Spatial Wavenumber Research Articles

Detection of delamination using laser-generated Lamb waves with improved wavenumber analysis

Abstract Delamination is a typical failure mode in multilayered materials, which may potentially threaten the safety and reliability of the materials if not detected promptly. This paper proposes a novel quantitative detection method for delamination in multilayered materials based on laser-generated Lamb waves with improved wavenumber analysis. First, a three-dimensional(3D) finite element model is established to simulate the interaction between delamination and laser-generated Lamb waves. The propagation characteristics of Lamb waves in multilayered materials without defects and with delamination of three different shapes, i.e., rectangular, circular and triangular are analyzed. And the mechanism that delamination can lead to the appearance of scattered wave and new wavenumber components is investigated, facilitating the quantitative detection of delamination. Then, an improved wavenumber analysis method for quantitative detection of delamination is proposed. The new wavenumber components caused by delamination are extracted by broadband adaptive wavenumber filtering to reduce imaging interference and artifacts caused by irrelevant components, and the spatial wavenumber spectrum is obtained by fast broadband local wavenumber estimation algorithm to enhance the delamination imaging accuracy and spatial resolution. The experimental results indicate that, across various experimental scenarios, the proposed method achieves superior imaging precision compared to traditional wavenumber filtering or local wavenumber estimation methods, and can quantitatively identify delamination defects of various shapes and sizes.

The Response of Turbulent Channel Flow to Standing Wave-like Wall Motion

The effect of wall deformations on wall turbulence is a topic of fundamental importance for the advancement of flow control strategies aimed at reducing the frictional drag. Dynamic wall deformations in the form of wall-normal of in-plane oscillations represents an area that is yet to be fully explored, and that can open a new realm of drag control strategies, as well as provide fresh insights into the structure of wall turbulence. In this study, we present several results from direct numerical simulations aimed at understanding the response of wall turbulence to standing wave-like wall motion, arranged in a checkerboard pattern. More specifically, here we target a low Reynolds number turbulent channel flow, featuring standing wave-like dynamic wall deformations on both bottom and top walls, with parameterizations in terms of the frequency of oscillations, roughness height, and spacing. We quantify the effect that this type of wall motion can have on the skin friction drag, various turbulent statistics, and turbulent flow structures. In addition, taking advantage of the periodicity and the symmetry of the flow, an improved phase-averaging procedure is introduced, which enhances the smoothness of the data. The results show that this type of dynamic wall deflection can have a significant effect on the turbulent flow in proximity to the wall, and that the variation of the spatial wavenumbers of the wall deflections can make a big difference. A slight total drag reduction, in the order of 2%, was observed for some combinations of wavenumbers and frequencies, especially for the highest streamwise wavenumber case.

Global Existence for Long Wave Hopf Unstable Spatially Extended Systems with a Conservation Law

AbstractWe are interested in reaction–diffusion systems, with a conservation law, exhibiting a Hopf bifurcation at the spatial wave number $$ k = 0 $$ k = 0 . With the help of a multiple scaling perturbation ansatz a Ginzburg–Landau equation coupled to a scalar conservation law can be derived as an amplitude system for the approximate description of the dynamics of the original reaction–diffusion system near the first instability. We use the amplitude system to show the global existence of all solutions starting in a small neighborhood of the weakly unstable ground state for original systems posed on a large spatial interval with periodic boundary conditions.

