Edge Waves Research Articles

Unsteady edge waves generated by time-harmonic pressure: exact solutions

An analytical description of unsteady edge waves over a uniform slope is proposed. It is assumed that the waves are excited by time-harmonic external pressure with inhomogeneous spatial distribution. The problem is considered in Lagrangian variables. An exact solution of the hydrodynamic equations is obtained. It generalizes the stationary Gerstner–Constantin solution. The proposed model describes the dynamics of coastal splashes of arbitrary initial shape. An important feature of the new solution is that it describes waves both propagating and standing in the longshore direction.

The influence of edge waves in local surface skimming longitudinal wave generation using a focused PVDF transducer

Acoustic microscopy is extensively used for high-frequency imaging and material characterization. In a focused ultrasonic transducer, the presence of edge waves from the edge of the transducer is usually considered a disadvantage. For high-frequency imaging applications, the edge waves adversely affect the quality of the image. This paper discusses edge wave's influence on generating a surface wave in bulk metal samples using a limited aperture PVDF transducer. Acoustic microscopy-based defocusing experiments are conducted on aluminum, stainless steel, copper, and brass samples. A detailed wave-path analysis is done to understand the different wave components in a signal as obtained from defocusing experiments. The travel path of each wave component is analytically obtained and compared with the experimental results. The different wave modes observed in the experiments are identified by overlaying the analytical plots on the experimentally obtained B-scans. A good correlation is obtained between the experimental and analytical results. The surface wave velocity of the samples is calculated using the time-resolved method, and the percentage of error in the measurement is estimated. The challenges for using this method in measuring surface wave velocities in samples with bulk longitudinal velocities <5000m/s are also discussed.

The Mechanisms of Tsunami Amplification and the Earthquake Source of the 2021 M 7 Acapulco, Mexico, Earthquake

ABSTRACT We present a slip model for the 2021 M 7 Acapulco, Mexico, earthquake produced by inversion of strong motion, Global Navigation Satellite Systems, tide gauge, and Interferometric Synthetic Aperture Radar data. The earthquake occurs within the Guerrero gap, identified as a region of concern for its seismogenic potential and paucity of large events. We find that rupture was compact, constrained to depths between 10 and 20 km, and consistent of two main slip patches. The slip model leaves a broad swath of the megathrust unbroken, and, whether the event signals a reactivation of large earthquakes in the region remains unknown. We find that tide gauge recordings inside Acapulco Bay for the M 7 1962 earthquake and the 2021 event are strikingly similar, thus we interpret this as weak evidence that 2021 is a repeat of 1962. We also produce a high-resolution hydrodynamic model of the resulting tsunami using the slip model as initial condition and place special emphasis in understanding the long duration (∼17 hr) of waves inside the bay. We find that simple bay resonance alone does not account for the features of the event. Rather it is a complex interaction with shelf modes and edge waves that continuously re-excite the bay resonance that leads to the protracted tsunami disturbances. Furthermore, we find that significant currents in excess of 1 m/s occur in localized portions of the bay even when wave amplitudes remain small.

Near-field chiral excitation of universal spin-momentum locking transport of edge waves in microwave metamaterials

Controlling energy flow in waveguides has attractive potential in integrated devices from radio frequencies to optical bands. Due to the spin-orbit coupling, the mirror symmetry will be broken, and the handedness of the near-field source will determine the direction of energy transport. Compared with well-established theories about spin-momentum locking, experimental visualization of unidirectional coupling is usually challenging due to the lack of generic chiral sources and the strict environmental requirement. In this work, we design a broadband near-field chiral source in the microwave band and discuss experimental details to visualize spin-momentum locking in three different metamaterial waveguides, including spoof surface plasmon polaritons, line waves, and valley topological insulators. The similarity of these edge waves relies on the abrupt sign change of intrinsic characteristics of two media across the interface. In addition to the development of experimental technology, the advantages and research status of interface waveguides are summarized, and perspectives on future research are presented to explore an avenue for designing controllable spin-sorting devices in the microwave band.

