Wavefront Research Articles

Suppression of vortex electromagnetic wave divergence by modulating the wave front dislocation line

Abstract When the beam is transmitted in the atmosphere, under the influence of atmospheric turbulence, the beam will occur energy attenuation, wavefront distortion and other phenomena, which will seriously affect the transmission and reception of information. Based on the PB phase principle enhances the focusing capability of the auto-focusing Airy Gaussian vortex beam by regulating the wavefront error curvature of the vortex beam, and then enhances the resistance of the beam against atmospheric turbulence. The results reveal the curvature of the wavefront error curve and the peak intensity of the light field of the beam can be changed by changing the beam polarization state parameters n and m in the focal plane. The auto-focusing Airy Gaussian vortex beam with the polarization state parameters m=1, n=4 increases the peak magnitude of the light field intensity in the focal plane of the auto-focusing Airy Gaussian vortex beam with the polarization state parameters m=0, n=0 to 1.99 times. Demonstrate that geometric phase tuning the auto-focusing Airy Gaussian vortex beams can enhance resistance to atmospheric turbulence. Furthermore, this paper extends this method to the field of millimeter wave. Under the transmission distance of 1km, the peak intensity of the initial vortex electromagnetic wave after the geometric phase adjustment is increased to 3.33 times, and the receiving radius of the target surface is reduced to 0.24 of the initial vortex electromagnetic wave. It shows that geometric phase-regulated vortex electromagnetic wave can suppress vortex electromagnetic wave divergence and have potential applications in wireless communication.

Observations of Locally Excited Waves in the Low Solar Atmosphere Using the Daniel K. Inouye Solar Telescope

We present an interpretation of the recent Daniel K. Inouye Solar Telescope (DKIST) observations of propagating wave fronts in the lower solar atmosphere. Using MPS/University of Chicago MHD radiative magnetohydrodynamic simulations spanning the solar photosphere, the overshoot region, and the lower chromosphere, we identify three acoustic-wave source mechanisms, each occur at a different atmospheric height. We synthesize the DKIST Visible Broadband Imager G-band, blue-continuum, and Ca ii K signatures of these waves at high spatial and temporal resolution, and conclude that the wave fronts observed by DKIST likely originate from acoustic sources at the top of the solar photosphere overshoot region and in the chromosphere proper. The overall importance of these local sources to the atmospheric energy and momentum budget of the solar atmosphere is unknown, but one of the excitation mechanisms identified (upward propagating shock interaction with down-welling chromospheric plasma resulting in acoustic radiation) may be an important shock dissipation mechanism. Additionally, the observed wave fronts may prove useful for ultralocal helioseismological inversions and promise to play an important diagnostic role at multiple atmospheric heights.

Stress Wave Propagation and Decay Based on Micro-Scale Modelling in the Topology of Polymer Composite with Circular Particles.

This article deals with stress wave decay performance, analysing the stress wave propagation generated by an impulsive unit load in a 2D representative unit cell (RUC) of a polymer composite with circular particles representing spherical particles, elliptical particles, and short fibres. The micro-scale numerical simulation uses explicit finite element analysis (FEA). The micro-response to an impulsive unit load creates a stress wave amplitude interacting with the material structure and tends to weaken and absorb energy. The stress wave damping is determined by the decaying amplitudes of Mises stress at the front of the stress wave. The stress wave damping is evaluated for different ratios of tensile modules and material densities of matrix and reinforcing material and other factors, such as percentage and particle size, applied to nine topologies of RUCs, and even the presence of an interfacial region is analysed. Moreover, the article visualises the phases of stress wave decay in various particle distributions, i.e., various topologies. Analysing the different topologies of the same particle volume (area) percentage, the study proved that the composite topology and resulting wave-particle and wave-wave interactions are other sources of material damping. The presence of even a small percentage, 3.5 area%, of reinforcing circular particles in the matrix brings a significant increase in stress wave damping up to about 40-43% (depending on the topology) compared to a homogeneous matrix with stress wave damping of 12.5% under the same conditions. Moreover, the topology with the same volume (area) percentage can increase particle stress wave damping by 15.3%.