Investigating Flow-Induced Vibration by Regarding the Alignment of Flow Modes and Structural Modes

In this work, a modal matching approach is developed to investigate the impact of the spatial correlation of wall pressure fluctuations on structural vibration and its role in suppressing flow-induced vibration in aircraft. The modal matching method defines the wavelength ratio between the convection wave and the flexural wave to capture the spatial characteristics of both the flow mode and the structural mode. In comparison to conventional methods such as the finite element method and analytical method, the proposed modal matching approach allows for obtaining the vibration response in the spatial–wavenumber domain. To validate the spatial correlation effect on structural vibrations obtained with the modal matching approach, a wind tunnel test was conducted to measure flow-induced vibrations. The calculated spatial–wavenumber data for flow-induced vibrations reveal that the crests and troughs of the vibration velocity alternate periodically as the wavelength of the wall pressure fluctuations changes. At the resonance frequency, a vibration velocity trough can be observed when the spatial correlation of wall pressure fluctuations aligns with the structural mode. Additionally, the concept of resonance independence of flow-induced vibrations is introduced to describe the phenomenon where the most severe structural vibration, determined by the matching value between the aerodynamic mode and the structural mode, does not always occur at the resonance frequency. The modal matching approach effectively suppresses structural vibration by utilizing the spatial correlation of wall pressure fluctuations, offering a new perspective on controlling flow-induced vibrations.

Existence of small-scale Rossby waves points to low convective velocity amplitudes in the Sun

Inertial waves occur naturally in rotating fluids such as the Sun and the Earth's atmosphere. Rossby waves in the Sun have the potential to shed fresh light on interior turbulence and convection that prior seismic methods, reliant on sound waves, have been unable to accomplish. Here, we utilize ∼13 years of observational products taken by the space-based helioseismic and magnetic imager, onboard the solar dynamics observatory, to characterize solar equatorial Rossby waves. By examining maps of motions at the surface using two different methods, we are able to identify Rossby modes up to azimuthal order m = 30, approximately up to twice the spatial wavenumber limit of previous studies. The dispersion relation of these modes departs significantly from the classical two-dimensional Rossby-Haurwitz description. A parameter study of the effect of superadiabaticity and viscous diffusion on these inertial modes indicates that each parameter plays a role in influencing both the frequencies and linewidths of high m modes. Using the Rhines-scale relation, we constrain the root mean square amplitude of turbulent convection more tightly to ∼2 m/s, adding more evidence to the paradigm of weakly convective amplitudes at large scales.

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence.

We consider a nearly collisionless plasma consisting of a species of "test particles" in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field-a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space-known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C_{2}∝∫∫dxdv〈f^{2}〉-a quantity that here plays the role of (negative) entropy of the distribution function. We find that C_{2} is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C_{2} in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equationfor the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C_{2} to high s (towards the collisional dissipation range) at every k, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C_{2} is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k-space (s-space) flux of C_{2} is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the (k,s) plane, with power-law asymptotics at large k and s. Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a "critical balance" in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.

Vibration and underwater noise simulation of a river-crossing tunnel based on a 2.5D structural-acoustic finite element method

To protect the underwater ecosystem and species, the vehicle-induced vibration and underwater radiated noise of river-crossing tunnels need to be calculated efficiently and accurately. For this purpose, this study proposed a 2.5-dimensional (2.5D) structural-acoustic finite element method which combines 2.5D finite element vibration algorithm and 2.5D infinite element acoustic algorithm. The proposed method utilizes the spatial wave number transformation theory and the acoustic transfer vector (ATV) method. Based on a river-crossing tunnel, a 2.5D numerical simulation model was established in this study to analyze the vehicle-induced tunnel-soil vibration as well as the underwater radiated noise during operation. The results showed that the tunnel vibration and the associated radiated noise mainly distributed in the range of 10 to 40 Hz, with two peaks at 15.6 Hz and 31.5 Hz, respectively. The total sound pressure level (SPL) of the predicted noise at each field point reached a maximum value of 126 dB. The 2.5D algorithm proposed in this study achieves higher computational efficiency compared to traditional 3D vibration and noise analysis methods, which can provide theoretical and technical supports for the protection of underwater ecological diversity.

