Edge Waves Research Articles

Dispersive and dispersive-like bores in channels with sloping banks

In this paper a detailed analysis of undular bore dynamics in channels of variable cross-section is presented. Two undular bore regimes, low Froude number (LFN) and high Froude number (HFN), are simulated with a Serre–Green–Naghdi model, and the results are compared with the experiments by Treske (1994). We show that contrary to Favre waves and HFN bores, which are controlled by dispersive non-hydrostatic mechanisms, LFN bores correspond to a hydrostatic phenomenon. The dispersive-like properties of the LFN bores is related to wave refraction on the banks in a way similar to that of edge waves in the near shore. A fully hydrostatic asymptotic model for these dispersive-like bores is derived and compared to the observations, confirming our claim.

Edge Waves in an Initially Stressed Visco-Poroelastic Plate under Plane Stress Condition

The purpose of this paper is to investigate the propagation of edge waves in a homogeneous visco-poroelastic plate which is initially stressed in horizontal direction. The pertinent governing equations are derived and the frequency equation is obtained in the framework of Biot’s theory. Frequency and attenuation are computed as a function of wavenumber. For the numerical process, solids namely, sandstone saturated with kerosene, sandstone saturated with water is considered and the results are presented graphically.

Quantum spin Hall phase in honeycomb nanoribbons with two different atoms: edge shape effect to bulk-edge correspondence

In this study, we consider a quantum spin Hall (QSH) phase in both the zigzag and the armchair type of honeycomb nanoribbons with two different atoms from the viewpoint of bulk-edge correspondence. Generally, the QSH phase in honeycomb nanoribbons is determined by the topology of the bulk Hamiltonian. However, the armchair type of nanoribbons seems to become the QSH phase in a very different region compared with bulk materials. On the other hand, the zigzag type of nanoribbons seems to become the QSH phase in almost the same region as bulk materials. We study the reason why the QSH phase in nanoribbons seems to be different from that of bulk materials using the extended Kane-Mele Hamiltonian. As a result, there is a clear difference in the edge states in the QSH phase between the zigzag and the armchair type of nanoribbons. We find that the QSH phase region in nanoribbons is actually different from that of bulk materials. This is because the coherence lengths of edge wave functions of nanoribbons are extremely influenced by their edge-shapes. We can conclude that the bulk-edge correspondence does not hold for relatively narrow nanoribbons compared with their coherence lengths and that the edge shapes of nanoribbons make their coherence lengths of edge wavefunctions different, which largely influences the QSH phase.

A robust optimization design method for sheet metal roll forming and its application in roll forming circular cross-section pipe

Sheet metal roll forming (SMRF) is affected by many factors, including forming speed, forming passes, roller diameter, and material properties. It is easy to produce quality defects, such as longitudinal bending, edge wave, and springback, which eventually lead to poor quality stability of SMRF. At present, SMRF design relies mainly on the experience of engineers and its technological parameters must be adjusted repeatedly through experiments, resulting in a long product design cycle and difficult quality stability control. This paper discusses a mathematical model for a robust optimization design for SMRF. Support vector machine (SVM) classification and support vector regression (SVR) are adopted to construct a model of the response surface and to separate feasible variables and infeasible variables. High-dimensional robust optimization problems in SMRF are solved. Using roll forming of a circular cross-section pipe as an example, the result shows that the roundness error standard deviation of the robust optimization design method is 62.2% less than the roundness error standard deviation of the deterministic optimization design method, along with significant improvement in reliability probability. The method is validated as effective in reducing quality defects, including longitudinal bending, edge wave, and springback. This robust optimization design method can improve the quality stability of SMRF.

