Incident Surface Waves Research Articles

TOPOGRAPHICAL EFFECTS ON WAVE SCATTERING BY AN ELASTIC PLATE FLOATING ON TWO-LAYER FLUID

This article illustrates the hydroelastic interactions between surface gravity waves and a floating elastic plate in a two-layer liquid with variable bottom topography under the assumptions of small amplitude waves and potential flow theory. In this study, semi-infinite and finite-length plates are considered. The eigenfunction expansion method is applied in the fluid region with uniform bottom topography. A system of differential equations (mild-slope equations) is solved in the fluid region with variable bottom topography. From the matching and jump conditions, the solution is expressed as a linear algebraic system from which all the unknown constants are computed. We explored the effects of density ratio, depth ratio, and bottom topography on the bending moment, shear force, and the deflection of the elastic plate. Results show that when the density ratio becomes closer to one, the occurred bending moment and shear forces to the elastic plates tend to diminish. The bending moment and shear forces to the pates are higher and lower at a smaller depth ratiofor the incident surface wave and interfacial waves, respectively. The variations in the bending moment, shear force, and plate deflection, caused by surface and interfacial waves, are observed to be in opposite trends, respectively. Bottom profiles similarly affect semi-infinite and finite-length plates when they undergo free-edge conditions. These effects, however, are substantial when the plate is simply supported at the edges. Elastic plate with free edges experiences lower deflection for concave-up and plane-sloping bottoms for incident surface and interfacial waves, respectively.

Resonance frequency of an orthotropic layer to non-principal vertically incident SH body and surface waves

Resonance frequency of an orthotropic layer to non-principal vertically incident SH body and surface waves

Application of the Reciprocity Theorem to Scattering of Surface Waves by a Surface Crack in Viscoelastic Material

In this paper, the scattered surface waves created by a surface crack in a homogeneous, isotropic, viscoelastic half space within a plane strain condition was studied. The amplitude of the scattered surface wave in the far field was determined by using the reciprocity theory and a virtual surface wave. It was shown that the amplitude of the scattered surface wave was related to the crack-opening displacement and the crack length. In the special case of low frequency and low viscosity, the tractions due to the incident surface wave applying on the crack surface can be regarded as uniform, and a finite element method (FEM) based on rubber material was performed to verify the theoretical results. It was shown that the numerical results were consistent with the theoretical solutions, which proves the reliability of the theoretical analysis. The reciprocity theorem avoids complex integral transformation and reveals the relationship between the scattered surface wave and the size of the surface crack, which is promising in the characterization of surface cracks.

Ultrasonic characterization of distributed cracking damage in concrete using multiply scattered wave fields

This paper reports work to detect, visualize, and characterize alkali–silica reactivity cracking damage in concrete using multiply scattered ultrasonic wave fields. Numerical simulations and laboratory-scale experiments are performed to understand ultrasonic surface wave scattering caused by distributed cracks in concrete, distinguishing that caused by the internal aggregate network. The simulations and experimental results reveal that incident ultrasonic surface waves undergo complicated multiple scattering set up by distributed cracks. To extract the crack-induced multiply scattered ultrasonic wave fields, a frequency-wavenumber (f-k) domain signal filtering approach is proposed. The feasibility of the signal analysis approach is then established by a series of experiments on large steel reinforced concrete blocks with known and controlled cracking damage. The experimental results demonstrate that distributed cracks can be detected and visualized using the proposed ultrasonic signal analysis approach, even at very early stages of the damage process. In addition, we demonstrate that the progress of damage over time can be monitored, where the cracking damage extent is closely related to the extracted multiply scattered wave field energy.