Modulated flexural edge waves in a plate with its free edge structured by an array of grooves

A flexural edge wave (FEW) is a guided wave propagating along the free edge of a semi-infinite isotropic elastic thin plate. Here, we investigate the FEW in a plate with its free edge structured by an array of grooves, revealing the essence of a kind of modulated FEW. We analytically solve the dispersion relation of the modulated FEW by developing the coupled mode theory (usually used in diffraction optics and acoustics) that couples diffraction modes and high-order flexural waveguide modes, and discuss the propagation characteristics of the first- and second-order modulated FEWs (symmetric and antisymmetric modes, respectively). Based on the features of the dispersion curves corresponding to the unit cells of the plate with grooves of graded depths, we numerically and experimentally realize the rainbow trapping of the first-order modulated FEW and the mode conversion of the second-order modulated FEW to the bulk wave. Our work provides new ideas for the manipulation of flexural waves and has the potential to develop corresponding acoustic devices based on the FEW.

Maximum Run-Up and Alongshore Mass Transport Due to Edge Waves

The edge wave on a uniform-sloped seabed was described by the velocity-potential function by Mok and Yeh in 1999. Edge waves cannot be extended above a certain level from the still-water level, and the upper limit of the run-up of the edge waves for given conditions is found here. In this study, quantitative mass transport by the edge waves of the beach is introduced. The maximum run-up height is decided from the wave’s amplitude at shoreline, and the maximum run-up distance from the shoreline is proportional to the wavelength of the edge waves. The fluid alongshore-mass-transport profile shows that the strongest mass transport rate corresponds to the position offshoreward multiplied by 0.0362 times the wavelength, and its magnitude is 1.23 times the mass-transport rate at the shoreline. The maximum cross-sectional total mass-transport rate is 0.214 times the mass transport at the shoreline, multiplied by the wavelength for the maximum run-up condition. This study suggests that edge waves cannot be increased infinitely and that there is a maximum run-up on the coast.

Vision‐based edge wave detection for cold‐rolled steel plate using 3D camera

Edge wave detection is a key technology in steel plate quality inspection, which is beneficial to improve the production quality of steel products and the efficiency of enterprises. In this letter, a novel algorithm based on visual projection and pixel statistics is proposed to detect the edge wave using 3D camera. The proposed algorithm first uses a series of image preprocessing to effectively remove the influence of irrelevant interference, and transforms the colour image into the binary image. Subsequently, three key positions of the edge wave in range image are precisely determined based on visual projection and pixel statistics. Finally, two 3D cameras are used to acquire the range images to evaluate the proposed algorithm's performance. The results show that the proposed algorithm can accurately detect the edge wave instead of human eye detection.

Anomalous bulk-edge correspondence and dual-band topologically protected edge states in magnetized plasma

Magnetized plasma as a topological material has been demonstrated recently. However, a comprehensive description of the bulk-edge correspondence in magnetized plasma is still lacking. In this work, we systematically reveal all types of anomalous bulk-edge correspondence in magnetized plasma. The bulk-edge correspondence can be formally restored by avoiding the unphysical response at the large wave number when the spatial cutoff of magnetized plasma is appropriately considered. Remarkably, a different type of dual-band topologically protected edge states is uncovered when the bulk-edge correspondence is restored. The topology of the dual-band system is verified by the stable propagation of edge waves around defects. The topological wave division of the dual-band edge states is realized by designing a four-channel junction. Our work may provide more flexibility for multiband and multichannel photonic devices.

Energy Flux in Thin Plates

Summary A formula for energy flux due to vibrations in a thin plate modelled by Kirchhoff theory is derived by considering a Mindlin plate and taking the low frequency (or low thickness) limit. It is shown that a term that is usually neglected in Kirchhoff theory persists close to free edges. This term does not affect the transverse displacement, but it does affect the energy flux. The new flux formula conserves energy and evaluates to zero along fixed, free and simply supported edges. An example problem, in which edge waves are excited by a point source located in a semi-infinite plate, is considered. Numerical calculations show that the energy radiated into the far field matches the energy introduced by the source.

Localised Waves In Elastic Thin-Walled Structures

In this paper the authors provide a review of our investigations pertaining to localized bending waves in thinwalled structures. The authors also present the statements and analytical results fortwo new problems related to bending edge wave propagation in homogeneous infinite plate reinforced by inclusions, modelled as elastic beam or elastic plate.