Seasonality of Subsurface Shear Instabilities at Tropical Instability Wave Fronts in the Atlantic Ocean in a High‐Resolution Simulation

AbstractTropical Instability Waves (TIWs) have been shown to modulate upper ocean mixing. However, previous studies on the modulation of TIW related mixing are based on small numbers of TIWs and have not considered temporal variability, which can lead to discrepancies in the findings. In this study, using a 12‐year simulation carried out with a comprehensive, global, high‐resolution ocean model, we present evidence of seasonally modulated shear instabilities at TIW fronts in the Atlantic Ocean that reach down to the thermocline depth, potentially inducing mixing below the mixed layer depth. We find that, regardless of whether TIWs are present earlier in the year, frontal instabilities and potential mixing primarily occur in boreal summer, coinciding with a vertical shear maximum between the mean zonal currents. We argue that in the Atlantic Ocean, vertical shear at TIW fronts does usually not suffice to cause frontal instabilities below the mixed layer depth. Instead, the background shear needs to be sufficiently large in addition to TIW shear, to overcome the stability. The background shear in turn varies seasonally and is strongly driven by the variability of the northern branch of the South Equatorial Current (nSEC). As such, the variability of the nSEC strongly contributes to the generation and modulation of instabilities at TIW fronts that reach below the mixed layer depth and have the potential to induce mixing. Our results highlight the importance of seasonal variability when studying TIW impacts and their effect on mixing.

Understanding the unusual life of the Cartwheel galaxy using stellar populations

Collisional ring galaxies (RiGs) are the result of the impact between two galaxies, with one of them passing close to the centre of the other, piercing its gaseous and stellar disc. In this framework, the impact generates a shock wave front that propagates within the disc of the target galaxy soon after the encounter, producing a characteristic expanding ring-shaped structure. RiGs represent one of the most extreme environments in which we can study the physical properties of galaxies and the transformations they undergo during collisions. The paradigm RiG is the Cartwheel galaxy at z = 0.03. This galaxy has been the object of both theoretical and observational studies, but the details of the mechanisms that lead to its peculiar morphology of double rings with connecting spokes and to its physical properties are still far from clear. To shed light on the history of the Cartwheel galaxy, we performed a spatially resolved analysis as a function of galactocentric distance, exploiting spectroscopic data from VLT/MUSE observations combined with photometric data covering a large wavelength range, from the UV GALEX to the IR JWST/MIRI. Using full-index fitting of the stellar spectra, an analysis of the nebular emission, and joint full spectral and photometry fitting, we derived stellar ages, gas and stellar metallicities, and star formation histories (SFHs) in four spatially distinct regions of the galaxy. We find that, apart from the peculiar morphology, a large fraction of the Cartwheel galaxy is not affected by the recent impact from the companion bullet, and retains the characteristics of a typical spiral galaxy. On the contrary, the outer ring is strongly affected by the recent impact, and is completely dominated by stars formed not earlier than ∼400 Myr ago. Our picture suggests that the collision shock wave, while moving forward to the external region of the galaxy, drags the already formed stars, sweeping the inner areas outwards, as proposed by recent collision models. At the same time, the ages found in the external ring are older than the predicted timescale of the ring expansion after the collision.

Experimental study on the evolution of shock waves in the near field of cylindrical charge explosion

Cylindrical charges are frequently used in blasting engineering and military operations, often detonated very close to target structures. Obtaining the characteristics of the flow field distribution in the near field of explosions through experimentation consistently poses challenges. These challenges constrain efforts to elucidate the evolutionary processes of explosive shock waves. Employing the explosive schlieren experimental system yields a clearer depiction of the near field flow than previous studies, thereby facilitating a more comprehensive understanding of the characteristics of cylindrical charge explosions. The overall flow field adopts a droplet shape, with the interface of the detonation products and the shock wave front forming continuous concave shapes. The detonation process in cylindrical charges can be conceptualized as the detonation wave propelling the detonation products at supersonic speeds. The formation of explosive shock waves can be elucidated through the dynamics of oblique shock waves generated by two-dimensional curved surfaces. This mechanism influences the relationship between the deflection angles of detonation products and the shock wave angles resulting from different detonation velocities. Theoretical calculations of shock wave positions align with experimental images. Significant variations in shock wave velocities at different positions within cylindrical charges are observed, identifying patterns of these variations. The research findings clarify the formation mechanisms of explosive shock waves in cylindrical charges and deepen the understanding of shock wave evolution in the near field.

