Incident Surface Waves Research Articles

Laser-Induced Formation of Periodic Structures on the Metal Surfaces and Surface Plasmons Excitation

Quasiperiodic microstructures are formed on the surfaces of metals under irradiation with high-power femtosecond laser pulses. Interpretation of microstructures as a result of interference of the incident plane wave and surface waves leads to the logical conclusion about the relationship of dislocations in the interference fringes with optical vortices in surface wave. Other peculiarities observed in these structures contain different periods and nanogranular fine structure. It is demonstrated that such laser-induced structures can find applications for surface plasmon excitation and surface enhanced Raman scattering.

Scattering of oblique surface waves by the edge of small deformation on a porous ocean bed

The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. Using perturbation analysis, the corresponding problem governed by modified Helmholtz equation is reduced to a boundary value problem for the first-order correction of the potential function. The first-order potential and, hence, the reflection and transmission coefficients are obtained by a method based on Green's integral theorem with the introduction of appropriate Green’s function. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number along x-direction and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the free-surface, and the reflection coefficient becomes a multiple of the number of ripples. Again, for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. It is also observed that the reflected energy is somewhat sensitive to the changes in the porosity of the ocean bed. From the derived results, the solutions for problems with impermeable ocean bed can be obtained as particular cases.

Radiation and oblique diffraction by submerged prolate spheroids in water of finite depth

In the present study we present a general methodology for estimating the hydrodynamic (added-mass and damping) coefficients of a fully submerged (below a free-surface) elongated axisymmetric ocean-going body (approximated by a prolate spheroid) in water of finite depth (rigid even sea bottom). Using the same approach, we also provide a solution for the corresponding linearized diffraction problem and analytically determine the exciting hydrodynamic forces and moments exerted on the body due to obliquely incident monochromatic surface waves. A comprehensive series of numerical simulations is presented for the relevant hydrodynamic parameters depending on the wave encounter frequency and angle of incidence, including body submergence and slenderness-ratio as well as the water depth. Numerical validations are also provided as limiting cases for spherical shapes in finite water and for spheroidal geometries in water of infinite depth.

Manifestation of optical vortices on the surface of solids under irradiation with femtosecond laser pulses

Quasi-periodic microstructures containing dislocations are formed on the surfaces of metals and semiconductors under irradiation with high-power femtosecond laser pulses. Interpretation of microstructures as a result of interference of the incident plane wave and surface waves leads to the logical conclusion about the relationship of dislocations in the interference fringes with optical vortices in surface wave.

Oblique wave trapping by porous and flexible structures in a two-layer fluid

Trapping of obliquely incident surface waves by permeable flexible barriers placed near a vertical rigid wall in a two-layer fluid having free surface and an interface is studied for both surface-piercing and bottom-standing partial barriers. For the surface-piercing permeable flexible barrier, the barrier is assumed to be fixed near the free surface and is free at the submerged end. On the other hand, for the bottom standing permeable flexible barrier, the barrier is assumed to be fixed at the bottom and the other end is free. As special cases of the permeable flexible barrier, the results associated with surface-piercing and bottom-standing permeable membrane barriers are obtained by assuming that the two ends of the barriers are fixed. Appropriate continuity conditions are used to deal with the interface-piercing flexible/membrane barriers. The mathematical problem is handled for solution using a generalized orthogonal relation suitable for two-layer fluid along with the least square approximation method. Explicit relations are derived to ensure full reflection by porous flexible barriers of any configuration placed near a vertical rigid wall for waves in surface and internal modes, which are validated through numerical computations in various cases. The effect of critical angle of incidence on wave reflection and trapping by barriers, surface and interface wave elevations, deflection of the flexible barrier under wave action, pressure distribution on the barrier, wave loads on barrier and rigid wall are analyzed. The finding of the present study is likely to play a significant role in the design of marine facilities with less wave force on the infrastructure. The present concept and methodology can be easily extended to similar problems in acoustic-structure interactions.