Scattering of a surface wave in a polygonal domain with impedance boundary

The two-dimensional (2D) domain under study is bounded from below by two semi-infinite and, between them, two finite straight lines; on each of the straight lines (segments), a usually individual impedance boundary condition is imposed. An incident surface wave, propagating from infinity along one semi-infinite segment of the polygonal domain, excites outgoing surface waves both on the same segment (a reflected wave) and on the second semi-infinite segment (a transmitted wave); in addition, a circular (cylindrical) outgoing wave will be generated in the far field. The scattered wave field satisfies the Helmholtz equation and the Robin (in other words, impedance) boundary conditions as well as some special integral form of the Sommerfeld radiation conditions. It is shown that a classical solution of the problem is unique. By the use of some known extension of the Sommerfeld–Malyuzhinets technique, the problem is reduced to functional Malyuzhinets equations and then to a system of integral equations of the second kind with integral operator depending on a characteristic parameter. The Fredholm property of the equations is established, which also leads to the existence of the solution for noncharacteristic values of the parameter. From the Sommerfeld integral representation of the solution, the far-field asymptotics is developed. Numerical results for the scattering diagram are also presented.

Formation of leaf-shaped microstructure on Zr-based metallic glass via nanosecond pulsed laser irradiation

Formation of regular micro/nano-structures on the surface of metallic glasses (MGs) is beneficial to their functional applications. To pattern the MG surface, in this work, a polished Zr-based MG sample was processed by using a nanosecond pulsed laser under various parameters. Experimental results showed that the regular leaf-shaped microstructure consisting of ripples and vein-like structures was generated in the irradiated area. The effects of processing parameters, including the average power, scanning speed, repetition frequency and pulse overlap rate, on the formation and evolution of leaf-shaped microstructure were investigated in detail. Furthermore, by analyzing the surface characteristics and morphological evolution, the formation mechanism of the leaf-shaped microstructure was analyzed. The ripples with spacing slightly smaller than the wavelength of incident laser were caused by interaction of the incident laser and excited molten surface waves, and the vein-like structures were formed by the subsequent laser pulses induced evolution of precedingly generated micro-cracks. The interaction between the ripples and the vein-like structures resulted in the formation of the leaf-shaped microstructure. After patterning, the MG surface with leaf-shaped microstructure showed enhanced hydrophilicity.

On-Chip Metasurface for Optical Directional Rectification

On-chip two-dimensional (2D) metasurfaces create a new degree of freedom of light manipulation within a 2D surface, which is an emerging research area with fascinating possibilities for realization of very dense integration and miniaturization in photonic systems. As a longstanding challenge in optics steering, light rectification, which means to manipulate beams with multiple directional wavevectors to exit to the same outgoing direction, could hardly be made possible based on conventional optics unless with zero-index medium. However, on-chip metasurface could potentially come to rescue with deep-subwavelength features and its engineered phase signature depending on wavevectors. Here, we design and demonstrate a surface-wave rectification on-chip metasurface (SROM) for visible light, which realizes light rectification for oblique incidences within +/-20°. The SROM is formed by cascading two plasmonic on-chip nanowires of semi-elliptical and trapezoidal structures as its unit cell. Through the geometrical change induced by the semi-elliptical and trapezoidal structures and the plasmonic interaction between the two cascaded nanowires, the incident surface waves with multiple wavevector angles would exit and propagate normally along 0° around 500 nm wavelength, thus mimicking a zero-index-like phenomenon. The equal-frequency contour (EFC) of the designed SROM is also numerically retrieved to exhibit flat angular dispersion, which verifies the proof-of-concept light reification phenomenon. The on-chip miniature SROM is of merely ~ 3 μm length, and the light rectification performance remains for the visible-frequency band of 500 - 560 nm. Such new on-chip architecture only involves the mature and conventional nanofabrication techniques to manufacture without any alignment for multilayer metasurfaces. We envision that the created beam-steering freedom of light rectification opens a viable and compatible route towards new invention of photonic integrated devices.