О рассеянии релеевских и продольных сейсмических волн на локальной неровности грунта

A three-dimensional (3D) numerical simulation of scattering of seismic surface Rayleigh and longitudinal waves propagating through the ground, the density and elasticity of which are typical of geomedium. At the soil boundary, there is local unevenness in the form of a hollow hemispherical notch (a truncated sphere). The dependence of the direction of the scattering field on the type of inhomogeneity is shown. From literature it is known that in the transition to another type of heterogeneity, for instance, to covering the boundary with a thin inert (massive) layer in the form of a circle, the forward scattering occurs. A pulsed mode of inhomogeneity probing is considered. As an emitter, it is proposed to use a short pulse source, e.g., a hydroacoustic emitter, or something similar - a pulsating monopole, shallowly immersed under the free boundary. This leads to the generation of such elastic waves as the surface Rayleigh and back-reflected longitudinal waves, which are usually recorded using an array of seismic receivers installed on the free boundary according to the grid pattern. The spatial amplitude distribution of the wave field is analyzed in the vertical (at the center of the inhomogeneity) and horizontal (at the free boundary) sections of the medium. The characteristic features of the wave field are caused by the influence of its scattering on the local inhomogeneity. The features in the image of wave reliefs that arise at the intersection of the wave fronts of longitudinal waves - reflected from the free boundary and scattered on the local inhomogeneity - are studied. Informative signs, indicating the presence of the local heterogeneity and enable diagnostics of its parameters are established. The ways to improve the validity and reliability of algorithms for detection and classification of inhomogeneities and for evaluation of their difficulties using the listed types of waves are discussed. Based on the use of increasingly shorter probing pulses, the possibility of a detailed representation of reliefs and, consequently, the potentially achievable spatial resolution in probing the local subsurface inhomogeneities are demonstrated.

Spatiotemporal characteristics of magneto-acousto-electric fields generated by Bessel beams

The magneto-acousto-electric (MAE) effect shows great significance in neural modulation, whereas the high-precision stimulation cannot be realized by the unidirectional electric distribution perpendicular to the orthogonal acoustic and magnetic fields. A new MAE model is established based on helical wave fronts of Bessel beams in a coaxial magnetic field. Numerical and experimental studies are conducted for quasi-Bessel beams constructed by the saw-tooth phase modulation for a sectorial planar transducer array in a coaxial toroidal magnet. The MAE field induced by the Bessel beam of lth order is determined by those of (l-1)th and (l + 1)th orders. The rotary MAE field with a constant peak-intensity center can only be constructed by the Bessel beam of 1st order, which is effective for neural stimulation. Assisted by therapeutic effects of center-captured drug particles by acoustic-vortex tweezers, the center-converging MAE field may advance a new collaborative stimulation strategy with improved accuracy and reduced acoustic energy.

Detection of a glass fiber-reinforced polymer with defects by terahertz computed tomography

Terahertz (THz) computed tomography (THz CT) exhibits the potential to provide a wealth of data, surpassing that of THz tomographic imaging in applications such as detecting embedded defects, particularly defect evolution within a glass fiber-reinforced polymer. To realize high-resolution THz CT, a systematic approach guided by wave propagation simulation was employed. First, the front wave of the THz beam was fine-tuned to realize a beam diameter of <2 mm. To mitigate the strong refractive effect and minimize Fresnel reflection loss, a refractive-index-matching material was fabricated and utilized as a rounded enclosure for samples with sharp corners. To further improve the reconstruction resolution, a flat surface enclosure was applied to collect all incident beams at the detector. To realize comparable results to those of full-angle CT, a limited-angle CT approach was implemented, and the frequency range 0.1–3 THz was used in the image reconstruction study. The experimental and simulated images were used to validate the findings, and conductive and non-conductive defects measuring 200 µm were successfully visualized. Additionally, a custom-built user interface enabled us to visualize the field spatial distribution of the THz beam with respect to frequency.

Shock response of two epoxy resins at up to 330 GPa pressure

Experimental studies of the shock wave properties of two epoxy resins with the same composition but different curing temperatures (160 and 200 °C) at up to 330 GPa pressure have been carried out. Laser interferometry was used to record particle velocity profiles at up to 73 GPa pressure while measuring the shock wave velocity. The release sound velocity was experimentally determined in the 3–73 GPa pressure range. Cumulative explosive shock wave generators were used to study the shock Hugoniot of epoxy resins at pressures above 100 GPa. It was shown that the shock compressibility data of both samples are approximated by a single shock Hugoniot within the experimental error. A kink on Hugoniot recorded close to 25 GPa pressure indicates a chemical decomposition in epoxy resin. Above this kink, a change in the shock wave front structure was recorded. Hugoniots of epoxy resin and unidirectional carbon/epoxy composite were compared at up to 370 GPa pressure.

