Normal Incident Wave Research Articles

Reflected Energy Spectrum from Slotted Breakwaters Due to Irregular Waves

A slotted breakwater is a kind of perforated breakwater with vertical slots in the front wall of the structure. It can provide a sheltered area for loading and unloading of ships and crafts. In this study, a modified model to the one proposed by Suh et al. (2001) was developed to calculate the frequency-averaged reflection coefficient by means of the velocity potential. Using this model, the reflected energy spectrum from slotted breakwaters for normal incident waves can be calculated. A comparison with experimental and analytical works shows that this model can accurately predict frequency-averaged reflection from this type of breakwater. This model can provide a good trend to predict frequency-averaged reflection and is a powerful tool for predicting the reflected energy spectrum from slotted breakwaters. The effect of effective parameters such as relative wave chamber width, relative significant wave height, significant wave period, and porosity of the slotted wall was also considered on the frequency-averaged reflection and reflected energy spectrum in this model. One of the most important results is the calculation of frequencies in the reflected spectrum that have a minimum energy close to zero, denoted as zeroth frequency points. This means that a large part of the wave energy in such frequencies is absorbed by the structure of the breakwater.

Iterative technique for analysis of periodic structures at oblique incidence in the finite-difference time-domain method

Normal incidence of a plane electromagnetic wave on a periodical structure can be simulated by the finite-difference time-domain method using a single unit cell with periodical boundary conditions imposed on its borders. For the oblique wave incidence, the boundary conditions would contain time delays and thus are difficult to implement in the time-domain method. We propose a method of oblique incidence simulation, based on an iterative algorithm. The accuracy of this method is demonstrated by comparing it with the layer Korringa-Kohn-Rostoker frequency-domain method for calculation of transmission spectra of a monolayered photonic crystal.

Scattering of ultrasonic waves in randomly layered materials

The goal of the paper is the proposal of a new macroscopic description of scattering of elastic waves at internal inhomogeneities of the material. Within the studies the microscopic inhomogeneity of the medium is modeled as the alternately arranged two kinds of elastic layers of random thicknesses and different mechanical properties. Calculations of the acoustical characteristics of such medium (reflection and transmission coefficients) are performed in two stages: (i) first the problem of interaction of plane harmonic wave with the half space of the randomly layered medium for the case of normal wave incidence is analyzed; (ii) then the interaction of the harmonic wave with the slice composed of randomly layered structure is considered. Such approach allowed to derive analytical relations for the phase velocity of wave propagation and attenuation as the explicit functions of frequency, stochastic structural parameters of the medium and material properties of layers. The obtained formulas are helpful for interpretation of experimental ultrasonic data and may serve for identification of the characteristic size of material inhomogeneity based on the measured wave parameters like frequency dependent phase velocity, attenuation as well as backscattering coefficient.

Shock-induced fast reactions of zinc nanoparticles and RDX

Fast reactions of zinc nanoparticles and RDX were investigated in normal incident shock waves. The emergence time and emission spectra intensity of partial products such as NO2, H, C2, O, CO, CH2O, CO2, H2O and ZnO were observed by a TDS5054 oscilloscope. The results indicate that NO2 appears first in each experiment, which is in agreement with the theoretical results. The addition of zinc nanoparticles to RDX can not only shorten the ignition delay time by 20% but also double the shockwave diffusion velocity to 2180 ± 50 m s−1 and triple the temperature to 2020 ± 60 K. The emergence time of products shortens by around 10–40% and the emission spectra intensity of H2O and CH2O rises by about three times and one times, respectively. CO2, H2O and O2 in various concentrations were introduced into the zinc–RDX reaction, respectively, which indicate that O2 made the ignition delay time shorten by over 30%, the effect of H2O was not prominent while CO2 made the ignition delay time lag by around 30%. The results indicate that the Zn–O2 reaction mainly occurs in O2, CO2 and H2O.

