Two-dimensional Energy Spectra Research Articles

Exploring multiple phases and first-order phase transitions in Kármán Vortex Street

Kármán Vortex Street, a fascinating phenomenon of fluid dynamics, has intrigued the scientific community for a long time. Many researchers have dedicated their efforts to unraveling the essence of this intriguing flow pattern. Here, we apply the lattice Boltzmann method with curved boundary conditions to simulate flows around a circular cylinder and study the emergence of Kármán Vortex Street using the eigen microstate approach, which can identify phase transition and its order-parameter. At low Reynolds number, there is only one dominant eigen microstate W1 of laminar flow. At Rec1 = 53.6, there is a phase transition with the emergence of an eigen microstate pair W2,3 of pressure and velocity fields. Further at Rec2. = 56, there is another phase transition with the emergence of two eigen microstate pairs W4,5 and W6,7. Using the renormalization group theory of eigen microstate, both phase transitions are determined to be first-order. The two-dimensional energy spectrum of eigen microstate for W1, W2,3 after Rec1, W4–7 after Rec2 exhibit −5/3 power-law behavior of Kolnogorov’s K41 theory. These results reveal the complexity and provide an analysis of the Kármán Vortex Street from the perspective of phase transitions.

Model-based spectral coherence analysis

Recent data-driven efforts have utilized spectral decomposition techniques to uncover the geometric self-similarity of dominant motions in the logarithmic layer, and thereby validate the attached eddy model. In this paper, we evaluate the predictive capability of the stochastically forced linearized Navier–Stokes equations in capturing such structural features in turbulent channel flow at$Re_\tau =2003$. We use the linear coherence spectrum to quantify the wall-normal coherence within the velocity field generated by the linearized dynamics. In addition to the linearized Navier–Stokes equations around the turbulent mean velocity profile, we consider an enhanced variant in which molecular viscosity is augmented with turbulent eddy-viscosity. We use judiciously shaped white- and coloured-in-time stochastic forcing to generate a statistical response with energetic attributes that are consistent with the results of direct numerical simulation (DNS). Specifically, white-in-time forcing is scaled to ensure that the two-dimensional energy spectrum is reproduced and coloured-in-time forcing is shaped to match normal and shear stress profiles. We show that the addition of eddy-viscosity significantly strengthens the self-similar attributes of the resulting stochastic velocity field within the logarithmic layer and leads to an inner-scaled coherence spectrum. We use this coherence spectrum to extract the energetic signature of self-similar motions that actively contribute to momentum transfer and are responsible for producing Reynolds shear stress. Our findings support the use of coloured-in-time forcing in conjunction with the dynamic damping afforded by turbulent eddy-viscosity in improving predictions of the scaling trends associated with such active motions in accordance with DNS-based spectral decomposition.

Power Equipment Fault Diagnosis Method Based on Energy Spectrogram and Deep Learning.

With the development of industrial manufacturing intelligence, the role of rotating machinery in industrial production and life is more and more important. Aiming at the problems of the complex and changeable working environment of rolling bearings and limited computing ability, fault feature information cannot be effectively extracted, and the current deep learning model is difficult to be compatible with lightweight and high efficiency. Therefore, this paper proposes a fault detection method for power equipment based on an energy spectrum diagram and deep learning. Firstly, a novel two-dimensional time-frequency feature representation method and energy spectrum feature map based on wavelet packet transform is proposed, and an energy spectrum feature map dataset is made for subsequent diagnosis. This method can realize multi-resolution analysis, fully extract the feature information contained in the fault signal, and accelerate the convergence of the subsequent diagnosis model. Secondly, a lightweight residual dense convolutional neural network model (LR-DenseNet) is proposed. This model combines the advantages of residual learning and a dense connection, and can not only extract deep features more easily, but can also effectively use shallow features. Then, based on the lightweight residual dense convolutional neural network model, an LR-DenseSENet model is proposed. By introducing the transfer learning strategy and adding the channel domain, an attention mechanism is added to the channel feature fusion layer, with the accuracy of detection up to 99.4%, and the amount of parameter calculation greatly reduced to one-fifth of that of VGG. Finally, through an experimental analysis, it is verified that the fault detection model designed in this paper based on the combination of an energy spectrum feature map and LR-DenseSENet achieves a satisfactory detection effect.

Theory of anisotropic superfluid 4He counterflow turbulence.