Investigation on the effects of Bragg reflection on harbor oscillations

Periodic undulating topographies (such as sandwaves and sandbars) are very common in coastal and estuarine areas. Normally incident water surface waves propagating from open sea to coastal areas may interact strongly with such topographies. The wave reflection by the periodic undulating topography can be significantly amplified when the surface wavelength is approximately twice the wavelength of the bottom undulations, which is often called as Bragg resonant reflection. Although the investigations on the hydrodynamic characteristics related to Bragg reflection of a region of undulating topography have been widely implemented, the effects of Bragg reflection on harbors have not yet been studied. Bragg resonant reflection can effectively reduce the incident waves. Meanwhile, however, it can also significantly hinder the wave radiation from the harbor entrance to the open sea. Whether Bragg reflection can be utilized as a potential measure to alleviate harbor oscillations is unknown.In the present study, Bragg reflection and their interactions with the harbor are simulated using a fully nonlinear Boussinesq model, FUNWAVE 2.0. For the purpose, an elongated harbor with constant depth is considered, and a series of sinusoidal bars with various amplitudes and numbers are deployed outside the harbor. The incident waves considered in this paper include regular long waves and bichromatic short wave groups. It is revealed for the first time that for both kinds of incident waves, Bragg resonant reflection can significantly alleviate harbor resonance. The influences of the number and the amplitude of sinusoidal bars on the mitigation effect of harbor resonance and on the optimal wavelength of sinusoidal bars that can achieve the best mitigation effect are comprehensively investigated, and it is found that the former two factors have remarkable influences on the latter two parameters. The present research provides a new option for the mitigation of harbor oscillations via changing the bottom profile, which is feasible as long as the navigating depth is guaranteed.

Modified Stokes drift due to resonant interactions between surface waves and corrugated sea floor with and without a mean current

A unidirectional surface gravity wave over a flat bottom topography causes a unidirectional Stokes drift of floating particles. However, rippled bottom topography can resonantly interact with incident surface waves and generate reflected waves. This introduces a backward drift component that counters the unidirectional forward motion of the floating particles. Hence rippled bottom topography can act as a non-surface-invasive particle trap or reflector and thus help in mitigating ocean pollution.

Application of the reciprocity theorem to scattering of surface waves by an inclined subsurface crack

In this paper the scattering of incident surface waves by an inclined subsurface crack in a homogenous, isotropic and linearly elastic half-space has been investigated in a two-dimensional plane strain configuration. The elastodynamic reciprocity theorem together with a virtual wave has been used to determine the amplitude of the scattered surface waves in the far field. It is found that the amplitude is in terms of the crack opening volume due to the incident surface waves. A special case of low frequency, for which the wavelength of the surface wave is sufficiently larger than the crack length, has been considered to illustrate the method. A specific expression of the amplitude has been obtained, which provides information on the angle, length and depth of the crack. It shows that the amplitude of the scattered surface wave increases first and then decreases as the crack angle changes from 0° to 90°. For the case of an inclined crack, the results of the numerical analysis together with the analytical solutions show excellent agreement when the crack length is much smaller than the wavelength. The results in this paper should be useful for the quantitative measurement of subsurface cracks.

Effects of Wave Streaming and Wave Variations on Nearshore Wave-Driven Circulation

AbstractWave streaming is a near-bottom mean current induced by the bottom drag on surface gravity waves. Wave variations include the variations in wave heights, periods, and directions. Here we use numerical simulations to study the effects of wave streaming and wave variations on the circulation that is driven by incident surface waves. Wave streaming induces an inner-shelf Lagrangian overturning circulation, which links the inner shelf with the surf zone. Wave variations cause alongshore-variable wave breaking that produces surf eddies; however, such eddies can be suppressed by wave streaming. Moreover, with passive tracers we show that wave streaming and wave variations together enhance the cross-shelf material transport.

Water Wave Scattering by a Bottom-Standing Thick Rectangular Barrier in the Presence of an Ice Cover

The problem of scattering of a normally incident surface wave train by an obstacle in the form of a thick rectangular vertical bottom-standing barrier submerged in finite-depth water with a free surface is extended here with an ice cover modelled as a thin uniform elastic plate. The problem is reduced to a set of singular integral equations of the first kind. The Galerkin approximation in terms of simple polynomials multiplied by appropriate weight functions whose form is dictated by the behavior of the fluid velocity near the barrier edges is used for solving the integral equations. The reflection and transmission coefficients are obtained numerically, and they are depicted graphically against the wavenumber for various ice cover parameters. It is observed that the barrier thickness plays a significant role in modelling of efficient breakwaters.