Transient growth of wavelet-based resolvent modes in the buffer layer of wall-bounded turbulence

In this work, we study the transient growth of the principal resolvent modes in the minimal flow unit using a reformulation of resolvent analysis in a time-localized wavelet basis. We target the most energetic spatial wavenumbers for the minimal flow unit and obtain modes that are constant in the streamwise direction and once-periodic in the spanwise direction. The forcing modes are in the shape of streamwise rolls, though pulse-like in time, and the response modes are in the form of transiently growing streaks. We inject the principal transient forcing mode at different intensities into a simulation of the minimal flow unit and compare the resulting nonlinear response to the linear one. The peak energy amplification scales quadratically with the intensity of the injected mode, and this peak occurs roughly at the same time for all forcing intensities. However, the larger energy amplification intensifies the magnitude of the nonlinear terms, which play an important role in damping the energy growth and accelerating energy decay of the principal resolvent mode. We also observe that the damping effect of the nonlinearities is less prominent close to the wall. Finally, we find that the principal resolvent forcing mode is more effective than other structures at amplifying the streak energy in the turbulent minimal-flow unit. In addition to lending support to the claim that linear mechanisms are important to near-wall turbulence, this work identifies time scales for the nonlinear breakdown of linearly-generated streaks.

Transducer Resolution Effect on Pressure Fluctuations Beneath Hypersonic Turbulent Boundary Layers

The size of a pressure transducer is known to affect the accuracy of measurements of wall-pressure fluctuations beneath a turbulent boundary layer because of spatial averaging over the sensing area of the transducer. In this paper, the effect of finite transducer size is investigated by applying spatial averaging or wavenumber filters to a database of hypersonic wall pressure generated from a direct numerical simulation (DNS) that simulates the turbulent portion of the boundary layer over a sharp 7° half-angle cone at nominally Mach 8. A good comparison between the DNS and the experiment in the Sandia Hypersonic Wind Tunnel at Mach 8 is achieved after spatial averaging is applied to the DNS data over an area similar to the sensing area of the transducer. The study shows that a finite sensor size similar to that of the PCB132 transducer can cause significant attenuation in the root-mean-square and power spectral density (PSD) of wall-pressure fluctuations, and the attenuation effect is identical between cone and flat plate configurations at the same friction Reynolds number. The Corcos theory is found to successfully compensate for the attenuated high-frequency components of the wall-pressure PSD.

Axisymmetric reflectors in wave energy converter arrays: Harnessing scattering to increase energy extraction

We elucidate the effect of non-extracting reflectors on the performance of wave energy converter (WEC) arrays. We consider an infinitely periodic row of converters parallel to an infinitely periodic row of discrete axisymmetric reflectors (C-R arrays), and we study how the spatial configuration affects energy extraction. Using a multiple-scattering algorithm for linear wave-array interactions, we conduct a series of simulations of C-R arrays for a range of spatial configuration parameters, wavenumbers, and wave incident angles. We find that C-R arrays can significantly increase energy extraction compared to a WEC array by itself. We offer a simplified theoretical model, based on the far-field response of periodic rows in isolation, which shows that the large increases in energy extraction result from the constructive Bragg and Laue interferences caused by wave interactions with the reflector row. For the pertinent case of incident waves of the WEC-resonant frequency, we find that optimized C-R arrays can achieve energy extraction gains of O(500%). Remarkably, the optimal C-R array extracts more energy than two rows of converters of optimal configuration even though the C-R array consists of only half as many WECs.

Imprinting Spatial Helicity Structure of Vector Vortex Beam on Spin Texture in Semiconductors

We present the transfer of the spatially variant polarization of topologically structured light to the spatial spin texture in a semiconductor quantum well. The electron spin texture, which is a circular pattern with repeating spin-up and spin-down states whose repetition rate is determined by the topological charge, is directly excited by a vector vortex beam with a spatial helicity structure. The generated spin texture efficiently evolves into a helical spin wave pattern owing to the spin-orbit effective magnetic fields in the persistent spin helix state by controlling the spatial wave number of the excited spin mode. By tuning the repetition length and azimuthal angle, we simultaneously generate helical spin waves with opposite phases by a single beam.

