Numerical Simulated Study on the Separation of Oblique Incident and Reflected Waves

The Goda's method of separating the frequency spectrum of the unidirectional incident and reflected waves is improved. The proposed method can be applied to the separation of oblique incident and reflected waves and the two wave gauges can be arranged in an arbitrary angle in front of a structure. When the projected distance of the two probes on the incident wave direction is the multiple ofthe half length of the incident waves, the singular problem will emerge by using the method. It is advised that when the projected distance of the two measured points on the incident wave direction is 0.05～0.45 times the wave length of peak frequency wave, good results can be obtained. The simulated resultant waves are separated by the method of numerical simulation and the separated wave spectra are basically corresponding to the target spectra input. The wave trains calculated by the separated incident and reflected wave frequency spectrum are approximated to the input wave trains and the reflected coefficient can be derived correctly. Therefore, the method proposed in this paper is reliable.

Tests and Applications of An Approach to Absorbing Reflected Waves Towards Incident Boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.

Estimating Directional Distribution for Co-Existent Field of Incident and Reflected Waves

In the nearshore, the wave field contains reflected and incident waves in which there is correlation between their phases due to the effect of reflection by some obstacles. Based on the extended eigenvector method (EEV) derived by Guan et al., a modified method (MEEV) is proposed as a general and practical approach to estimating directional spectra for the co-existent field of incident and reflected waves and a formula is given for direct calculation of the reflection coefficient. The results of numerical simulations show that MEEV is superior to EEV in resolution power, and the computed reflection coefficient agrees well with the real value within a certain range of incident angle.

Analysis of Directional Spectra and Reflection Coefficients in Incident and Reflected Wave Field

In this paper, the modified Bayesian method for the analysis of directional wave spectra and reflection coefficients is verified by numerical and physical simulation of waves. The results show that the method can basically separate the incident and reflected directional spectra. In addition, the effect of the type of wave gage arrays, the number of measured wave properties, and the distance between the wave gage array and the reflection line on the resolution of the method are investigated. Some suggestions are proposed for practical application.

Reflection of Oblique Incident Waves by Breakwaters with Partially-Perforated Wall

The reflection of oblique incident waves from breakwaters with a partially-perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigenfunction expansion method is applied to expand velocity potentials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with experimental data. The effect of porosity, the relative chamber width, the relative water depth in the wave absorbing chamber and the water depth in front of the structure are discussed.

Hilbert Transferin Applied to Separation of Waves

The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is applicable to both regular and irregular trains; of waves. The wave data series measured with two wave gauges in the experiments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily obtained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient. The reflection performance of the physical model can be estimated exactly without calculation of wave height and phase difference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conducted and compared with Goda's method and satisfactory results are obtained.

Separation of diffracted waves via SVD filter

Diffracted seismic waves may be used to help identify and track geologically heterogeneous bodies or zones.However,the energy of diffracted waves is weaker than that of reflections.Therefore,the extraction of diffracted waves is the basis for the effective utilization of diffracted waves.Based on the difference in travel times between diffracted and reflected waves,we developed a method for separating the diffracted waves via singular value decomposition filters and presented an effective processing flowchart for diffracted wave separation and imaging.The research results show that the horizontally coherent difference between the reflected and diffracted waves can be further improved using normal move-out(NMO) correction.Then,a band-rank or high-rank approximation is used to suppress the reflected waves with better transverse coherence.Following,separation of reflected and diffracted waves is achieved after the filtered data are transformed into the original data domain by inverse NMO.Synthetic and field examples show that our proposed method has the advantages of fewer constraints,fast processing speed and complete extraction of diffracted waves.And the diffracted wave imaging results can effectively improve the identification accuracy of geological heterogeneous bodies or zones.

Determination of the parameters of a linear-viscoelastic thin layer using the normally-incident ultrasonic waves

This paper proposes a method of simultaneous determination of the four layer parameters （mass density, longitudinal velocity, the thickness and attenuation） of an immersed linear-viscoelastic thin layer by using the normally-incident reflected and transmitted ultrasonic waves. The analytical formula of the layer thickness related to the measured trans- mitted transfer functions is derived. The two determination steps of the four layer parameters are developed, in which acoustic impedance, time-of-flight and attenuation are first determined by the reflected transfer functions. Using the derived formula, it successively calculates and determines the layer thickness, longitudinal velocity and mass density by the measured transmitted transfer functions. According to the two determination steps, a more feasible and simplified measurement setups is described. It is found that only three signals （the reference waves, the reflected and transmitted waves） need to be recorded in the whole measurement for the determination of the four layer parameters. A study of the stability of the determination method against the experimental noises and the error analysis of the four layer parameters are made. This study lays the theoretical foundation of the practical measurement of a linear-viscoelastic thin layer.