Dynamic analysis of the sinusoidal actuation of a flexible fin for paired fin propulsion

In this research, the sinusoidal actuation of a flexible fin for median and/or paired fin propulsion is studied. A prototype of an underwater robot is built, and the computer-aided engineering simulation method is used for the transmission system of the flexible fin. The fin ray at the end of the trajectory and the crankshaft drive the parameters as a function of the fin ray output parameters. Given the fin and the fin surface motion for the coupled simulation analysis, the flexible fin surface and the fin sinusoidal oscillation are studied. The deformation of the fin surface is established outside the edge wave trajectory equation of motion. The equations of motion are verified by simulation. The single fin wave model is solved with the computational fluid dynamics method, and the hydrodynamic performance of the fin surface is obtained. Using the dynamic mesh technique, the complex large fluctuation motion of the fin surface is solved. With different amplitudes and periods of the fin wave as the input parameters, a simulation of the fin wave propulsion is conducted, and the relationship between the fin wave propulsion force and the fin wave resistance is calculated. The correctness of the simulation results of the sinusoidal fixed wave of the fin surface is verified by a fin wave ink experiment.

Asymptotically correct boundary conditions for the higher-order theory of plate bending

The construction of refined boundary conditions for the case of edge loading, corresponding to the theory with modified inertia in respect to the order of asymptotic approximation, is considered. The methods of investigation are based on the works of A. L. Goldenveizer and A. V. Kolos. The solution of three-dimensional (3D) problem is constructed as a superposition of the long-wave approximation and boundary layers. The traction on the edge is presented as generalized Fourier expansions, using the Legendre polynomials. This approach allows to obtain explicit expressions for the coefficients of boundary layers via an iteration procedure, in course of which the boundary conditions are satisfied with a pure asymptotic error. As a result, the refined boundary conditions (RBCs) are constructed. Effective stress resultants and couples are introduced, the coefficients of which (the Goldenveizer–Kolos constants) are the simple polynomial functions of Poisson’s ratio. In addition, the contribution of boundary layers to edge displacements is determined. The comparison of the dispersion curve for the edge wave, calculated on the basis of the theory with modified inertia and RBC, with the 3D solution show good agreement in the 10 times wider frequency range than that of the Kirchhoff’s theory. The same result is obtained for the amplitude of a transient edge wave, excited by edge loading. It is also shown that with making use of RBC one can consider the action of a self-equilibrated edge load in the framework of two-dimensional (2D) theory.

Flexural Edge Waves in a Thick Piezoelectric Film Resting on a Winkler Foundation

This paper is concerned with the analysis of bending edge waves travelling in a thick Kirchhoff-type piezoelectric film resting on a Winkler–Fuss foundation. The electromechanical coupling is accounted for in defining flexural rigidities to embrace piezoelectric and dielectric material constants. Dynamics is solved analytically and demonstrated numerically by assuming harmonic wave propagation. It is observed that an increase of the voltage leads to a decrease of the critical velocity, while an increase of the Winkler’s constant leads to an increase of the critical velocity.

The transition of tidal Kelvin waves to hybrid Kelvin edge and internal waves in the global ocean

In this study, we investigate the transition of semidiurnal Kelvin waves into Hybrid Kelvin-Edge (HKE) waves and associated generation of internal tides at widening shelves using theory, a realistic global baroclinic ocean model simulation, and quasi-realistic regional barotropic model simulations. Using the global model simulation, we identify several areas where a tidal HKE wave transition co-exists with internal wave generation. Of all areas considered, the Celtic Sea/Bay of Biscay shelf has the widest shelf and the strongest internal tide generation. We find that the global simulation agrees better with the theoretical Kelvin modes on the narrow than with the hybrid edge modes on the wide shelves. To help us understand the effect of complex, realistic bathymetry on the HKE wave transition, we perform quasi-realistic 1/25° barotropic simulations of the Celtic Sea/Bay of Biscay shelf areas. In these simulations, we gradually change the realistic bathymetry to a more idealized bathymetry. The idealized simulations show that the complex bathymetry steers the barotropic energy flux and causes standing wave patterns, which mask the HKE wave transition. Based on this analysis, we conclude that the HKE wave transition in the Celtic Sea/Bay of Biscay and other shelf areas in the global ocean is most likely masked by the effects of complex bathymetry and that offshelf baroclinic fluxes cannot be exclusively attributed to the HKE wave transition.

