from this method to in‐situ plasma density and magnetic field observations from the Swarm mission. We show that there is a remarkable similarity between echo clustering spectra in the E‐region and the field‐aligned current structuring spectrum observed in the F‐region: a clear and characteristic preferred scale (5 km) both in the E‐ and F‐region spectra. We discuss the possibility that this represents evidence of an energy injection into the ionospheric irregularity field via energetic particle precipitation, but offer alternative interpretations with wider connotations for the ionosphere‐magnetosphere system. These findings open new and promising avenues of research for the study of the location of ionospheric scatter echoes with 3D information. It constitutes a novel way to consider the pattern of ionospheric irregularities over wide fields of view when there is an abundance of radar echoes, which allows for the analysis of radar data as point clouds.

Digital twin of atmospheric turbulence phase screens based on deep neural networks.

The digital twin of optical systems can imitate its response to outer environments through connecting outputs from data-driven optical element models with numerical simulation methods, which could be used for system design, test and troubleshooting. Data-driven optical element models are essential blocks in digital twins. It can not only transform data obtained from sensors in real optical systems to states of optical elements in digital twins, but also simulate behaviors of optical elements with real measurements as prior conditions. For ground based optical telescopes, the digital twin of atmospheric turbulence phase screens is an important block to be developed. The digital twin of atmospheric turbulence phase screens should be able to generate phase screens with infinite length and high similarities to real measurements. In this paper, we propose a novel method to build the digital twin of atmospheric turbulence phase screens. Our method uses two deep neural networks to learn mapping functions between the space of parameters and the space of phase screens and vice versa. Meanwhile, a forecasting deep neural network is proposed to generate parameters for the next phase screen according to parameters extracted from a previous phase screen. The method proposed in this paper could be used to directly produce phase screens with infinite length and of any temporal or spatial power spectral density that follows statistical distributions of real measurements, which makes it an appropriate block in digital twins of ground based optical systems.

Marine aerosols produced by ocean internal waves

The objective of this work was to investigate the hypothesis that oceanic internal waves could modulate the production of atmospheric aerosols by modulating sea surface roughness. Airborne profiling lidar was used to measure the displacement of the subsurface scattering layer by internal waves, the distribution of surface roughness, and the aerosol concentration over the internal waves. The direct correlation between internal wave displacement and aerosol density was not statistically significant, primarily due to other processes causing mixing in the atmosphere. However, we found that the magnitude of the aerosol spatial power spectral density at the internal wave wavelength was significantly correlated with the internal wave magnitude. We developed a simple model to describe the interactions, which provided excellent agreement with the measurements for two out of three flights. The disagreement for the third flight is thought to be a result of the deeper thermocline on that day, which put the deeper parts of the internal waves out of the depth range covered by the lidar. The conclusion is that internal waves affect aerosol production over the ocean under certain environmental conditions.

Effect of Manufacturing Inaccuracies on the Wake Past Asymmetric Airfoil by PIV

The effect of manufacturing geometry deviations on the flow past a NACA 64(3)-618 asymmetric airfoil is studied. This airfoil is 3D printed according to the coordinates from a public database. An optical high-precision 3D scanner, GOM Atos, measures the difference from the idealized model. Based on this difference, another model is prepared with a physical output closer to the ideal model. The velocity in the near wake (0–0.4 chord) is measured by using the Particle Image Velocimetry (PIV) technique. This work compares the wakes past three airfoil realizations, which differ in their similarity to the original design (none of the realizations is identical to the original design). The chord-based Reynolds number ranges from 1.6×104 to 1.6×105. The ensemble average velocity is used for the determination of the wake width and for the rough estimation of the drag coefficient. The lift coefficient is measured directly by using force balance. We discuss the origin of turbulent kinetic energy in terms of anisotropy (at least in 2D) and the length-scales of fluctuations across the wake. The spatial power spectral density is shown. The autocorrelation function of the cross-stream velocity detects the regime of the von Karmán vortex street at lower velocities.