Toward high-fidelity imaging: Dynamic matching FWI and its applications

Full-waveform inversion (FWI) is firmly established within our industry as a powerful velocity model building tool. FWI carries significant theoretical advantages over conventional velocity model building methods such as refraction and reflection tomography. Specifically, by solving a nonlinear inverse problem through the wave equation, FWI is able to recover a broadband velocity model containing both high and low spatial wavenumbers, thus extending the approximation of residual moveout correction inherent in traditional velocity model building approaches. Moreover, FWI is capable of inverting information from the entire wavefield (i.e., early arrivals, reflections, refractions, and multiple energy) rather than from a subset as in conventional approaches (i.e., first break and primary reflections), thereby availing itself of more information to better constrain its model estimate. However, these theoretical benefits cannot be realized easily in practice because various complexities of real seismic data often conspire to violate algorithmic assumptions, leading to unsatisfactory results. Dynamic matching FWI (DMFWI) is a newly developed algorithm that solves an inversion problem that maximizes the cross correlation of two dynamically matched data sets — one recorded and the other synthetic. Dynamic matching of the two data sets de-emphasizes the amplitude impact, which allows the algorithm to focus on minimizing their kinematic differences rather than amplitude in the data-fitting process. The multichannel correlation makes the algorithm robust for data with low signal-to-noise ratio. Applications of DMFWI across different types of acquisition and geologic settings demonstrate that this novel FWI approach can resolve complex velocity errors and provide high-quality migrated images that exhibit a high degree of geologic plausibility. Additionally, reflectivity images can be obtained in a straightforward manner as natural byproducts through computation of the directional derivative of the inverted FWI velocity models.

A revisit of Rayleigh capillary jet breakup at low Ohnesorge number

The average Rayleigh capillary breakup length of a cylindrical Newtonian viscous liquid jet moving with homogeneous velocity must be determined by the selection of normal modes with time-independent amplitude and wavelength. Invariant modes (IMs) with both positive and negative group and phase velocities exist in ample ranges of the parameter domain (Weber and Ohnesorge), which explains (i) the self-sustained average breakup length (long-term resonance) and (ii) the governing role on breakup of both spatial growth rate and wave number of the dominant positive group velocity IM. Published experimental results at low Ohnesorge numbers confirm our proposal.

Material Interface in the Finite-Difference Modeling: A Fundamental View

ABSTRACT By analyzing the equations of motion and constitutive relations in the wavenumber domain, we gain important insight into attributes determining the accuracy of finite-difference (FD) schemes. We present heterogeneous formulations of the equations of motion and constitutive relations for four configurations of a wavefield in an elastic isotropic medium. We Fourier-transform the entire equations to the wavenumber domain. Subsequently, we apply the band-limited inverse Fourier transform back to the space domain. We analyze consequences of spatial discretization and wavenumber band limitation. The heterogeneity of the medium and the Nyquist-wavenumber band limitation of the entire equations has important implications for an FD modeling: The grid representation of the heterogeneous medium must be limited by the Nyquist wavenumber. The wavenumber band limitation replaces spatial derivatives both in the homogeneous medium and across a material interface by continuous spatial convolutions. The latter means that the wavenumber band limitation removes discontinuities of the spatial derivatives of the particle velocity and stress at the material interface. This allows to apply proper FD operators across material interfaces. A wavenumber band-limited heterogeneous formulation of the equations of motion and constitutive relations is the general condition for a heterogeneous FD scheme.