On beach cusp formation

A system of shallow water equations and a bed evolution equation are used to examine the evolution of perturbations on an erodible, initially plane beach subject to normal wave incidence. Both a permeable (under Darcy's law) and an impermeable beach are considered. It is found that alongshore-periodic morphological features reminiscent of swash beach cusps form after a number of incident wave periods on both beaches. On the permeable (impermeable) beach these patterns are accretional (erosional). In both cases flow is ‘horn divergent’. Spacings of the cusps are consistent with observations, and are close to those provided by a standing synchronous linear edge wave. An analysis of the processes leading to bed change is presented. Two physical mechanisms are identified: concentration gradient and flow divergence, which are dominant in the lower and upper swash respectively, and their difference over a wave cycle leads to erosion or deposition on an impermeable beach. Infiltration enters this balance in the upper swash. A bed wave of elevation is shown to advance up the beach at the tip of the uprush, with a smaller wave of depression on the backwash. It is found that cusp horns can grow by a positive feedback mechanism stemming from decreased (increased) backwash on positive (negative) bed perturbations.

Rhythmic surf zone bars and morphodynamic self-organization

Work undertaken in the EU HUMOR project on morphodynamical modelling, particularly with regard to simulating and understanding rhythmic surf zone bars and related morphodynamic self-organization, is presented. These features are reviewed and their engineering context stated. Hydrodynamical and morphodynamical models developed and/or applied within the HUMOR project in order to address these issues are briefly presented. The linear stability modelling concept and stability studies using fully nonlinear models are contrasted. The stability of a shore-parallel bar under normal or oblique wave incidence is chosen as a test case for the different models. The results are compared and discussed. Lastly, modelling efforts and main results from the project are summarized. Recommendations for further work are made.

ULTRA WIDE BAND RCS OPTIMIZATION OF MULTILAYERD CYLINDRICAL STRUCTURES FOR ARBITRARILY POLARIZED INCIDENT PLANE WAVES

The addition theorems are applied to analyze the normal incidence of plane waves onto infinitely long conducting or dielectric circular cylinders with multilayer coatings made of common and uncommon materials (er ,µ r ,σ ) with the objective of minimization and maximization of radar cross-section (RCS). TE, TM and circular polarizations of the incident wave are considered. Optimization of RCS by the method of least squares leads to the determination of layer thicknesses and the material complex permittivities and permeabilities. A sensitivity analysis of RCS with respect to the geometrical and material parameters of the multilayer coated conducting cylinder is also performed. It is observed that broadband reduction of RCS is mostly achievable by a combination of conventional materials (er ,µ r > 1), and unconventional materials (0 0). It is seen that RCS reduction is due to the diversion and dissipation of radar signals. The results agree very well with the experimental and theoretical data available in the literature.

Genetic algorithm approach on pyramidal dielectric absorbers

Array of absorbing pyramid cones are widely used in anechoic chambers. When the period of the array is small compared with wavelength, which is in the low-frequency limit; the plane wave reflection problem is simplified and can be studied in one-dimensionally inhomogeneous media. This article deals with the optimal design parameters of pyramid cone absorbers via genetic algorithm for the normal and oblique incidence of plane wave. The optimization parameters are the dielectric permittivity and the length of the absorber over a wide frequency band and incidence angle range. The cost function of the optimization algorithm is the reflection coefficient of the absorber which is to be minimized. The algorithm is applied to different frequency bands and incidence angles. The results show that the minimized reflection coefficients and corresponding relative permittivities and absorber lengths are acceptable for each application. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008.