Asymmetric dynamics of edge exchange spin waves in honeycomb nanoribbons with zigzag and bearded edge boundaries

We report on the theoretical prediction of asymmetric edge spin waves, propagating in opposite directions at the boundaries of antiferromagnetic honeycomb nanoribbons with zigzag and bearded edges. The simultaneous propagation of edge spin waves along the same direction on both edges of the nanoribbons is forbidden. These asymmetric exchange spin waves at the edge boundaries are analogous to the nonreciprocal surface spin waves reported in magnetic thin films. Their existence is related to the nontrivial symmetry underlying these nanoribbons types. The discretized bulk and the edge exchange spin waves are calculated for the long wavelength part of the nanoribbon Brillouin zone (BZ), using the classical field spin wave theory and notably appropriate boundary conditions. In the absence of an external magnetic field in our study, the asymmetric edge spin waves propagate with equal frequencies and along opposite directions. The edge spin waves are characterized by linear dispersion relations for magnetically isotropic nanoribbons. For magnetically anisotropic nanoribbons, our calculations show that the energy gap between the edge and bulk spin waves is enhanced for both types of zigzag and bearded nanoribbons. The large energy gap separates the edge modes from overlapping the bulk ones. Also, we explain why our results for anisotropic zigzag nanoribbons go beyond previous studies based on a quantum approach in the linear spin wave approximation.

Wave refocusing for linear diffractor using the time‐reversal principle

ABSTRACTOne of the problems encountered in a variety of near‐surface investigations is detecting and mapping localized heterogeneities. The heterogeneities may be classified under two kinds of objects: (1) a point diffractor that can be considered as an approximation of a small quasi‐isometric, such as small karstic cavities and caves; (2) a linear diffractor roughly approximating an elongated object, such as a tube or fault plane. The point and linear diffractors generate two types of seismic diffraction: tip and edge waves, respectively. During the last few decades, different methods were proposed by many researchers for detecting these heterogeneities utilizing seismic waves diffracted by them. An alternative method for detecting point diffractors using a time‐reversal principle combined with focusing analysis is proposed in this study: we present an extension of the time‐reversal method for linear diffractors. It consists of a coherent summation of seismic energy along edge‐diffraction traveltimes. Real data examples show the feasibility and efficiency of the proposed method.

Subharmonic edge wave excitation by narrow-band, random incident waves

A monochromatic, small amplitude, normally incident standing wave on a sloping beach is unstable to perturbation by subharmonic (half the frequency) edge waves. At equilibrium, edge wave shoreline amplitudes can exceed incident wave amplitudes. Here, the effect of incident wave randomness on subharmonic edge wave excitation is explored following a weakly nonlinear stability analysis under the assumption of narrow-band incident random waves. Edge waves respond to variations in both incident wave phase and amplitude, and the edge wave amplitudes and incident wave groups vary on similar time scales. When bottom friction is included, intermittent subharmonic edge wave excitation is predicted due to the combination of bottom friction and wave phase. Edge wave amplitude can be near zero for long times, but for short periods reaches relatively large values, similar to amplitudes with monochromatic incident waves and no friction.

Sound diffraction prediction of a rectangular rigid plate using the physical theory of diffraction

For the purpose of numerical efficiency in room acoustic modeling, the physical theory of diffraction (PTD) is applied to approximate solutions of a finite-sized, rigid rectangular plate. The application of the PTD enables sound diffraction contributions from the two edge pairs of the rigid plate to be predicted separately while ignoring the edge waves around the corners in far-field. This paper discusses numerical implementations of the theoretical predictions to show the efficiency of the application of the PTD in finite-sized objects. The numerical results implemented will also be compared with preliminary experimental results carried out using an acoustical goniometer.