Ground roll intelligent suppression based on spatial domain synchrosqueezing wavelet transform convolutional neural network

AbstractGround roll is usually considered as a common linear noise in land seismic data. The existence of the ground roll often masks the effective reflection information of underground media, resulting in the deterioration of seismic data quality. Therefore, ground roll suppression is one of the main tasks in seismic data processing. A large number of previous studies have proved that the time‐frequency signal processing method based on mathematical transformation has shown excellent performance in ground roll attenuation and still has development potential. Meanwhile, a convolutional neural network, as one of the popular deep learning technologies, has also been widely used in the field of seismic signal processing. In this paper, we combine the convolutional neural network with the time‐frequency signal processing method based on mathematical transformation, that is, spatial domain synchrosqueezing wavelet transform, and propose a complete ground roll suppression workflow of shot gathers in spatial wavenumber domain, realizing high‐precision and automatic ground roll removal. Field data examples show that compared with bandpass filtering, FK filtering, time domain synchrosqueezing wavelet transform, spatial domain synchrosqueezing wavelet transform and the convolutional neural network, the spatial domain synchrosqueezing wavelet transform convolutional neural network has achieved satisfactory results in effectively attenuating ground roll and retaining valid information.

Constrained least-squares based adaptive-order finite-volume WENO scheme for the simulation of viscous compressible flows on unstructured grids

We develop a novel constrained least-squares technique for fourth-order weighted essentially non-oscillatory (WENO) polynomial reconstruction on general unstructured grids composed of curved-edged quadrilateral elements. Our technique relies on a segregation of the conditions that match the spatial averages of the candidate WENO polynomial and the reconstructed state variable over stencil-forming cells into two sets. The first set consists of exactly enforced linearly independent constraints that are applied only over the central cell and its edge-sharing neighbors. The second set consists of the remaining conditions and are enforced only approximately in a least-squares sense. We develop a specialized technique that reduces the computational burden associated with the numerical solution of the constrained least-squares system for the WENO interpolation coefficients. For a comparable computational expense, our constrained reconstruction approach yields pointwise estimates that are consistently more accurate than the conventional least-squares based estimates over a wide spectrum of spatial wavenumbers. This enhanced spectral resolution yields a significant, over two-fold increase in the accuracy with which unsteady smooth flow features, such as an advecting isentropic vortex, are captured over highly distorted curvilinear unstructured grids. Our constraint based reconstruction framework is generic, facilitates implementation of high-order boundary closures, and is amenable to large scale parallelization over several thousand CPU cores. Numerical tests over a range of inviscid and viscous flow configurations are presented to demonstrate the accuracy and robustness of our technique. Our constrained least-squares based adaptive WENO discretization faithfully captures intricate features that arise in strongly shocked, and highly unsteady and separated complex geometry flows. Our results suggest exact preservation of the match between the cell averages of the interpolant and the reconstructed state variable over the nearest neighbors to be quite an effective strategy that dramatically enhances the accuracy and spectral resolution of the high-order finite-volume reconstruction operation.

Research on 3D finite element simulation model of aluminium beam with lamination defects based on 2D Fourier transform

In order to solve the problems of low detection accuracy and poor modelling effect when building the laminated defect aluminium beam model, a 3D finite element simulation model of laminated defect aluminium beam based on 2D Fourier transform is proposed. The two-dimensional Fourier transform method was used to obtain the full wave field signal and spatial position wave number curve of aluminium beam structure. The three-dimensional point cloud image was generated by MATLAB software, and the solid model of aluminium beam with delamination defect was established. The three-dimensional finite element simulation model of aluminium beam with laminated defects was obtained by introducing it into the worktable. The experimental results show that the accuracy of the method is 98.91%, the average texture number and frame rate are 17.105 ms and 95.507 frames/second, respectively. It has a good effect on the establishment of 3D finite element simulation model of aluminium beam.