State-of-the-Art Versus Deep Learning: A Comparative Study of Motor Imagery Decoding Techniques

State-of-the-art techniques (SOTA) for motor imagery decoding have largely involved the use of common spatial patterns (CSP) and power spectral density (PSD), for feature extraction. Other frequency transforms, such as wavelets and empirical mode decomposition (EMD) have also been used but the aforementioned two have been the most popular. For classification, linear discriminant analysis (LDA) and support vector machines (SVM) have been mostly used. It is, however, worth investigating other approaches, such as deep learning, which offer a potential for improvement, but are not yet mainstream. Deep learning techniques based on neural networks (NNs) have been underexplored in motor imagery processing. Considering their success in other fields, which speaks to their potential for obtaining improved results over the SOTA, they should be explored for motor imagery decoding. This study takes a comparative approach in the use of deep learning as compared with the SOTA. From our findings, we infer that neural networks are suitable for motor imagery decoding and might be preferable over the SOTA. The use of specific feature extraction is also not as necessary as seen with SOTA approaches, though it might offer some gains in performance. Our results show a statistically significant improvement in decoding accuracies, up to 20% increase, with the use of NNs as compared with the SOTA. Also, we conclude that the use of crops for data augmentation might yield better results with shallow architectures as against deeper ones and that there might be other factors affecting the effectiveness of crops, needing further investigation.

Sea Surface Temperature Intercomparison in the Framework of the Copernicus Climate Change Service (C3S)

AbstractA joint effort between the Copernicus Climate Change Service (C3S) and the Group for High Resolution Sea Surface Temperature (GHRSST) has been dedicated to an intercomparison study of eight global gap-free sea surface temperature (SST) products to assess their accurate representation of the SST relevant to climate analysis. In general, all SST products show consistent spatial patterns and temporal variability during the overlapping time period (2003–18). The main differences between each product are located in the western boundary current and Antarctic Circumpolar Current regions. Linear trends display consistent SST spatial patterns among all products and exhibit a strong warming trend from 2012 to 2018 with the Pacific Ocean basin as the main contributor. The SST discrepancy between all SST products is very small compared to the significant warming trend. Spatial power spectral density shows that the interpolation into 1° spatial resolution has negligible impacts on our results. The global mean SST time series reveals larger differences among all SST products during the early period of the satellite era (1982–2002) when there were fewer observations, indicating that the observation frequency is the main constraint of the SST climatology. The maturity matrix scores, which present the maturity of each product in terms of documentation, storage, and dissemination but not the scientific quality, demonstrate that ESA-CCI and OSTIA SST are well documented for users’ convenience. Improvements could be made for MGDSST and BoM SST. Finally, we have recommended that these SST products can be used for fundamental climate applications and climate studies (e.g., El Niño).

Simulation of Pavement Random Excitation Based on Harmonic Superposition Method

The road input model is very important in the analysis of vehicle ride comfort and handling stability. Based on the analysis of the relationship between the spatial frequency power spectral density and the time power spectral density of the road, the road signal generation model is established. The simulation is carried out under different vehicle speeds, and the B and C-level random road time excitation signals are generated. The power spectral density is used to compare the simulation results of the model with the road classification standard. The experimental results show that the results are accurate and can provide reliable excitation signals for vehicle control research.

Analytical and experimental investigation of vibration characteristics induced by tribofilm-asperity interactions in hydrodynamic journal bearings