Shape Defects in The Flexible Roll Forming of Automotive Parts

Flexible roll forming allows variable cross sections of profiles to be made by using adaptive roll stands. The most common shape defects that occur during flexible roll forming are edge wave and longitudinal bow. These two defects are necessary to consider together for relatively thin-walled blanks because they usually occur simultaneously during flexible roll forming. To understand the occurrence of these defects, finite element (FE) simulations based on the rigid shell concept were carried out using three blanks with different shapes: trapezoid, concave, and convex. The FE analysis on the flexible roll forming process was performed first, and then the gap of rigid shell has been decreased for reducing the longitudinal bow in roll formed blank. The reduction of longitudinal bow in the web part usually causes edge wave in the flange part. The occurrence of shape defects is investigated based on the relationships among edge curvature, longitudinal stress at the edge, and longitudinal bow height. When longitudinal bow is reduced, the longitudinal stress at the edge of roll formed blank is changed from tensile to compressive in convex blank but in concave blank, tensile residual stress increases. Edge waves occur in the flanges of trapezoid and convex blanks as a result of decreased longitudinal bow. Lab-scale flexible roll forming experiments show multi-stand forming with a leveling roll is desirable to reduce both edge wave and longitudinal bow.

Analysis of generation and arrival time of landslide tsunami to Palu City due to the 2018 Sulawesi earthquake

Tsunami waves severely damaged the densely populated coast of Palu City immediately after the 2018 Mw 7.5 Sulawesi earthquake. Among the several tsunami waves that arrived to the city, the two initial waveforms were most likely generated by a landslide at the south-western shore of Palu Bay, about 5 km away from one of the city’s shopping malls. The authors accurately identified the arrival time and direction of the waves by comparing multiple videos taken by a pilot from the cockpit of a plane and local people who witnessed waves approaching the coast. Although the authors’ bathymetric survey only covered a limited area of 0.78 km2, it was found that about 3.2 million m3 of mass disappeared from it, causing a maximum decrease in the seabed elevation of 40 m. A landslide scarp up to 5 m height was also investigated in the southwestern shore of the bay, which seems to be relatively minor compared to the submarine mass failure. Visible clue for liquefaction was not observed at this particular site. A simplified numerical model suggests that the landslide tsunami propagated as an edge wave and split into two separate waves due to the presence of an underwater shallow area just north of Palu City. Both waves arrived to the coast of this city within several minutes: one from North-West and the other from the North. Three major waves were witnessed by residents, who felt horizontal and vertical ground movements and heard the sound of an explosion just after the earthquake. Wave splash exceeded the height of trees on the beach. Given the results, the authors conclude that any modern early warning system is unlikely to work well against such short-warning time tsunamis, and thus, it is necessary for disaster risk managers to consider a way to help people quickly become aware of the potential disaster and evacuate.

Programmable elastic valley Hall insulator with tunable interface propagation routes

A challenge in the area of topologically protected edge waves in elastic media is how to tune the topological interface propagation route as needed. This paper proposes a tunable elastic valley Hall insulator, whose unit cell consists of two cavities and magnetic fluid with the same volume as the cavity. Interface route with arbitrary shape for propagating topologically protected edge waves can be achieved by controlling the distribution of magnetic fluid in each unit cell through a designed programmable magnet lifting array. As demonstrated through numerical simulations and experimental testing, the flexural wave is confined to propagate along the topological interface routes of different configurations. Finally, it is indicated that the proposed valley Hall insulator can be applied to achieve desired localized elastic energy which is robust to defects, sharp corners and so on.

Diffraction simulation from wedges to finite-sized plates based on the physical theory of diffraction

Efficient predictions of sound diffraction around objects are of critical significance in room-acoustic simulations. An advanced diffraction theory has recently been investigated for potential applications in room acoustics for some semi-infinite, canonical wedges and for finite-sized rectangular plates [Rozynova and Xiang, J. Acoust. Soc. Am. 144 (to be published)]. The physical theory of diffraction (PTD) still relies on both geometrical and physical principles, yet emphasizes the physical one. Important features of the PTD approach are its computational efficiency and the high degree of accuracy for the diffracted sound field. This paper reviews the fringe field predictions of canonical semi-infinite wedges and further discusses solutions of diffraction problems on finite, rigid rectangular plates. The PTD is applied to approximate the solutions of a finite-sized, rigid rectangular plate that achieves high numerical efficiency. The PTD simulation allows sound diffraction contributions to be determined independently from two pairs of edges of the rigid plate, while ignoring the edge waves around the corner in far-field. This paper uses numerical implementations of the PTD predictions to demonstrate the simulation efficiency of the PTD in finite-sized objects. The numerical simulations are also validated by some preliminary experimental results carried out using an acoustic goniometer.