Diffraction of a surface wave on a conducting rectangular wedge

Diffraction of a surface wave on a rectangular wedge with impedance faces is studied using the Sommerfeld-Malyuzhinets technique. An analog of Landau's bypass rule in the theory of plasma waves is introduced for selection of a correct branch of the Sommerfeld integral, and the exact solution is given in terms of imaginary error function. The formula derived is valid both in the near-field and far-wave zones. It is shown that a diffracted surface wave is completely scattered into freely propagating electromagnetic waves and neither reflected nor transmitted surface waves are generated in case of bare metals which have positive real part of surface impedance. The scattered waves propagate predominantly at a grazing angle along the direction of propagation of the incident surface wave and mainly in the upper hemisphere regarding the wedge face. The profile of radiated intensity is nonmonotonic and does not resemble the surface wave profile which exponentially evanesces with the distance from the wedge face. Comparison with experiments carried out in the terahertz spectral range at Novosibirsk free electron laser has shown a good agreement of the theory and the experiments.

Mutual conversion of bulk and surface acoustic waves in gratings of finite length on half-infinite substrates. II. FE analysis of bulk wave generation

The paper studies numerically the bulk acoustic wave generation by the surface acoustic wave propagating across a grating created on the surface of an elastically anisotropic half-infinite substrate. The computations are fully based on the finite element method. Applying the discrete Fourier transformation to the displacement field found inside the substrate and using an orthogonality relation valid for plane modes we determine separately the spacial spectrum of the quasi longitudinal and the quasi transverse bulk waves, that is, the dependence of the amplitudes of these waves on the tangential component of the wave vector. The dependence is investigated of the central spectral peak height and shape on the frequency of the incident surface wave as well as on the thickness, the width, and the number of strips forming the grating. In particular, it is found that under certain conditions the central peak can be approximated fairly precisely by the central peak of a sinc-function describing the spectrum of the bounded acoustic beam of rectangular shape and of width equal to the length of the grating.

Asymptotics of the frequency of a surface wave trapped by a slightly inclined barrier in a liquid layer

A two-dimensional statement of the scattering problem for an oblique incident surface wave by an obstacle in the form of a submerged barrier is considered. If the barrier is vertical, the discrete spectrum of the problem is shown to be empty, but for an inclined barrier an eigenvalue appears below the threshold of the continuous spectrum and the corresponding trapped made decays exponentially in the direction perpendicular to the obstacle. The behavior of the eigenvalue is analyzed for small values of the angle of inclination from the vertical. Bibliography: 48 titles.

Design and efficiency of a composite vibration isolating screen in soil

This paper reports on the design, the installation, and the efficiency of a vibration isolating screen that has been installed in the soil near a test track of the Brussels public transport company in 1995. The dynamic soil characteristics of the site have been determined by means of a seismic cross-hole test, a seismic refraction test, and a Spectral Analysis of Surface Waves test. The screen is designed to isolate frequencies above 20Hz, which requires a screen depth of 8m to effectively reflect the incident surface waves. The vibration isolating screen is conceived as a sandwich panel, using extruded polystyrene as core material and concrete side panels, which act as a ballast material to prevent uplift of the screen during installation. The efficiency of the screen is measured in situ by means of hammer impacts on a foundation installed in front of the screen. The isolation performance is further studied by means of a coupled finite element- boundary element model, comparing the performance of the screen to the ideal case of an open trench, and a polystyrene screen without concrete side panels. The analysis shows that the polystyrene screen has a lower performance than an open trench, whereas the concrete side panels do not significantly modify the effectiveness of the vibration isolating screen. It is demonstrated that the stiffness contrast between the soil and the in-fill material is the key factor determining the performance of the in-fill material. The isolation performance could therefore have been improved by using a material with a lower Young's modulus. A further study also shows that a higher performance could have been achieved using a concrete isolating screen.

Conversion from surface wave to surface wave on reflection

We discuss the reflection and transmission of an incident surface wave to a pure surfacewave state at another interface. This is allowed only for special media parameters: at leastone of the media must be magnetic. We found such material characteristics that theobliquely incident surface wave can be transmitted without changing its direction(nevertheless the amplitude varies). For other media parameters, only normally incidentsurface waves can be converted to surface waves. We propose applications of thepredicted conversion as a beam splitter and polarization filter for surface waves.