We develop a theory of strong anisotropy of the energy spectra in the thermally driven turbulent counterflow of superfluid 4He. The key ingredients of the theory are the three-dimensional differential closure for the vector of the energy flux and the anisotropy of the mutual friction force. We suggest an approximate analytic solution of the resulting energy-rate equation, which is fully supported by our numerical solution. The two-dimensional energy spectrum is strongly confined in the direction of the counterflow velocity. In agreement with the experiments, the energy spectra in the direction orthogonal to the counterflow exhibit two scaling ranges: a near-classical non-universal cascade dominated range and a universal critical regime at large wavenumbers. The theory predicts the dependence of various details of the spectra and the transition to the universal critical regime on the flow parameters.This article is part of the theme issue ‘Scaling the turbulence edifice (part 2)’.

Turbulent flow in curved channels

Fully developed turbulent flow in channels with mild to strong longitudinal curvature is studied by direct numerical simulations. The Reynolds based on the bulk mean velocity and channel half-width $\delta$ is fixed at $20\,000$ , resulting in a friction Reynolds number of approximately 1000. Four cases are considered with curvature varying from $\gamma = 2\delta /r_c = 0.033$ to 0.333, where $r_c$ is the curvature radius at the channel centre. Substantial differences between the mean wall shear stress on the convex and concave walls are already observed for $\gamma = 0.033$ . A log-law region is absent and a region with nearly constant mean angular momentum develops in the channel centre for strong curvatures. Spanwise and wall-normal velocity fluctuations are strongly amplified by curvature in the outer region of the concave channel side. Only near the walls, where curvature effects are relatively weak, do the mean velocity and velocity fluctuation profiles approximately collapse when scaled by wall units based on the local friction velocity. Budgets of the streamwise and wall-normal Reynolds-stress equations are presented and turbulence structures are investigated through visualizations and spectra. In the case with strongest curvature, the flow relaminarizes locally near the convex wall. On the concave channel side, large elongated streamwise vortices reminiscent of Taylor–Görtler vortices develop for all curvatures considered. The maximum in the premultiplied two-dimensional wall-normal energy spectrum and co-spectrum shifts towards larger scales with increasing curvature. The large scales substantially contribute to the wall-normal velocity fluctuations and momentum transport on the concave channel side.

A Nuclide Recognition Method for Nuclear Robot System

In the real energy spectrum attenuation environment, many traditional nuclide identification methods for nuclear robot systems have problems such as using only part of the energy spectrum curve, being susceptible to noise, and having low recognition accuracy. Proposes an energy spectrum nuclide recognition method based on S-transform (ST) and Mahalanobis distance-based support vector machine (MSVM). Regarding the energy spectrum curve as a non-stationary signal, combined with the widely used S transformation method in signal transformation, the energy spectrum data is two-dimensional, Then use two-dimensional principal component analysis(2D-PCA) to reduce the dimension of the two-dimensional energy spectrum data for feature extraction, and design a support vector machine (SVM) classifier based on Mahalanobis distance to realize the identification of energy spectrum nuclides. Finally, experiments are carried out with simulated nuclide energy spectrum data based on Geant4. The experimental results show that this method effectively improves the accuracy of energy spectrum nuclide recognition by using full spectrum information. At the same time, experiments are carried out on the nuclide energy spectrum data of different detection distances obtained by the NaI detector in the real environment, and it is verified that the algorithm proposed in this paper also has a good recognition performance for the nuclide energy spectrum collected in the real environment.

Terahertz plasmons in doped HgTe quantum well heterostructures: dispersion, losses, and amplification.

We have calculated two-dimensional plasmon energy spectra in HgTe/CdHgTe quantum wells with normal, gapless, and inverted energy spectra with different electron concentrations, taking into account spatial dispersion of electron polarizability and plasmon interaction with the optical phonons. The spectra of the absorption coefficients of two-dimensional plasmons are found. It is shown that an increase of electron concentration in a quantum well leads to a decrease in the plasmon absorption coefficient. We have calculated the probabilities to recombine via the plasmon emission for nonequilibrium holes. The threshold concentrations of the nonequilibrium holes, above which the plasmon amplification is possible, have been calculated for various electron concentrations. It is shown that the presence of equilibrium electrons can significantly reduce the threshold hole concentration required for amplification of plasmon in the terahertz wavelength region. The dependencies of threshold hole concentration on electron concentration for different quantum wells are discussed. Gain spectra of the two-dimension plasmon are calculated.