Vibration analysis is an effective approach to condition monitoring of hydrodynamic journal bearings. However, the analysis is largely based on the understanding of asperity-asperity interactions due to severe wears in the late phase of bearing lifetime. It often provides very tight leading time for maintenance actions. Aiming at developing effective techniques for early wear monitoring, this paper investigates the excitation mechanisms and contributions of Tribofilm-Asperity Interaction (TAI) that occurs in the hydrodynamic lubrication regime of journal bearings. Analytical expressions for the microscopic pressure fluctuations with respect to the surface topography are derived using the perturbation techniques. The Spatial Power Spectral Density (SPSD), a feature of the non-Gaussian roughness surfaces for early wear, is used to analyse the microscopic pressure fluctuations. The effect of the SPSD and operating conditions on the random excitation are evaluated through numerical simulations. The bandwidth of such random excitation depends on the SPSD of dynamic asperities and rotational speeds simultaneously. The excitation intensity increases when the standard deviation or correlation length of the surface parameters increases. These agree well with the measurements for wide bearing conditions including different degrees of wears. This new efficient analysis and insightful findings provide new understanding for characterising noisy vibration signals for early wear monitoring of journal bearings.

Effect and its mechanism of spatial coherence of track irregularity on dynamic responses of railway vehicles

A running vehicle is subjected to multiple stochastic excitations due to the irregular profiles of the wheels and rails. The combined wheel-rail irregularities on each wheel can be partly incoherent and partly coherent in reality. As a result, different assumptions for the coherence of such irregularities have been adopted in vibration and noise simulations so that vehicle-track dynamic analysis can be conducted. Less attention has been paid to the effects of these assumptions on dynamic responses of railway vehicles in a wide frequency range. The aim of this study is to theoretically investigate the effects of the spatial coherence of track irregularities on the dynamic behaviors of a two-dimensional vehicle. Two frequency-domain methods that have been verified using a time-domain method are presented first to calculate the dynamic responses of the vehicle. A new expression of the power spectral density (PSD) function of the excitations comprises an admittance coefficient, a coherence matrix, and a spatial PSD function of the track irregularities. The PSD functions of the responses of the vehicle are derived analytically. It is then illustrated that the periodic fluctuations of response spectra are caused by the spatial coherence of the excitations by introducing the concept of coherence scales. Finally, it is proved that the difference between the responses under coherent and incoherent excitations become insignificant when the wavelength of the irregularity is less than the critical wavelength.

Effects of mirror seeing on high-contrast adaptive optics instruments

Ground-based direct imaging surveys like the Gemini Planet Imager Exoplanet Survey (GPIES) rely on Adaptive Optics (AO) systems to image and characterize exoplanets that are up to a million times fainter than their host stars. One factor that can reduce AO performance is turbulence induced by temperature differences in the instrument's immediate surroundings (e.g.: "dome seeing" or "mirror seeing"). In this analysis we use science observations, AO telemetry, and environmental data from September 2014 to February 2017 of the GPIES campaign to quantify the effects of "mirror seeing" on the performance of the GPI instrument. We show that GPI performance is optimal when the primary mirror (M1) is in equilibrium with the outside air temperature. We then examine the characteristics of mirror seeing by calculating the power spectral densities (PSD) of spatial and temporal Fourier modes. Inside the inertial range of the PSDs, we find that the spatial PSD amplitude increases when M1 is out of equilibrium and that the integrated turbulence may exhibit deviations from Kolmogorov atmospheric turbulence models and from the 1-layer frozen flow model. We conclude with an assessment of the current temperature control and ventilation strategy at Gemini South.

Stochastic analysis of nonlinear wave energy converters via statistical linearization

In the initial stages of wave energy converter development, a wide range of design parameters should be tested and analyzed across all operational sea states. As a result, it is required to conduct a large number of time domain simulations that are computationally expensive. The following study presents the application of a fast and high-fidelity alternative technique, named statistical linearization (SL), that can be used for the stochastic analysis of nonlinear wave energy converters. The method consists of an approximate solution that allows one to quickly estimate the contribution of nonlinear terms using a probabilistic model. The application of the statistical linearization is demonstrated using three conceptually different wave energy converters, a point absorber, an oscillating wave surge converter, and an oscillating water column, with distinct nonlinear dynamics. The performance of SL is assessed against nonlinear time-domain simulations in terms of spatial response distributions and power spectral densities of responses and excitation loads, mean offsets, mean absorbed power and equivalent linear terms. The results show a good agreement between the two types of models for all wave energy converters considered, while showing that SL is approximately 3 to 4 orders of magnitude faster than the time domain model.