EFFECT OF AN IRREGULAR GROUND ON MICROTREMOR H/V SPECTRA AND DISPERSION CURVES

In this paper, wave propagation in an irregular ground due to incident surface waves is formulated by combining the 2.5 dimensional thin layered element method and the 2.5 dimensional finite element method. From this study, the following conclusions are made: 1. From the analysis of the microtremor wave field due to various incident surface (Rayleigh and Love) waves, it has pointed out that H/V spectra and dispersion curves are influenced by both body and surface waves generated from the irregularity (slope in this study) of the ground. 2. It is also confirmed that effect of interference between the incident wave and waves generated from the slope changes depending on the angle of incidence. 3. A comparison with the observation data has shown that the 2.5-D analysis can give good results when compared to the 1-D or 2-D analysis. 4. Estimated phase velocities from observation data show a tendency of accuracy degradation in the vicinity of the H/V spectral peak.

Scattering of an acoustic axially symmetric surface wave propagating to the vertex of a right-circular impedance cone

The work deals with the scattering of an incident surface wave propagating to the vertex of a circular impedance cone. Diffraction of the incident surface wave by the vertex gives rise to the reflected surface wave as well to the spherical wave from the vertex of the cone in the far-field approximation. The study is based on the Sommerfeld integrals, Fourier transform and on the incomplete separation of the spherical variables for the problem at hand. The analytic formulas for the reflected surface wave and for the diffraction coefficient of the spherical wave are obtained.

Control of Traffic-Induced Ground Vibrations by Placing Heavy Masses on the Ground Surface

Although the main mechanisms of generating ground vibrations at source, e.g. by rail and road traffic, are now well understood, there are still very few investigations aimed to protect the affected buildings by influencing the propagation of ground vibrations, mainly Rayleigh surface waves, from a source to a receiver. A promising and cost effective method of screening the affected properties can be using heavy masses placed on the ground surface near the roads (e.g. concrete or stone blocks, specially designed brick walls, etc). The principle of operation of such masses is based on the fact that their natural frequencies of vibration, which depend on the mass value and on the local ground stiffness, can be chosen within the frequency range of railway- or road-generated ground vibrations (normally from 5 to 50 Hz). When the mass is shaken under the impact of incident Rayleigh surface waves, it scatters the incident waves into the depth of the ground and at different directions on the surface, thus resulting in noticeable resonant attenuation of transmitted ground vibrations. Using suitable combinations of such mass scatterers, one can expect to achieve efficient vibro-isolation of affected buildings. While some initial efforts have been made in the past to investigate the above-mentioned mass scatterers, largely by means of numerical calculations, very little progress in understanding their behaviour has been made so far. The aim of the present paper is to give a brief introduction to the theory of resonant mass scatterers and to discuss some problems that still need to be considered to achieve a fuller understanding of their operation as means of control of low frequency ground vibrations.

Obliquely incident surface waves in shallow water of slowly varying depth

Obliquely incident surface waves in shallow water of slowly varying depth

Obliquely incident surface waves in shallow water of slowly varying depth

The propagation properties of obliquely incident, weakly nonlinear surface waves in shallow water of slowly varying depth are studied analytically. The depth changes slowly in a direction that makes a constant angle with the propagation direction of the incident wave, initially travelling in a region of uniform depth. In the adjacent inhomogeneous region, the depth variations occur on a scale shorter than that on which the wave evolves. It is shown that the problem then reduces to an evolution equation with constant coefficients. Since weak three-dimensional effects are also taken into account, this equation is related to the KP equation. The effect of oblique incidence on mass transfer is studied in detail. In addition, it is shown that the conditions for fission of an incident solitary wave differ from the case of normal incidence.

Surface Plasmon Scattering by Gold Nanoparticles and Two-Dimensional Agglomerates

There has long been an interest in nanosized metallic particles for numerous novel applications, from the productions of colored glass in medieval times to the molecular-level sensors of today. These particles are known to display considerably different, and size-dependent, optical properties than those of their bulk counterparts. Yet it is very difficult to determine the size and structure of these particles in situ, such as monitoring the actual self-assembly process, because of their small size. In this paper, we present a methodology to predict the patterns of nanosized particles and agglomerates subjected to surface plasmon waves. For this characterization, the scattering patterns of different types of particles and agglomerates on or near the surface are needed. A combination of the T-matrix method, image theory, and a double interaction model are considered. The incident and scattered fields are expanded by employing spherical harmonic functions. The surface effects are incorporated using the Fresnel equations, in the incident-field expansion coefficients, and by including particle-surface interaction fields. The premise of the method is that the T-matrix is independent of incident and scattered fields and hence can be used effectively for cases involving incident surface waves. By obtaining the T-matrix for clusters or agglomerates of metallic particles, the scattering matrix elements (M11, M12, M33, and M34) of agglomerated structures on the surface are calculated using an additional T-matrix operation. The effect of size, shape, and orientation of gold nanosized particles on their scattering patterns are explored both in the visible spectrum and at resonance wavelengths. The results show that the normalized scattering matrix elements at certain observation angles and incident wavelengths provide significant information to monitor the structural change of gold nanosized particles on a gold substrate.