Local amplification of tsunami waves along the west coast of Negros Island and Panay Island

Panay Island and Negros Island in the east of the Sulu Sea face hazard of near-field earthquake-generated tsunami. This study aims to assess the tsunami hazard along the west coast of the two islands caused by near-field earthquakes with the largest possible magnitude, and focuses on the high hazard spots which are always attacked by higher tsunami waves. The Negros Trench is considered to be the potential source of seismic tsunami based on the historical tsunami and earthquake data, and special attention is given to the hazard associated with edge waves caused by near-field earthquake and other wave energy convergence mechanisms. A series of tsunami scenarios in this area are numerically simulated based on the widely-used ocean dynamic model FVCOM (an unstructured grid, Finite-Volume Community Ocean Model). The largest historical tsunami in the recent century is simulated and reproduced, and the results are in reasonable agreement with the historical observation. Further, a set of possible scenarios considering earthquakes with largest historical magnitude are simulated, and other seismic parameters are determined through the statistical analysis of the regional historical seismic data and the previous studies. The maximum tsunami wave along the coast in each scenario is analyzed and given. The results show that the near-shore tsunami is greatly affected by the epicenter location and other seismic parameters. The influences of seismic parameters on each coast location are different and complex, due to the winding shoreline and local topography. However, the spatial distribution of tsunami waves along the coast has certain regularity. It is found that there are some spots which always face a higher tsunami hazard. From the analysis of wave propagation, the high hazard along the west coast of Negros Island is ascribed to edge waves formed by the trap of wave energy in shallow water. Moreover, a variety of interesting phenomena associating with other high hazard spots can be found in this area, including wave convergence by bell-shaped mouth, the superposition of incident and reflected waves, and wave refraction around a cape. More attention in coastal protection should be paid on those high hazard spots.

Experimental validation and numerical simulation of flexible and microscale roll gap control technology

This paper proposes a new flexible and microscale roll gap control technology to obtain a stronger strip flatness control ability. According to the principle of microscale roll gap control technology, an electromagnetic control rolling mill with the function of roll profile control and large diameter ratio rolling is designed and built. To analyze the flatness control ability, a comprehensive finite element model (FEM) is established, and an indentation experiment and a rolling experiment are carried out. The simulation results show that under different rolling forces and tensions, the average quadratic crown control ability is more than 40 μm, and the average quartic crown control ability is more than − 3 μm. The control ability increment of the quadratic crown is greater than that of the quartic crown. In the indentation experiment, a stable roll profile can be achieved by PID control after reaching the target roll profile. Increasing the regulation amount can change the strip crown from positive to negative. Even under high rolling force conditions, microscale roll gap control technology can also realize a strip crown adjustment of 19.5 to 0.5 μm. Moreover, this technology can adjust the strip shape from edge waves to non-waves and middle waves in the rolling experiment. In this paper, the feasibility of using this technology to adjust the roll gap shape has been verified, and we demonstrate that the roll gap control goal of uniform transverse size distribution can be achieved.

CNN-Based Image Reconstruction Method for Ultrafast Ultrasound Imaging.

Ultrafast ultrasound (US) revolutionized biomedical imaging with its capability of acquiring full-view frames at over 1 kHz, unlocking breakthrough modalities such as shear-wave elastography and functional US neuroimaging. Yet, it suffers from strong diffraction artifacts, mainly caused by grating lobes, sidelobes, or edge waves. Multiple acquisitions are typically required to obtain a sufficient image quality, at the cost of a reduced frame rate. To answer the increasing demand for high-quality imaging from single unfocused acquisitions, we propose a two-step convolutional neural network (CNN)-based image reconstruction method, compatible with real-time imaging. A low-quality estimate is obtained by means of a backprojection-based operation, akin to conventional delay-and-sum beamforming, from which a high-quality image is restored using a residual CNN with multiscale and multichannel filtering properties, trained specifically to remove the diffraction artifacts inherent to ultrafast US imaging. To account for both the high dynamic range and the oscillating properties of radio frequency US images, we introduce the mean signed logarithmic absolute error (MSLAE) as a training loss function. Experiments were conducted with a linear transducer array, in single plane-wave (PW) imaging. Trainings were performed on a simulated dataset, crafted to contain a wide diversity of structures and echogenicities. Extensive numerical evaluations demonstrate that the proposed approach can reconstruct images from single PWs with a quality similar to that of gold-standard synthetic aperture imaging, on a dynamic range in excess of 60 dB. In vitro and in vivo experiments show that trainings carried out on simulated data perform well in experimental settings.