Scattering of a Rayleigh wave by a near surface crack which is normal to the free surface

In this paper, scattering of a Rayleigh surface wave by a 2D near-surface crack which is normal to the free surface of a homogenous, isotropic and linearly elastic half-space has been investigated. The scattered field is represented by the radiation from equivalent body forces, which are expressed in terms of the crack-opening volumes generated by the incident Rayleigh wave. The reciprocity theorem together with a virtual wave has been used to determine the amplitude of the far field of the scattered Rayleigh wave. A special case of low frequency, and small ratio of the crack length to the wavelength of the incident Rayleigh wave, has been considered to illustrate the method for different values of the ratio of crack length to the wavelength of the incident surface wave. The displacements of the analytical solution on the free surface at some distance from the crack are compared with the displacements obtained numerically. Analytical and numerical results show excellent agreement when the Rayleigh wavelength is sufficiently larger than the crack length. The results of this paper should be useful for the quantitative non-destructive evaluation of a near-surface crack.

Programmable mode conversion and bandgap formation for surface acoustic waves using piezoelectric metamaterials

A spatially reversible and programmable piezoelectric metamaterial concept is introduced for the manipulation of surface acoustic waves to achieve on-demand wave mode conversion and reflection. The concept uses an array of inductive-shunted piezoelectric elements (with gradually varying inductors in space) attached to the surface of an elastic propagation domain. The value of each inductor directly controls the phase velocity of the Rayleigh wave locally as quantified through unit cell band diagram analysis that guides the design process. By varying the spatial inductance distribution, the proposed piezoelectric metamaterial domain can be programed to convert incident surface waves into bulk shear waves or reflect them completely. The location of surface-to-bulk wave mode conversion or wave reflection can be tailored by means of the inductance distribution, and the directional behavior in space can be reversed. The proposed concept may enable novel surface acoustic wave devices and filters, via digital or analog programmable shunt circuits.

Mitigation of structural responses of a very large floating structure in the presence of vertical porous barrier

The effectiveness of partial vertical permeable barriers of three different configurations located at a finite distance from a very large floating structure is analyzed for mitigating the wave-induced response of the structure. The eigenfunction expansion method is employed to obtain solution in case of normal incidence and the study is extended to the case of oblique incident waves. In case of normalized incident waves, a detailed analysis of the results on various physical quantities such as the reflection and transmission coefficients, wave force on the barrier, free surface elevation, plate deflection, shear force and surface strain on the floating structure are presented. For the case of oblique incidence, results on reflection coefficient for various structural parameters are presented. Using Green's identity, energy balance relations are derived in both the cases of normally and obliquely incident surface waves and certain results for normally incident waves are compared for accuracy. The study reveals that wave reflection follows an oscillatory pattern and the minima in the oscillatory pattern increase with an increase in structural porosity. Wave reflection and dissipation attain their optima for the same wave number irrespective of barrier configurations. Occurrences of wave diffraction are observed in case of long waves for barriers of varied configurations with a narrow gap which decreases with the introduction of barrier permeability. Moreover, when the distance between the barrier and the very large floating structure is close to an integer multiple of half of the wavelength, both the wave reflected by the barrier as well as wave forces acting on the barrier attains their optima.

Oblique scattering by thin vertical barriers in deep water : solution by multi-term Galerkin technique using simple polynomials as basis

This paper is concerned with scattering of obliquely incident surface waves by a thin vertical barrier which may be either partially immersed or completely submerged extending infinitely downwards in deep water. Instead of one-term Galerkin approximation involving the known solution of the integral equation arising in the normal incidence problem, two-term Galerkin approximation involving simple polynomials as basis multiplied by appropriate weight function is used to solve the integral equations arising in the mathematical analysis of the oblique scattering problem. Very accurate numerical estimates for the reflection coefficient for each configuration of the barrier are obtained. The reflection coefficient is depicted graphically against the wavenumber and the incident angle for each configuration.