Hydroelasticity of a circular plate on water of finite or infinite depth

This paper considers the diffraction of incident surface waves by a floating elastic circular plate. We investigate the hydroelastic response of the plate to a plane incident wave for two cases of water depth. An analytic and numerical study is presented. An integro-differential equation is derived for the problem and an algorithm of its numerical solution is proposed. The representation of the solution as series of Bessel functions is the key idea of the approach. After a brief introduction and formulation of the problem, we derive the main integro-differential equation by the use of the thin plate theory and Green's theorem. The plate deflection, the free-surface elevation and the Green's function are expressed in cylindrical coordinates as series of Bessel functions. For the coefficients, a set of algebraic equations is obtained, yielding the approximate solution for the case of infinite water depth. Then a solution is obtained for the general case of finite water depth analogously. The exact solution is approximated by taking a finite number of roots of the dispersion relation into account. Numerical results for the plate deflection, initiated wave pattern and free-surface elevation are presented for various physical parameters of the problem, together with some remarks on the computation and discussion.

An asymptotic theory for the interaction of waves and currents in coastal waters

A multi-scale asymptotic theory is derived for the evolution and interaction of currents and surface gravity waves in water of finite depth, under conditions typical of coastal shelf waters outside the surf zone. The theory provides a practical and useful model with which wave–current coupling may be explored without the necessity of resolving features of the flow on space and time scales of the primary gravity-wave oscillations. The essential nature of the dynamical interaction is currents modulating the slowly evolving phase of the wave field and waves providing both phase-averaged forcing of long infra-gravity waves and wave-averaged vortex and Bernoulli-head forces and hydrostatic static set-up for the low-frequency current and sea-level evolution equations. Analogous relations are derived for wave-averaged material tracers and density stratification that include advection by horizontal Stokes drift and by a vertical Stokes pseudo-velocity that is the incompressible companion to the horizontal Stokes velocity. Illustrative solutions are analysed for the special case of depth-independent currents and tracers associated with an incident surface wave field and a vortex with O(1) Rossby number above continental shelf topography.

Strong Motion in Central Mexico: A Model Based on Data Analysis and Simple Modeling

Predictions of ground motion for Mexico City during future large earthquakes are currently based on statistical analysis of the large quantity of data recorded by the Mexico City Accelerograph Network (MCAN). In spite of the robustness of these predictions, large uncertanties come from our lack of a physical model that is able to account for the observations. In this article we present such a model based on analysis of strong-motion records obtained during the 25 April 1989, Guerrero earthquake and on numerical modeling. Data analysis suggests that the large amplitudes and very long duration of ground motion observed in the lake-bed zone in Mexico City result from the interaction of diffracted wave trains of Rayleigh waves and the very soft, clay layer that covers the ancient lake of Mexico City. Numerical modeling supports this hypothesis and indicates that this interaction is possible in spite of the largely different scales (kilometers for the incident surface waves, and tens of meters for the clay layer). Lateral heterogeneities split incoming wave trains into different modes. Each is strongly amplified, and its duration is increased by the soft clay layer at its resonant frequency, resulting in the very long monochromatic ground motion that has been the subject of a large number of articles since the 1985 Michoacan earthquake. Manuscript received 23 August 2001.

Wave scattering by a submerged plate in presence of a steady uniform current

The purpose of this experimental work was the study of the influence of a homogeneous current in the incident surface wave direction on the wave-reflecting power of a submerged plate. Results concerning reflection versus the wave period (in a fixed frame) for various amplitudes have shown a weak influence of the current both on the location of maxima and minima and on their amplitude. The locations of the maximum reflected energy are then weakly modified by the current contrary to the energy that is decreased. Moreover, reflections measured either for various amplitudes at given frequency or for bichromatic waves show a wave behaviour correctly described by a linear approach.