Designing near-perfect invisibility cloaks

Invisibility cloaks are a favorite device used by science-fiction and fantasy authors. Yet, despite the fact that invisibility fascinates many people, its practical realization has rarely been treated as a serious research topic in science and technology. Very recently, researchers noticed that one can deduce the exact material requirement for making a completely passive cloaking device using the theory of transformation optics.1, 2 The basic principle is illustrated in Figure 1. Even for the simplest cylindrical cloak structure, however, the ideal material parameters prove difficult to match with current metamaterial fabrication technology. Therefore, one would prefer to simplify the material required for a cloak. Here we describe two promising approaches for constructing a simplified cylindrical invisibility cloak that should ease implementation while retaining good performance. In a cylindrical coordinate system (r, θ, z), one can simplify the cloak’s materials parameters ez, μθ , and μr for normal wave incidence—with a single transverse electric (TE) polarization (in which the electric field is solely aligned along the axial or z direction of the cloak)—by keeping intact the products ezμθ and ezμr. In the simplest case, a cylindrical cloak can be obtained through linear radial spatial mapping, i.e. r′ = (r− a) b b−a , where a and b are the cloak’s inner and outer radii, respectively, and r′ and r are the radial coordinates in electromagnetic and physical spaces, respectively. The corresponding ideal material parameters are shown in the left column of Table 1. Based on this ideal cloak, a simplified version, as proposed by John Pentry’s group3, has material parameters shown in the middle column in Table 1. However, such a simplified cloak still scatters electromagnetic fields considerably, largely due to its unmatched impedance to free space.4 Wepropose a new version of a simplified cylindrical cloak that restores impedance matching to the space outside the cloak. We do not vary the products ezμθ and ezμr. This improved set of Figure 1. Formatting a cloak of an arbitrary shape by transformation optics (a): and (b) depict correlated coordinates’ lines in electromagnetic space and physical space, respectively. A void region S2 in (b) has appeared, which is obtained by blowing up a point (or a line, if the structure is invariant along the paper-normal direction) of zero size in (a). The annular shape bounded by S1 and S2 in (b) is electromagnetically equivalent to the region bounded by S1 in (a). However the regions’ material parameters are different owing to a change of coordinate. The region bounded by S1 and S2 in (b) constitutes a cloak, whose interior can conceal objects. Notice that the coordinate changes only for a finite spatial region bounded by S1 in both panels. As a consequence, the material outside S1 (which we assume is air) remains the same in both panels.

Thin AMC Structure for Radar Cross-Section Reduction

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> A thin artificial magnetic conductor (AMC) structure is designed and breadboarded for radar cross-section (RCS) Reduction applications. The design presented in this paper shows the advantage of geometrical simplicity while simultaneously reducing the overall thickness (for the current design <formula formulatype="inline"><tex>$\lambda/16$</tex></formula>). The design is very pragmatic and is based on a combination of AMC and perfect electric conductor (PEC) cells in a chessboard like configuration. An array of Sievenpiper's mushrooms constitutes the AMC part, while the PEC part is formed by full metallic patches. Around the operational frequency of the AMC-elements, the reflection of the AMC and PEC have opposite phase, so for any normal incident plane wave the reflections cancel out, thus reducing the RCS. The same applies to specular reflections for off-normal incidence angles. A simple basic model has been implemented in order to verify the behavior of this structure, while Ansoft-HFSS software has been used to provide a more thorough analysis. Both bistatic and monostatic measurements have been performed to validate the approach. </para>

Some analytical results for acoustic scattering through a periodic array of elastic membranes

In the context of wave propagation through acoustic media, an analytical approach is developed to study the (normal) incidence of a pressure wave into a periodic array of (thin) elastic membranes. The frequency of this wave is assumed in a range implying the so-called one-mode (far field) propagation, so that mild approximations holding in this range can be employed. Thus, the problem is reduced to some integral equations based on the opening between adjacent membranes and independent of the frequency. By means of the (analytical) solutions of such equations, an explicit formula for the transmission coefficient is set up and reflected in some figures for concrete values of the various parameters involved. The peculiarities of the scattering structure are discussed.

Quantitative evaluation of crack orientation in aluminium plates based on Lambwaves

The forward- and back-scattering of Lamb waves by through-thickness cracks of varyinglength and orientation was studied by numerical simulation and experimental validation.Surface-bonded piezoelectric discs were arrayed as actuators and sensors to generate andcollect Lamb waves, respectively, and the effect of crack orientation on Lamb wavepropagation was evaluated. Lamb waves reflected and transmitted by cracks of finite sizewere assessed to obtain the reflection and transmission coefficients subject to crackorientation, with the aid of a Hilbert transform. Using this relationship, crack orientationwas quantitatively determined by evaluating the different amplitudes of energy peaks in theHilbert spectra. The distribution of scattered waves around a crack was further studied forthe circumstance of normal wave incidence. The limitation of the proposed technique foreffective damage identification based on forward analysis of wave scattering was alsodiscussed.