Rayleigh–Bloch, topological edge and interface waves for structured elastic plates

Galvanised by the emergent fields of metamaterials and topological wave physics, there is currently much interest in controlling wave propagation along structured arrays, and interfacial waves between geometrically different crystal arrangements. We model array and interface waves for structured thin elastic plates, so-called platonic crystals, that share many analogies with their electromagnetic and acoustic counterparts, photonic and phononic crystals, and much of what we present carries across to those systems. These crystals support several forms of edge or array-guided modes, that decay perpendicular to their direction of propagation. To rapidly, and accurately, characterise these modes and their decay we develop a spectral Galerkin method, using a Fourier–Hermite basis, to provide highly accurate dispersion diagrams and mode-shapes, that are confirmed with full scattering simulations. We illustrate this approach using Rayleigh Bloch modes, and generalise high frequency homogenisation, along a line array, to extract the envelope wavelength along the array. Rayleigh–Bloch modes along graded arrays of rings of point masses are investigated and novel forms of the rainbow trapping effect and wave hybridisation are demonstrated. Finally, the method is used to investigate the dispersion curves and mode-shapes of interfacial waves created by geometrical differences in adjoining media.

Edge Waves Durfing Motion of a Vessel in an Ice Channel

Edge Waves Durfing Motion of a Vessel in an Ice Channel

EDGE WAVE INDUCED BY AN ATMOSPHERIC PRESSURE DISTURBANCE MOVING ALONG A SLOPING BEACH

Edge wave can be generated by an atmospheric pressure disturbance moving along the shoreline on a sloping beach. A two-dimensional numerical model based on non-linear shallow water equations is established and a set of numerical experiments are conducted to study the edge wave packets evolution in coastal ocean. In light of the analytical solutions by Greenspan, some dominant factors are discussed, such as disturbance spatial size, translation speed, its location and the slope inclination, that influence the generation conditions and evolution process of edge waves. The results indicate on what circumstances significant edge waves will be excited and how long it takes for the wave growth.

ALONGSHORE VARIABILITY OF COASTAL MORHODYNAMICS IN EASTERN LAKE ERIE DUE TO LOW FREQUENCY OSCILLATIONS OF LAKE LEVEL

Lake Erie has the fourth largest surface area, shallowest water depth and smallest volume among the five Great Lakes in North America (NOAA). The dominant wind direction over Lake Erie’s is southwest-northeast, along the lake’s longitudinal axis. The atmospheric and water level data of the lake demonstrate that high wind and moving pressure systems can result in high storm surge of up to 3 m on the eastern end of the lake and significant drop in the water level at the western end of the lake Due to its shallow depth, such a water level gradient can trigger unique post-storm free water-level fluctuations or seiches in Lake Erie (Farhadzadeh, 2017). The morphodynamic implications of such low frequency oscillations are yet to be studied for the lake’s shorelines. Most of studies on the contributions of long waves to beach morphology changes focused on low frequency harmonics induced by short waves, e.g. infragravity waves, edge waves, etc., oscillations with periods of up to a few minutes. Wright and Short (1984) discussed the differences in hydrodynamic processes and relative contributions of various mechanisms to morphological changes of beaches of different states, i.e., reflective, dissipative or intermediate. They concluded that for reflective beaches, incident waves and subharmonic edge waves are dominant while for dissipative beaches currents associated with infragravity standing waves are dominant in nearshore areas. Russell (1993) stated that as low frequency wave energy increases toward a shoreline, the offshore-directed transport at low frequency can become more pronounced.