A Partial Near-infrared Guide Star Catalog for Thirty Meter Telescope Operations

At first light, the Thirty Meter Telescope (TMT) near-infrared (NIR) instruments will be fed by a multiconjugate adaptive optics instrument known as the Narrow Field Infrared Adaptive Optics System (NFIRAOS). NFIRAOS will use six laser guide stars to sense atmospheric turbulence in a volume corresponding to a field of view of 2′, but natural guide stars (NGSs) will be required to sense tip/tilt and focus. To achieve high sky coverage (50% at the north Galactic pole), the NFIRAOS client instruments use NIR on-instrument wave front sensors that take advantage of the sharpening of the stars by NFIRAOS. A catalog of guide stars with NIR magnitudes as faint as 22 mag in the J band (Vega system), covering the TMT-observable sky, will be a critical resource for the efficient operation of NFIRAOS, and no such catalog currently exists. Hence, it is essential to develop such a catalog by computing the expected NIR magnitudes of stellar sources identified in deep optical sky surveys using their optical magnitudes. This paper discusses the generation of a partial NIR Guide Star Catalog (IRGSC), similar to the final IRGSC for TMT operations. The partial catalog is generated by applying stellar atmospheric models to the optical data of stellar sources from the Panoramic Survey Telescope and Rapid Response System (Pan-STARRS) optical data and then computing their expected NIR magnitudes. We validated the computed NIR magnitudes of the sources in some fields by using the available NIR data for those fields. We identified the remaining challenges of this approach. We outlined the path for producing the final IRGSC using the Pan-STARRS data. We have named the Python code to generate the IRGSC as irgsctool, which generates a list of NGS for a field using optical data from the Pan-STARRS 3pi survey and also a list of NGSs having observed NIR data from the UKIRT Infrared Deep Sky Survey if they are available. irgsctool is available in the public domain on this GitHub public repository (https://github.com/sshah1502/irgsc), while the generated and validated IRGSC for the 20 test fields and additional Pan-STARRS Medium Deep Survey fields can be found on Zenodo.

Expanding wave packets and the quantum to classical transition

The standard description of the transition from quantum to classical mechanics presented in most text books is the proof that the quantum expectation values of position and momentum obey equations of Newtonian form. This is the Ehrenfest theorem. It is combined with the requirement that wave packets remain localised to describe a single particle moving according to classical mechanics. Hence, the natural spreading of wave packets is viewed as a quantum effect. In contradiction to this view, here it is argued that the spreading, where different momentum components separate, is the signature of the quantum to classical transition. The asymptotic spatial wave function becomes proportional to the initial momentum space wave function, which mirrors exactly the well-known far-field diffraction pattern in optics. Trajectories, defined as the locus of the normals to the expanding wave front, are used to illustrate the transition from quantum to classical motion. Again this is the analogue of the wave to beam transition in optics. It is suggested that this analysis of the quantum to classical transition should be incorporated routinely into introductory quantum mechanics courses.

Wigner Analysis of Operators. Part II: Schrödinger Equations

We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schrödinger equations with bounded perturbations. To reach this goal, we perform a so-called A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {A}}$$\\end{document}-Wigner analysis of the previous equations, as started in Part I, cf. Cordero and Rodino (Appl Comput Harmon Anal 58:85–123, 2022). Namely, the classical Wigner distribution is extended by considering a class of time–frequency representations constructed as images of metaplectic operators acting on symplectic matrices A∈Sp(2d,R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {A}}\\in Sp(2d,\\mathbb {R})$$\\end{document}. Sub-classes of these representations, related to covariant symplectic matrices, reveal to be particularly suited for the time–frequency study of the Schrödinger evolution. This testifies the effectiveness of this approach for such equations, highlighted by the development of a related wave front set. We first study the properties of A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {A}}$$\\end{document}-Wigner representations and related pseudodifferential operators needed for our goal. This approach paves the way to new quantization procedures. As a byproduct, we introduce new quasi-algebras of generalized metaplectic operators containing Schrödinger equations with more general potentials, extending the results contained in the previous works (Cordero et al. in J Math Pures Appl 99(2):219–233, 2013, J Math Phys 55(8):081506, 2014).