FDTD-PLRC Technique for Modeling of Anisotropic-Dispersive Media and Metamaterial Devices

The goal of this paper is to develop a versatile computational engine based on the finite-difference time-domain (FDTD) technique to comprehensively demonstrate the broadband behaviors of devices designed utilizing anisotropic-dispersive metamaterials. In this regard, the frequency-dependent behavior of dispersive materials is incorporated into the FDTD equations with the use of a piecewise linear recursive convolution (PLRC) approach. The FDTD domain is effectively terminated utilizing convolutional perfectly matched layered (CPML) absorbing walls, which are derived from the complex frequency-shifted (CFS) formulation. The CPML has the advantage that it operates only on the filed intensities and has nothing to do with the and constitutive relationships. The CPML is also highly absorptive to both propagating and evanescent waves. Therefore, it would be of great interest for terminating metamaterials having complex constitutive parameters. The developed method is also capable of characterizing periodic configurations illuminated by normal incident plane waves. The FDTD engine is successfully validated through the analyses of several complex metamaterials. The design and characterization of novel devices such as a patch antenna printed on metasubstrate with anisotropic epsiv (omega) - mu (omega)parameters, an electrically small antenna embedded in negative permittivity resonator, and an anisotropic-dispersive self-biased hexagonal ferrite-coupled line (FCL) circulator are highlighted.

Zero-offset seismic amplitude decomposition and migration

In an anisotropic medium, a normal-incidence wave is multiply transmitted and reflected down to a reflector where the phase-velocity vector is parallel to the interface normal. The ray code of the upgoing wave is equal to the ray code of the downgoing wave in reverse order. The geometric spreading, KMAH index, and transmission and reflection coefficients of the normal-incidence ray can be expressed in terms of products or sums of the corresponding quantities of the one-way normal and normal-incidence-point (NIP) waves. Here, we show that the amplitude of the ray-theoretic Green’s function for the reflected wave also follows a similar decomposition in terms of the amplitude of the Green’s function of the NIP wave and the normal wave. We use this property to propose three schemes for true-amplitude poststack depth migration in anisotropic media where the image represents an estimate of the zero-offset reflection coefficient. The first is a map migration procedure in which selected primary zero-offset reflections are converted into depth with attached true amplitudes. The second is a ray-based, Kirchhoff-type full migration. The third is a wave equation continuation algorithm to reverse-propagate the recorded wavefield in a half-velocity model with half the elastic constants and double the density. The image is formed by taking the reverse-propagated wavefield at time equal to zero followed by a geometric spreading correction.

A Varactor-Tunable High Impedance Surface With a Resistive-Lumped-Element Biasing Grid

A high impedance surface consisting of metallic square patches electrically connected through vias to the ground plane beneath them is made tunable. Tunability is achieved by connecting adjacent patches with varactor diodes thus altering the capacitance between the patches and hence the surface's resonance frequency. The varactor diodes are biased with the aid of a resistive grid. The grid is made resistive using surface mount resistors. Using an approximate equivalent circuit the effect of the varactor diode resistance is investigated for normal plane wave incidence. It is shown that at resonance, a small varactor resistance may lead to a significant absorption. The potential use of a waveguide simulator to characterize approximately the performance of the proposed metamaterial structure is investigated.

Reproducibility experiments on measuring acoustical properties of rigid-frame porous media (round-robin tests)

This paper reports the results of reproducibility experiments on the interlaboratory characterization of the acoustical properties of three types of consolidated porous media: granulated porous rubber, reticulated foam, and fiberglass. The measurements are conducted in several independent laboratories in Europe and North America. The studied acoustical characteristics are the surface complex acoustic impedance at normal incidence and plane wave absorption coefficient which are determined using the standard impedance tube method. The paper provides detailed procedures related to sample preparation and installation and it discusses the dispersion in the acoustical material property observed between individual material samples and laboratories. The importance of the boundary conditions, homogeneity of the porous material structure, and stability of the adopted signal processing method are highlighted.