Active and inactive components of the streamwise velocity in wall-bounded turbulence

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Optical fiber-based ZnS(Ag) detector for selectively detecting alpha particles

In alpha radionuclide therapy, an optical fiber-based alpha particle detector is a new tool that could possibly be employed for the direct detection of alpha particles in subjects. Thus, in the present study, we developed an optical fiber-based alpha particle detector. The alpha particle detector was made of a 1mm diameter, 10 cm long plastic double clad optical fiber drilled a 0.7 mm diameter, 2 mm depth open space at the one end of the fiber. Silver-doped zinc sulfide (ZnS (Ag)) was painted inside this open space to form a ZnS(Ag) small scintillation chamber. To conduct performance comparisons, we also developed a fiber detector using the same fiber in which a Ce-doped Lu1.8Y0·2SiO5 (LYSO(Ce)) scintillator with dimensions of 0.32 mm × 0.5 mm × 5 mm was inserted. Both fiber detectors were wrapped in aluminized Mylar and optically coupled to a position sensitive photomultiplier tube, before calculating the two-dimensional distributions, energy, and pulse shape spectra. For 5.5-MeV alpha particles, the ZnS(Ag) fiber detector produced ~ 5 times larger pulse heights and the count rate was ~2 times higher compared with those using the LYSO(Ce) fiber detector. For the maximum energy 2.28-MeV beta particles and 0.66-MeV gamma photons, the ZnS(Ag) fiber detector produced no counts, but it yielded small counts from natural alpha particles. Our results confirmed that the ZnS(Ag) fiber detector developed in this study could selectively detect alpha particles and it was insensitive to beta particles and gamma photons.

Statistical behaviour of self-similar structures in canonical wall turbulence

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Near-wall patch representation of wall-bounded turbulence

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Recovering the Eulerian energy spectrum from noisy Lagrangian tracers

We consider the time-sequential state estimation of a flow field given a stream of noisy measurements that are provided by instruments advected by the flow, known as Lagrangian tracers or drifters. Lagrangian drifters collect real-time data as they move through the velocity field and are an important data collection method for atmospheric and oceanic measurements. We quantify the recovery of the Eulerian energy spectra from observations of Lagrangian drifters. This is performed by utilizing special Lagrangian data assimilation algorithms, known as conditionally Gaussian nonlinear filters. We address the following questions: how much of the turbulent Eulerian energy spectra can be recovered from assimilation of Lagrangian trajectory data and how accurately are the various energetic scales recovered relative to the truth. These issues are primarily studied in the perfect model scenario, but we quantify recovery due to model error by reduced order models via spectral truncation of the forecast model. We demonstrate high recovery skill of the two-dimensional turbulent energy spectra for both an exact filter and an imperfect filter, based on extreme localization of the covariance matrix, which is vastly cheaper than the exact filter, for both an inverse cascade spectrum with slope k−5∕3 and a direct cascade spectrum with slope k−3. The dependence of the spectral energy recovery skill on the number of tracers and the spectral truncation grid size is also studied.

Photoelectron spectra after multiphoton ionization of Li atoms in the one-photon Rabi-flopping regime

We calculate two-dimensional photoelectron momentum distributions and energy spectra after multiphoton ionization of Li atoms subject to intense laser fields in one-photon Rabi-flopping regime. The time-dependent Schr\"{o}dinger equation is solved within the single-active-electron approximation using a model potential which reproduces accurately the binding energies and dipole matrix elements of the Li atom. Interaction with the external electromagnetic field is treated within the dipole approximation. We show that the Rabi oscillations of the population between the ground $2s$ state and the excited $2p$ state in the one-photon resonance regime are reflected in the energy spectra of emitted photoelectrons which manifest interference structures with minima. Transformations of the interference structures in the photoelectron energy spectra caused by the variation of the laser peak intensity and pulse duration are analyzed.