BASIN-SCALE MODEL FOR PREDICTING MARSH EDGE EROSION

Recent attempts to relate marsh edge retreat rate to wave power have met varying levels of success. Schwimmer (2001) correlated wave power to marsh boundary retreat rates over a five-year period along sites within Rehoboth Bay, Delaware, USA. Marani et al. (2011) derived a linear relationship between volumetric retreat rate and mean wave power density using Buckingham’s theorem of dimensional analysis. Leonardi and Fagherazzi (2015) added an exponential function to the Schwimmer (2001) equation to account for variability in soil resistance and mean wave height. These equations factor in soil type, water elevation, vegetation, and macrofauna through field-calibrated empirical constants, i.e., they are not explicitly considered. Consequently, the existing capability of predicting marsh edge erosion rate as a function of wave power and soil and vegetation properties is rather limited for engineering applications. For instance, Allison et al. (2017) show that without taking the marsh platform, soil, and vegetation into account, the relationships between marsh edge erosion rates and wave power on a basin or coastal-wide scale are not strong enough statistically to serve as a useful predictive model. The objective of this study is to develop a more robust marsh edge erosion model by characterizing the shear strength, wave power, and retreat rates in Terrebonne Bay, Louisiana.

ESTIMATING METEO-TSUNAMI OCCURRENCES FOR THE US EAST COAST

Meteorological tsunamis, also called meteo-tsunamis, are significant ocean surface waves generated by atmospheric forcing. The waves typically result from energy transfer from atmosphere to ocean through the Proudman resonance phenomena, where translation speed of the storm system in the atmosphere coincides with the free wave speed of long surface waves. These tsunami-like waves can be hazardous, either through direct inundation of shorelines or through generation of harbor oscillations and other disruptions to maritime activities. The wide continental shelf bathymetry of the United States (US) East Coast provides a long potential fetch length for the resonant generation process, making the region particularly susceptible to meteo-tsunamis. In this study, we carry out a probabilistic analysis of potential meteo-tsunami hazard on the US East Coast, extending the earlier work of Geist et al. (2014) to include a wider range of storm conditions and additional response types including coastally-trapped edge waves. The work, carried out under the auspices of the National Tsunami Hazard Mitigation Program (NTHMP), extends the previous efforts of Geist et al. to include a representation of inundation and maritime hazards in at-risk areas. The work is conducted using the fully nonlinear Boussinesq wave model FUNWAVE-TVD (Shi et al., 2012), extended to include atmospheric pressure and wind forcing.

EMPIRICAL AND NUMERICAL MODAL ANALYSIS OF COASTAL AREAS PRONE TO TSUNAMI RISK

In this paper the Empirical Orthogonal Function (EOF) method and the k-f spectral technique are applied to extract from experimental data related to landslide-tsunamis propagating around the coast of a conical island, the wave modes that contribute to the wave field. The relevant modes are then compared with those obtained through numerical eigenanalysis of the long wave equation around the considered island. It is shown that it is possible to associate each EOF mode with some eigenvectors and the corresponding eigenfrequencies, both on the basis of the spatial shape, the wavenumber calculated along the coast and the frequency. Results confirm that landslide-generated waves propagate along the coast as trapped edge waves and the zero-th order mode is the most important.

Plate profile control during ultra-thin strip rolling utilizing work roll edge contact

During ultra-thin strip cold rolling, a phenomenon of work roll edge contact always appears. Very serious work roll edge contact and an edge wave occur when the strip thickness decreases; however, it is difficult to eliminate these problems with traditional control methods. To accurately analyse the influence of the mechanism of work roll edge contact on the strip shape control for ultra-thin strips, a finite-length semi-infinite body model of the roll is established based on the boundary element method. Then, a new work roll edge contact model which is applied to the rolling process of a laboratory twenty-high mill was established. The results show that when very serious work roll edge contact and an edge wave occur, the strip shape defect cannot be eliminated by traversing the first intermediate roll. Therefore, the roll gap is adjusted by utilizing work roll edge contact to improve its profile.