Rip currents, mega-cusps, and eroding dunes

Dune erosion is shown to occur at the embayment of beach mega-cusps O(200 m alongshore) that are associated with rip currents. The beach is the narrowest at the embayment of the mega-cusps allowing the swash of large storm waves coincident with high tides to reach the toe of the dune, to undercut the dune and to cause dune erosion. Field measurements of dune, beach, and rip current morphology are acquired along an 18 km shoreline in southern Monterey Bay, California. This section of the bay consists of a sandy shoreline backed by extensive dunes, rising to heights exceeding 40 m. There is a large increase in wave height going from small wave heights in the shadow of a headland, to the center of the bay where convergence of waves owing to refraction over the Monterey Bay submarine canyon results in larger wave heights. The large alongshore gradient in wave height results in a concomitant alongshore gradient in morphodynamic scale. The strongly refracted waves and narrow bay aperture result in near normal wave incidence, resulting in well-developed, persistent rip currents along the entire shoreline. The alongshore variations of the cuspate shoreline are found significantly correlated with the alongshore variations in rip spacing at 95% confidence. The alongshore variations of the volume of dune erosion are found significantly correlated with alongshore variations of the cuspate shoreline at 95% confidence. Therefore, it is concluded the mega-cusps are associated with rip currents and that the location of dune erosion is associated with the embayment of the mega-cusp.

Shock-induced thermal behavior of aluminum nanoparticles in propylene oxide

The thermal behavior of aluminum nanoparticles reacting with propylene oxide was investigated in normal incident shock waves. Their reactive temperature, which is about 2705±150K, was experimentally determined by the emission strength of AlO. The reactive products were evaluated by x-ray diffraction, which shows that several different phases of Al2O3 are produced in different temperature regions. The scanning electron microscopy image of the reactive products shows that some holes, which were produced in the process of aluminum nanoparticles violently reacting with suboxides of aluminum, are found on the surface of the products. The data of transmission electron microscopy indicate that the grain diameters of the products were within the range of 20–90nm. The geometry of propylene oxide was calculated and optimized using the Rb31yp function and the 6–311+g(d,p) basis set. The calculated results show that the diameter of the molecule is about 0.435nm. The process of vaporizing and condensing of propylene oxide was investigated by electron microscopy, and the results show that the average drop diameter is 4.03μm at t=70s and then is 2.06μm at t=120s. It suggests that the average drop diameters tend to range from several nanometers to tens of nanometers, which is very close to the diameter of aluminum nanoparticles (average of 70nm). Thus, we may consider them to react with each other in the gas phase in normal incident shock waves in the experiment.

Quasi-three-dimensional modelling of the morphology of longshore bars

A morphological quasi-three-dimensional (Q3D) area model for barred coasts has been developed. The model combines a two-dimensional depth integrated model for wave-driven currents with a model for undertow circulation currents. The combined model makes a simultaneous simulation of the bar-forming processes associated with the undertow and the horizontal wave-driven circulation currents, which may cause instabilities of the bar and the formation of rip channels. Situations with normal and oblique wave incidence are considered. Compared to the depth integrated approach the Q3D model produces less pronounced alongshore irregularities for obliquely incident waves. For normal incident waves the Q3D model produces a crescentic bar while the depth integrated model predicts almost straight sections of the bar interrupted by rip channels. The sensitivity to variation of wave angle and beach slope is further investigated.

Optimization of metamaterial based subwavelength cavities for ultracompact directive antennas

AbstractArtificial magnetic conductors (AMC) are proposed for the fabrication of subwavelength cavities in the microstrip technology. These metamaterials can simultaneously present a low phase value at reflection and a high impedance for normal incident waves over a wide frequency band. Planar cavities using AMC‐based reflectors are applicable to the design of ultracompact directive antennas. An optimized cavity structure is presently shown to provide a significant enhancement of the gain and directivity of a microstrip antenna near 10 GHz. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 2573–2577, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21996