Nonlinear wave propagation in a bistable optical chain with nonreciprocal coupling

The propagation of nonlinear waves, such as fires, weather fronts, and disease spread, has drawn attention since the dawn of time. A well-known example of nonlinear wave–fronts–in our daily lives is the domino waves, which propagate equally toward the left or right flank due to their reciprocal coupling. However, there are other situations where front propagation is not fully understood, such as bistable fronts with nonreciprocal coupling. These couplings are characterised by the fact that the energy emitter and receiver are not interchangeable. Here, we study the propagation of nonlinear waves in a bistable optical chain forced by nonreciprocal optical feedback. The spatiotemporal evolution and the front speeds are characterised as a function of the nonreciprocal coupling. We derive an equation to describe the interacting optical elements in a liquid crystal light valve with nonreciprocal optical feedback and compare the experimental results with numerical simulations of the coupled bistable systems.

Physical and chemical processes during nitriding of chromium ferrosilicon by filtration combustion

In this paper, the nitriding of chromium ferrosilicon is carried out in the combustion mode under the condition of natural nitrogen filtration. The authors studied the effect of the key parameters (pressure of gaseous nitrogen, diameter and dispersity of starting samples) on the maximum temperature and combustion of the starting powder mixture based on chromium ferrosilicon. The combustion synthesis of chromium ferrosilicon proceeds steadily in the stationary mode with formation of a macrohomogeneous nitrided composition which, according to the results of X-ray phase analysis, contains two nitride phases - chromium nitride and silicon nitride. Interaction of the initial powder with gaseous nitrogen in the filtration combustion mode proceeds by the following probable chemical reaction: 3CrSi2 + 3Si + 3FeSi2 + 11.5N2 = 3CrN + 5Si3N4 + 3Fe. Increasing the diameter of the starting samples slightly affects the amount of absorbed nitrogen and slows the propagation of the combustion wave front. An increase in the pressure of gaseous nitrogen increases the amount of absorbed nitrogen and the combustion rate. Increasing the dispersity of the starting powder increases the amount of absorbed nitrogen and the combustion rate. It was found that the combustion reaction is not possible with a dense initial sample. The maximum combustion temperature, depending on the nitriding conditions, varies between 2400 and 2650 °C and increases with increasing gaseous nitrogen pressure, diameter of the initial samples and dispersion of chromium ferrosilicon powder. It is possible to realise nitriding of chrome ferrosilicon in the combustion mode at the pressure of gaseous nitrogen not less than 3 MPa, diameter of initial samples not less than 3.5 cm and size of initial particles not more than 100 μm. Optimal parameters of nitriding are gaseous nitrogen pressure of 5 MPa, diameter of samples 5 cm, size of initial particles less than 100 μm and bulk density of samples (2.23 g/cm3).

Influence of atmospheric wind on the propagation of radio waves

Background. It is necessary to study the influence of the physical characteristics of the atmosphere, in particular, wind on atmospheric turbulence and, consequently, on the characteristics of the radio signal it is shown. Aim. The dependence of the time-spectral function of the radio signal energy flux on the wind speed in the troposphere in the antenna plane is found. Methods. A method of transition from the Cartesian coordinate system in the antenna plane to the polar coordinate system of wave numbers has been developed. Based on this method the relationship between the Fourier spectral function of the correlation moment and the representation of the Bessel function is found. For the Fourier spectral function of the correlation moment, the previously obtained solution of the differential equation for the fluctuations of the eikonal amplitude of electromagnetic wave in a turbulent atmosphere at the front of the electromagnetic wave at the coordinate of the receiving antenna is used. Using the inverse Fourier transform the relationship between the time-spectral function of the radio signal energy flux and the time-correlation function of this flux is found. Results. Based on the study of the time-correlation function of the radio signal energy flow its relationship with the two-point correlation moment characterizing the fluctuations of the eikonal amplitude of the radio signal is found. To analyze the effect of wind, a turbulence model was used, reflecting the inertial turbulence interval, in which the energy flow from larger turbulent vortices to smaller vortices is determined by the viscous dissipation of the smallest vortices. Conclusion. Numerical calculations have shown that such a wind in the antenna plane blows away turbulent vortices in this plane, bettering the quality of the received radio signal.