Numerical investigation of inline wave force on a truncated vertical cylinder with different cross-sections in regular head waves

The non-linear wave amplification around a truncated vertical cylinder, the high-order horizontal wave loading from non-breaking steep waves and the associated physical process are studied numerically. Considering the high-order free-surface deformation due to high-frequency wave scattering Type-1 and Type-2, and lateral edge waves, the simulations are conducted for a stationary, surface-piercing cylinder with different cross-sections subject to the short and long waves, propagating in deep water. A numerical wave tank based on the Unsteady Navier-Stokes/VOF model is established, using OpenFOAM combined with the olaFlow toolbox for wave generation and absorption. The capabilities of the present numerical model are assessed in conjunction with the ITTC (OEC) benchmark, where the numerical results are in good agreement. Overall, the results indicate the high potential of the present numerical model for accurate modeling of nonlinear wave interaction with cylindrical columns. Variation of wavelength together with the corner ratio significantly influences the magnitude of high-order harmonic wave loading. Moreover, the numerical results indicate the important contribution of the cross-section shape on the non-linear wave field surrounding each cylinder. As the geometrical presence of corner becomes apparent from circular to the square cross-section, there is a systematic increase in the mean value, 1st, 2nd and 3rd harmonics of the inline force subject to both short and long incident waves. Furthermore, interestingly the formation of slightly developed wave scattering of Type-2 at the front of the cylinder in short waves is observed for cross-sections with corner ratios of (rc/R=0.25&0). The development of a secondary load cycle is also observed which is found to be closely related to the occurrence of wave scattering Type-2 and the lateral edge waves where the important contribution from, mean value, 3rd, and 4th harmonics of the inline force are apparent.

Engineering rainbow trapping and releasing in valley photonic crystal with electro-optical material

Topological photonic insulators provide a robust platform for controlling the flow of light. Here, we propose a method to realize slow light rainbow trapping and releasing based on valley photonic crystals, which is created by gradually increasing the structure parameter. The edge waves of different frequencies are spatially separated and trapped at different positions to form topological rainbow trapping. Furthermore, the system is constructed by electric-optical material whose refractive index is tuned by applied voltages. Therefore, the switchable between slow light trapping states and releasing states can be realized by tuning the external voltage. The position where the wave stops propagating is given by theoretical analysis and numerical simulation. These results offer a novel, to the best of our knowledge, scheme for realizing multi-frequency routing. Such a structure could find application prospects in optical buffers, optical storage, and other optical communication devices.

Broadside Radiation From Chern Photonic Topological Insulators

Broadside radiation from Chern photonic topological insulators (PTIs) is studied in this work. The one-way dispersion of the topological edge mode is located in the fast wave region, making leaky-wave radiation possible. In this communication, design guidelines are presented and validated by full-wave simulations: the Berry curvature and the Chern number of photonic crystals are calculated to design a topological edge mode, then a leaky-wave antenna is proposed where a perturbation is utilized around the source location to eliminate open-stopband behavior and generate broadside radiation with high efficiency. It is demonstrated that leakage of the topological edge mode is capable of both frequency and bias scanning to generate a steerable beam across the broadside direction. Moreover, the mechanism behind the immunity of PTIs to defects is also investigated in detail. Although topological edge waves can bypass PEC-slab defects ideally, the phase change along the defect affects the radiation pattern. The switch between sum-difference beams by tuning the scale of the PEC-slab is direct evidence to verify our analysis. To sum up, the open-stopband behavior is overcome to realize broadside radiation, and the conditional robustness of PTIs in terms of antennas is clarified.