The logarithmic variance of streamwise velocity and conundrum in wall turbulence

The logarithmic dependence of streamwise turbulence intensity has been observed repeatedly in recent experimental and direct numerical simulation data. However, its spectral counterpart, a well-developed $k^{-1}$ spectrum ( $k$ is the spatial wavenumber in a wall-parallel direction), has not been convincingly observed from the same data. In the present study, we revisit the spectrum-based attached eddy model of Perry and co-workers, who proposed the emergence of a $k^{-1}$ spectrum in the inviscid limit, for small but finite $z/\delta$ and for finite Reynolds numbers ( $z$ is the wall-normal coordinate, and $\delta$ is the outer length scale). In the upper logarithmic layer (or inertial sublayer), a reexamination reveals that the intensity of the spectrum must vary with the wall-normal location at order of $z/\delta$ , consistent with the early observation argued with ‘incomplete similarity’. The streamwise turbulence intensity is subsequently calculated, demonstrating that the existence of a well-developed $k^{-1}$ spectrum is not a necessary condition for the approximate logarithmic wall-normal dependence of turbulence intensity – a more general condition is the existence of a premultiplied power-spectral intensity of $O(1)$ for $O(1/\delta ) < k < O(1/z)$ . Furthermore, it is shown that the Townsend–Perry constant must be weakly dependent on the Reynolds number. Finally, the analysis is semi-empirically extended to the lower logarithmic layer (or mesolayer), and a near-wall correction for the turbulence intensity is subsequently proposed. All the predictions of the proposed model and the related analyses/assumptions are validated with high-fidelity experimental data (Samie et al., J. Fluid Mech., vol. 851, 2018, pp. 391–415).

Multi-Dimensional Deconvolution for Near-Field Thread Seismic Sources in Tunnels

In underground tunnel constructions, belt conveyors or subway trains can be used as passive sources for time-lapse seismic assessments of surrounding formations. The key technology of passive seismic processes is seismic interferometry (SI), which has the ability to extract the Green's function between any two points in a medium of interest. However, since the process results are typically required to meet certain premise assumptions, the current SI methods cannot be directly used for belt conveyors. In the current study, this type of source is referred to as a near-field thread source and the proposed new SI method is adapted to this type of source. There are mainly two types of SI methods: SI by cross-correlation and SI by multi-dimensional deconvolution. The former requires that the passive source be uniformly distributed in the far field, while the latter relaxes the requirements for uniform distribution yet still requires far field sources. When the first assumptions are violated, the correlation function is proportional to a Green's function with a blurred source. The source blurring is then quantified by what is referred to as an interferometric point-spread function, which can be derived from the observed data. Therefore, using SI by MDD can effectively deblur the source of the Green's function by deconvolving the PSF. In this study, one set of geophones is located in one tunnel as the passive source, and another set is in an adjacent tunnel. However, since the setup almost coincided with the distribution of the passive sources, the spatial (wavenumber) spectrum of the PSF is too broad to be inverted. Therefore, a conventional MDD method is not suitable for this study's experiments. This study found that another PSF could be obtained from the data of the adjacent tunnel. Subsequently, a new MDD formula based on the new PSF is derived and compared with the derivation processes of the conventional MDD formula. Then, the feasibility of the proposed method is verified using numerical simulations.

Investigating Toroidal Flows in the Sun Using Normal-mode Coupling

Abstract Helioseismic observations have provided valuable data sets with which to pursue the detailed investigation of solar interior dynamics. Among various methods to analyze these data, normal-mode coupling has proven to be a powerful tool, used to study Rossby waves, differential rotation, meridional circulation, and nonaxisymmetric multiscale subsurface flows. Here, we invert mode-coupling measurements from the Helioseismic Magnetic Imager and the Michelson Doppler Imager to obtain mass-conserving toroidal convective flow as a function of depth, spatial wavenumber, and temporal frequency. To ensure that the estimates of velocity magnitudes are proper, we also evaluate correlated realization noise, caused by the limited visibility of the Sun. We benchmark the near-surface inversions against results from local correlation tracking. The convective power likely assumes greater latitudinal isotropy with a decrease in spatial scale of the flow. We note the absence of a peak in toroidal-flow power at supergranular scales, in line with observations that show that supergranulation is dominantly poloidal in nature.