Experimental study on the impact of the second dam break heights on the evolution of two-dam failure floods

Dam-break floods, especially cascade dam-break floods, could be catastrophic and warranted further investigation to enhance understanding. This paper systematically investigated the impact of break heights of the second dam on the evolution of two-dam failure floods, comparing it with single-dam outburst floods. The experiments were carried out in an inclined rectangular flume with LiDAR technology to capture the free surface. Results indicated that a computational model for the moving hydraulic jump was developed, showing good agreement with experimental results with a relative error of about 10%. The wave height of dam-break flood increased with the increase of evolution distance. The wave front celerity (for dam spacing: L/H = 26) after the flood passed the second dam increased with the break heights. The peak discharges at the second dam site and the peak flow depth (for longitudinal coordinate: x/H = 59) both showed a linear relationship with the initial flow depth in reservoir and the break heights. An increase in the initial flow depth in reservoir or the break heights led to an increase in peak discharges and peak flow depth. This study offered constructive guidance for the risk assessment of multi-dam failure floods and disaster emergency management.

Multi-plane imaging based on cascade spintronic terahertz emitters with curved substrates.

As a novel terahertz (THz) source, a spintronic THz emitter (STE) has become a research hot topic recently due to its ultra-broadband emission, powerful scalability, simple fabrication, and ultrawide pump-wavelength range. To optimize the performance of a STE, its spintronic heterostructure has been extensively investigated and its accessories have been also appropriately improved. In this work, a curved substrate of a STE was proposed and utilized to achieve the modulation of the THz wave front as a new degree of freedom. A STE with a neutral-meniscus substrate was designed and fabricated to attain the focusing function of the emitted THz radiation. Coaxial THz bi-focus with a non-overlapping spatio-temporal distribution were effectively generated and applied in multi-plane imaging by properly using two cascade STEs. Amplitude- and phase-type objects consisting of bilayer structures were measured by the scheme. The focused and defocused regions of the samples were distinguished and analyzed on different cross sections. Furthermore, a STE with a spiral stair substrate was manufactured in this way and the generation of a THz vortex beam was fulfilled. The convenient approach offered more possibilities for developing THz optospintronic devices.

A damage localization technique using wave front shapes in composite laminates without knowing the velocity profile

Composite laminates are widely used in various fields, but their structures are prone to cracks and damage. Due to the difference in angles of the instantaneous direction of the wave front propagation and the direction of the energy flow in an anisotropic material, the use of Lamb waves for damage localization in composite laminates is a challenging task. Establishing the wave front shape equation can overcome the difficulty of damage localization caused by anisotropy, but this usually requires a priori knowledge of the acoustic velocity distribution of the laminates, which is not convenient for efficient damage localization. In this paper, a damage localization method based on wave front shapes for composite laminates without any knowledge of the velocity profile is presented. Numerical simulation and experimental results show that the proposed method works. This method shows good damage localization accuracy and has broad application prospects in non-destructive testing for plate structures with strong anisotropy.

Eulerian–Lagrangian multiscale numerical analysis of multimodal partial shedding dynamics

The objective of this paper is to investigate the multimodal partial shedding dynamics from a multiscale perspective of cloud cavitating flows under two distinct cavity shedding mechanisms, namely the re-entrant jet mechanism and the shock wave propagation mechanism. A two-way Eulerian–Lagrangian coupling algorithm is applied to capture the multiscale vapor topologies from microbubble to large-scale cavities. The large-scale cavity evolution is solved through large eddy simulations (LES) with the volume of fraction (VOF) method in Eulerian frame. The sub-grid microbubbles are tracked in Lagrangian frame based on the discrete bubble model (DBM) method. The predictions agree well with experimental observation of the periodical cavity evolution and microbubble dynamics under both the re-entrant jet mechanism and shock wave mechanism around a NACA66 hydrofoil. The numerical simulation provides detailed analysis of the cavitating turbulent flow on the microbubble behavior with emphasis on the spatial-temporal distribution characteristics of microbubbles. The results show that the number and mean size of microbubbles in the cavitation region increase gradually with the growth of attached sheet cavity, development of re-entrant jet and collapse of largescale cavity for both cavitation patterns. Meanwhile, microbubbles are mainly distributed on the largescale interfaces where have high value of vorticity and turbulent kinetic energy under the effect of re-entrant jet and vortex structures. And the probability density functions (PDFs) of microbubble exhibit gamma distributions with a dominant peak at approximately 50 μm for both shedding mechanisms. However, the shock wave formation and propagation process only occurs in the final stage of cavitating flow under shock wave mechanism causing the condensation of vapor and the decrease of the number and mean size of microbubbles. Moreover, the microbubbles are uniformly distributed along the streamwise and vertical directions behind shock wave front.