Semi-Supervised Multichannel Speech Enhancement With a Deep Speech Prior

This paper describes a semi-supervised multichannel speech enhancement method that uses clean speech data for prior training. Although multichannel nonnegative matrix factorization (MNMF) and its constrained variant called independent low-rank matrix analysis (ILRMA) have successfully been used for unsupervised speech enhancement, the low-rank assumption on the power spectral densities (PSDs) of all sources (speech and noise) does not hold in reality. To solve this problem, we replace a low-rank speech model with a deep generative speech model, i.e., formulate a probabilistic model of noisy speech by integrating a deep speech model, a low-rank noise model, and a full-rank or rank-1 model of spatial characteristics of speech and noise. The deep speech model is trained from clean speech data in an unsupervised auto-encoding variational Bayesian manner. Given multichannel noisy speech spectra, the full-rank or rank-1 spatial covariance matrices and PSDs of speech and noise are estimated in an unsupervised maximum-likelihood manner. Experimental results showed that the full-rank version of the proposed method was significantly better than MNMF, ILRMA, and the rank-1 version. We confirmed that the initialization-sensitivity and local-optimum problems of MNMF with many spatial parameters can be solved by incorporating the precise speech model.

Spatial power spectral density estimation using a Welch coprime sensor array processor.

A coprime sensor array (CSA) is a sparse array geometry that interleaves two spatially undersampled uniform linear arrays (ULAs) with coprime undersampling factors. The CSA product processor achieves an asymptotically unbiased spatial power spectral density (PSD) estimate using far fewer sensors than a conventional ULA beamformer, but at the expense of increased sidelobes and variance. Nonstationary underwater sonar environments often preclude increasing the number of snapshots required to achieve a desirable PSD variance. Bartlett's and Welch's methods improve PSD variance by O(K) at the expense of resolution without requiring additional snapshots by averaging uncorrelated PSD estimates obtained using K array segments. This paper proposes the Welch overlapping segment averaging product (WOSA-product) processor for coprime arrays to achieve unambiguous PSD estimates with desirable variance properties for passive direction of arrival estimation. The first two moments of the WOSA-product processor's spatial PSD estimate are derived in closed-form for spatially white Gaussian processes. Monte Carlo simulations verify the variance reduction predicted by the analytical derivation for white processes and planewave arrivals, and the effects of segment length on resolution, variance reduction, and peak sidelobe levels are discussed.

Beam smoothing by a diffraction-weakened lens array combining with induced spatial incoherence.

The smoothing scheme combining a diffraction-weakened lens array with the induced spatial incoherence method is proposed and demonstrated to be an efficient smoothing scheme for broadband laser systems. In our simulation, the RMS illumination nonuniformity of the target spot is reduced to 2% after sufficient smoothing time. The temporal characteristics and spatial power spectral density of the scheme are theoretically analyzed. When the incident light has intensity fluctuations, the uniformity of the target spot is stable, which means a robust smoothing scheme, and which predicts practical applications to the smoothing of broadband laser systems.

Detection and visualization of water surface three-wave resonance via a synthetic Schlieren method

Three-wave resonance is one of the most fundamental energy-transfer mechanisms that can occur among weakly nonlinear surface waves. Here we show experimentally that if two source waves are propagating at an angle to each other, the conditions for three-wave resonances are satisfied and a third resultant wave is produced. We present 3D visualization of surface waves using the Free-Surface Synthetic Schlieren method, which removes the need for the addition of a light-diffusing agent, thereby retaining the surface tension and viscous properties of water. For three triad frequencies, we compute the average temporal power spectral density (PSD) of the wave heights. The direction of wave propagation is visualized by integrating the temporal PSD and by obtaining the average spatial PSD for each triad. Our results are in good agreement with the theory.