3D hydroelastic analysis of very large floating bodies over variable bathymetry regions

The coupled-mode model developed by Belibassakis and Athanassoulis (J Fluid Mech 531:221–249, 2005) is extended and applied to the hydroelastic analysis of three-dimensional large floating bodies of shallow draft lying over variable bathymetry regions. The method is also applicable to the problem of wave interaction with ice sheets of small thickness. A general bathymetry is assumed, characterized by a continuous depth function, joining two regions of constant, but possibly different, depth. We consider the scattering problem of harmonic incident surface waves, under the combined effects of variable bathymetry and a floating elastic plate of orthogonal planform shape. Under the assumption of small-amplitude waves and plate deflections, the hydroelastic problem is formulated within the context of linearized water-wave and thin elastic-plate theory. To consistently treat the wave field beneath the elastic floating plate, down to the sloping bottom boundary, a complete, local, hydroelastic-mode series expansion of the wave field is used, enhanced by an appropriate sloping-bottom mode. The latter enables the consistent satisfaction of the Neumann bottom-boundary condition on a general topography. Numerical results concerning floating structures over flat and inhomogeneous seabed are presented, and the effects of wave direction, bottom slope and bottom corrugations on the hydroelastic responses are discussed.

The characteristics and dynamics of wave‐driven flow across a platform coral reef in the Red Sea

AbstractCurrent dynamics across a platform reef in the Red Sea near Jeddah, Saudi Arabia, are examined using 18 months of current profile, pressure, surface wave, and wind observations. The platform reef is 700 m long, 200 m across with spatial and temporal variations in water depth over the reef ranging from 0.6 to 1.6 m. Surface waves breaking at the seaward edge of the reef cause a 2–10 cm setup of sea level that drives cross‐reef currents of 5–20 cm s−1. Bottom stress is a significant component of the wave setup balance in the surf zone. Over the reef flat, where waves are not breaking, the cross‐reef pressure gradient associated with wave setup is balanced by bottom stress. The quadratic drag coefficient for the depth‐average flow decreases with increasing water depth from Cda = 0.17 in 0.4 m of water to Cda = 0.03 in 1.2 m of water. The observed dependence of the drag coefficient on water depth is consistent with open‐channel flow theory and a hydrodynamic roughness of zo = 0.06 m. A simple one‐dimensional model driven by incident surface waves and wind stress accurately reproduces the observed depth‐averaged cross‐reef currents and a portion of the weaker along‐reef currents over the focus reef and two other Red Sea platform reefs. The model indicates the cross‐reef current is wave forced and the along‐reef current is partially wind forced.

Switchable nonlinear metasurfaces for absorbing high power surface waves

We demonstrate a concept of a nonlinear metamaterial that provides power dependent absorption of incident surface waves. The metasurface includes nonlinear circuits which transform it from a low loss to high loss state when illuminated with high power waves. The proposed surface allows low power signals to propagate but strongly absorbs high power signals. It can potentially be used on enclosures for electric devices to protest against damage. We experimentally verify that the nonlinear metasurface has two distinct states controlled by the incoming signal power. We also demonstrate that it inhibits the propagation of large signals and dramatically decreases the field that is leaked through an opening in a conductive enclosure.

Automated Surface Wave Measurements for Evaluating the Depth of Surface-Breaking Cracks in Concrete

The primary objective of this study is to investigate the feasibility of an innovative surface-mount sensor, made of a piezoelectric disc (PZT sensor), as a consistent source for surface wave velocity and transmission measurements in concrete structures. To this end, one concrete slab with lateral dimensions of 1500 by 1500 mm and a thickness of 200 mm was prepared in the laboratory. The concrete slab had a notch-type, surface-breaking crack at its center, with depths increasing from 0 to 100 mm at stepwise intervals of 10 mm. A PZT sensor was attached to the concrete surface and used to generate incident surface waves for surface wave measurements. Two accelerometers were used to measure the surface waves. Signals generated by the PZT sensors show a broad bandwidth with a center frequency around 40 kHz, and very good signal consistency in the frequency range from 0 to 100 kHz. Furthermore, repeatability of the surface wave velocity and transmission measurements is significantly improved compared to that obtained using manual impact sources. In addition, the PZT sensors are demonstrated to be effective for monitoring an actual surface-breaking crack in a concrete beam specimen subjected to various external loadings (compressive and flexural loading with stepwise increases). The findings in this study demonstrate that the surface mount sensor has great potential as a consistent source for surface wave velocity and transmission measurements for automated health monitoring of concrete structures.