Exact solution of the compressible Euler–Helmholtz equation and the millennium prize problem generalization

SummaryFor the first time the exact strong solution of the three-dimensional (3D) compressible Euler–Helmholtz (EH) vortex equation in unbounded space is obtained. It corresponds to the general solution obtained in Euler variables for the 3D Riemann–Hopf (RH) equation and has a singularity in finite time. The exact closed description for the evolution of all one and multi point moments of the hydrodynamic fields and their spectra is now possible and thus, the mysterious turbulence problem has the exact solution for this case. As an example, for the first time the two-dimensional (2D) energy spectrum in the inertial scale interval is obtained directly from the exact solution of compressible 2D Navier–Stokes (NS) equation. For this purpose, a smooth continuation at all times for these exact solutions to the EH and RH equations is obtained by introducing a super-threshold homogeneous friction or any even extremely low effective viscosity. A new, smooth for all time, analytic solutions to the 1D, 2D and 3D NS equations is obtained. This solution coincides with the above-mentioned modified by viscosity solutions to the EH and RH equations, when also taking into account a linear relation between the pressure and the velocity field divergence, which is well known for the systems far from the equilibrium with relatively large second viscosity. This gives the positive answer to the generalization of the millennium prize problem (www.claymath.org) for the case of the compressible NS equation. Indeed, earlier only a negative answer to the problem of the existence of smooth solutions for any finite time has been a priori considered for the compressible case with the finite initial energy of the smooth velocity field in the unbounded space.

Characterizing ocean ambient noise using infrasound network

The ability of the International Monitoring System (IMS) global infrasound network to detect atmospheric explosions and events of interest strongly depends on station specific ambient noise signatures which include both incoherent wind noise and real coherent infrasonic waves. To characterize the coherent ambient noise, broadband array processing was performed on historical continuous IMS recordings. Ocean wave interactions contribute to the atmospheric coherent ambient noise field, and we apply wave action models to model these microbarom sources. We use two-dimensional energy spectrum ocean wave products to build a global reference database of oceanic noise sources. Then, we compare observed and modeled directional microbarom amplitudes at several stations. The expected benefits of such studies concern the use complementary data to finely characterize the coupling mechanisms at the ocean-atmosphere interface. In return, better knowledge of ambient ocean noise sources opens new perspectives not only by enhancing the characterization of explosive atmospheric events, but also by providing additional integrated constraints on middle atmosphere dynamics and disturbances where data coverage is otherwise sparse.

Computational domain length and Reynolds number effects on large-scale coherent motions in turbulent pipe flow

ABSTRACTWe present results from direct numerical simulations (DNS) of turbulent pipe flow at shear Reynolds numbers up to Reτ = 1500 using different computational domains with lengths up to . The objectives are to analyse the effect of the finite size of the periodic pipe domain on large flow structures in dependency of Reτ and to assess a minimum required for relevant turbulent scales to be captured and a minimum Reτ for very large-scale motions (VLSM) to be analysed. Analysing one-point statistics revealed that the mean velocity profile is invariant for . The wall-normal location at which deviations occur in shorter domains changes strongly with increasing Reτ from the near-wall region to the outer layer, where VLSM are believed to live. The root mean square velocity profiles exhibit domain length dependencies for pipes shorter than 14R and 7R depending on Reτ. For all Reτ, the higher-order statistical moments show only weak dependencies and only for the shortest domain considered here. However, the analysis of one- and two-dimensional pre-multiplied energy spectra revealed that even for larger , not all physically relevant scales are fully captured, even though the aforementioned statistics are in good agreement with the literature. We found to be sufficiently large to capture VLSM-relevant turbulent scales in the considered range of Reτ based on our definition of an integral energy threshold of 10%. The requirement to capture at least 1/10 of the global maximum energy level is justified by a 14% increase of the streamwise turbulence intensity in the outer region between Reτ = 720 and 1500, which can be related to VLSM-relevant length scales. Based on this scaling anomaly, we found Reτ⪆1500 to be a necessary minimum requirement to investigate VLSM-related effects in pipe flow, even though the streamwise energy spectra does not yet indicate sufficient scale separation between the most energetic and the very long motions.

Capturing Taylor–Görtler vortices in a streamwise-rotating channel at very high rotation numbers

In this paper, we study the scales and dynamics of Taylor–Görtler (TG) vortices in streamwise-rotating turbulent channel flows at moderate and high rotation numbers ($Ro_{\unicode[STIX]{x1D70F}}=7.5$, 15, 30, 75 and 150) with a fixed Reynolds number. In order to precisely capture TG vortices in the streamwise and spanwise directions, direct numerical simulations have been performed on 15 test cases of different domain sizes and rotation numbers. A two-layer pattern of TG vortices is identified, and the characteristic length scales of TG vortices are quantified using the premultiplied energy spectra. It is observed that as the rotation number increases, the spanwise scale of TG vortices remains stable but the streamwise scale increases rapidly. Three criteria have been used for judging a domain-size-independent solution in both physical and spectral spaces. The weakest criterion ensures accurate predictions of the first- and second-order statistical moments of the velocity, which requires a minimum streamwise domain size of $L_{1}=64\unicode[STIX]{x03C0}h$, where $h$ is one-half the channel height. However, the streamwise domain size needs to be stretched drastically to $L_{1}=512\unicode[STIX]{x03C0}h$ if the most stringent criterion is considered, which demands that all energetic eddies be fully captured based on a predefined threshold value (i.e. $12.5\,\%$ of the peak value) of the premultiplied two-dimensional energy spectrum. The effects of streamwise system rotation on the scales and dynamics of TG vortices are investigated by comparing the statistical results of rotating and non-rotating channel flows, and through the analysis of two-point correlations, premultiplied energy spectra, and budget balance of turbulent stresses.

Two-dimensional energy spectra in high-Reynolds-number turbulent boundary layers

Here, we report the measurements of two-dimensional (2-D) spectra of the streamwise velocity ($u$) in a high-Reynolds-number turbulent boundary layer. A novel experiment employing multiple hot-wire probes was carried out at friction Reynolds numbers ranging from 2400 to 26 000. Taylor’s frozen turbulence hypothesis is used to convert temporal-spanwise information into a 2-D spatial spectrum which shows the contribution of streamwise ($\unicode[STIX]{x1D706}_{x}$) and spanwise ($\unicode[STIX]{x1D706}_{y}$) length scales to the streamwise variance at a given wall height ($z$). At low Reynolds numbers, the shape of the 2-D spectra at a constant energy level shows$\unicode[STIX]{x1D706}_{y}/z\sim (\unicode[STIX]{x1D706}_{x}/z)^{1/2}$behaviour at larger scales, which is in agreement with the existing literature at a matched Reynolds number obtained from direct numerical simulations. However, at high Reynolds numbers, it is observed that the square-root relationship tends towards a linear relationship ($\unicode[STIX]{x1D706}_{y}\sim \unicode[STIX]{x1D706}_{x}$), as required for self-similarity and predicted by the attached eddy hypothesis.

Characterizing global infrasonic ocean ambient noise

The ability of the International Monitoring System (IMS) global infrasound network to detect atmospheric explosions and events of interest strongly depends on station specific ambient noise which includes both incoherent wind noise and real coherent infrasonic waves. To characterize the coherent ambient noise, a broadband array processing was performed on 10 years of continuous recordings at IMS stations. Multi-year comparisons between the observed and modeled directional microbarom amplitude variations at several IMS stations using two-dimensional wave energy spectrum ocean wave products are performed to build of a reference database of infrasound oceanic sources. Microseisms are attributed the same source processes as microbaroms, involving the interaction of standing ocean waves. To further evaluate oceanic wave action models, the infrasound analysis will be supplemented with several other approaches including microseisms collected at seismic instrumentation (single stations and arrays). The expected benefits of such studies concern the use of multi-year complementary data to finely characterize coupling mechanisms at the ocean-atmosphere interface. In return, a better knowledge of the source of the ambient ocean noise opens new perspectives by providing additional integrated constraints on the dynamics of the middle atmosphere and its disturbances where data coverage is sparse.

Flexible alpha camera for detecting plutonium contamination

We developed a new imaging detector called flexible alpha camera that can identify Pu contamination in narrow spaces at work sites. The thickness of the flexible alpha camera is only ∼1/5th that of the ZnS(Ag) scintillation detector which is commonly used for detecting Pu contamination, and its efficiency in the 4-pi direction is 42.7% for 5.5-MeV alpha particles. The minimal detectable activity (MDA) is 0.014 Bq measured in 30 min. Four types of PuO2 samples, taken from a duct, bag-in/bag-out port, glovebox glove, and vinyl sheet, were measured by the flexible alpha camera. In a two-dimensional distribution of alpha particles, PuO2 was identified automatically using the “AnalyzeParticle” function in the ImageJ plugin, and its activity was evaluated. When acquisition time increased from 10 min to 30 min, a Pu spot with low activity was identified. To verify the measurement in narrow space, a fume hood to which a PuO2 particle was attached was measured using the flexible alpha camera. Since the flexible alpha camera has the thin-thickness of 12 mm and can obtain two-dimensional distribution and energy spectrum of alpha particles, it is effective for detecting Pu contamination in narrow spaces of equipment.