A Calculation Method for Incidence and Reflection of Irregular Waves Along Seawalls

Some researches have been made in this aspect. In the method by Walton Jr.(1992), incident waves are supposed to be the overlapping result of M component waves with different frequencies which may take different directions, the direction of incident waves should be available in advance, but in fact the direction of incident waves is not available. In our study, incident waves are supposed to be composed of M overlapping component waves with different frequencies, and different frequencies have different directions. Based on the irregular wave reflection theory, the calculation formulas of wave direction, complex amplitude of incident waves, and complex amplitude of reflected waves in surface which are composed of component waves are derived by means of discrete Fourier transform. Then, the frequency spectra of incident waves and reflected waves and the reflection coefficient of waves with corresponding frequencies are obtained. Verification of the method and the calculation results from in-situ measured data indicate that the method is reliable and highly accurate.

Separation of Waves by Interpolation Method

The separation of waves by an interpolation method is presented in detail. The composite wave sequences measured with two wave gauges in the wave flume are separated very quickly into two series of incident and reflected waves in time domain via the simple interpolation and difference operations. Then, the reflection coefficient can be estimated easily and accurately without calculation of wave heights and phases. The intial phase of reflection can also be detected easily for improvement of the accuracy of calculation. The present method is applicable to both regular and irregular trains of waves based on the linear wave theory which are proved to be accurate through numerical sample tests. Physical experiments are conducted and compared with Goda′s method and analytical method with satisfactory results. Furthermore, the present method can be used for the absorbing wave maker to extract reflected waves in real time.

THE INTERACTION BETWEEN SHOCK WAVES AND FOAM IN A SHOCK TUBE

An experimental study and a numerical simulation were conducted to investigate the mechanical and thermodynamic processes involved in the interaction between shock waves and low density foam. The experiment was done in a stainless shock tube (80 mm in inner diameter, 10 mm in wall thickness and 5 360 mm in length). The velocities of the incident and reflected compression waves in the foam were measured by using piezo-ceramic pressure sensors. The end-wall peak pressure behind the reflected wave in the foam was measured by using a crystal piezoelectric sensor. It is suggested that the high end-wall pressure may be caused by a rapid contact between the foam and the end-wall surface. Both open-cell and closed-cell foams with different length and density were tested. Through comparing the numerical and experimental end-wall pressure, the permeability coefficients α and β are quantitatively determined.

The Interaction of Oblique Flexural Gravity Waves With a Small Bottom Deformation on a Porous Ocean-Bed： Green＇s Function Approach

The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter c^（〈〈l ）, which measures the smallness of the deformation, the governing Boundary Value Problem （BVP） is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green＇s integral theorem with the introduction of suitable Green＇s function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c（x） representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.

Reflection of Short Waves

According to the; energy equation, the relation between reflection and energy losses for short waves from mild beaches is established and analysed. A reflection coefficient varying with position and energy losses is proposed. Different reflection tests are conducted to check the theoretical analysis. A modified method to estimate the reflection coefficient at varied water depths is suggested based on the linear wave theory. The study indicates that the reflection coefficient from mild beaches has a changing trend for short waves approaching shoreline.

Separation Method of Bi-directional Reflected Waves and Oblique Incident Regular Waves

Wave reflection is one of the key problems affecting wave simulation quality in ocean engineering basin. The deep ocean engineering basin is equipped with two-sided segmented wavemakers and two wave absorbing beaches, which are located opposite to wave generators to reduce wave reflection effects. When an oblique longcrested wave is made by two-sided segmented wavemakers in a wave basin, two bi-directional reflected waves with the same azimuth but opposite propagation directions are generated. According to this feature, based on the two-point approach developed by Goda, a method to separate an incident regular wave from two bi-directional reflected waves using three wave gauges is proposed. The validity of this method is proved by numerical composite waves. The results indicate that the method can separate incident wave from reflected waves effectively. The method can be used to determine the reflection coefficient and verify the capacity of wave absorbing beaches in deep ocean engineering basin.

GPR绕射波与反射波分离的变分模态分解方法研究

针对传统绕射波与反射波分离方法易造成有效信号丢失的问题,本文利用二维变分模态分解(2D-VMD)进行探地雷达(GPR)数据的绕射波与反射波分离。对二维GPR数据进行2D-VMD分解后,可得到包含从低频低波数到高频高波数的各阶模态分量及各阶模态分量的F-K谱。通过分析绕射波与反射波在频率-波数域的差异,分别重构绕射波与反射波对应的模态分量,得到分离后的绕射波与反射波数据。数值模拟与实测数据处理结果表明,相比于传统方法,该方法可以有效分离绕射波与反射波,并且不损失任何有效信号。

A study on characteristics of shock train inside a shock tube

Shock tubes are devices which are used in the investigation of high speed and high temperature flow of compressible gas. lnside a shock tube, the interaction between the reflected shock wave and boundary layer leads to a complex flow phenomenon. Initially a normal shock wave is formed in the shock tube which migrates toward the closed end of the tube and that in turn leads to the reflection of shock. Due to the boundary layer interaction with the reflected shock, the bifurcation of shock wave takes place. The bifurcated shock wave then approaches the contact surface and shock train is generated. Till date only a few studies have been conducted to investigate this shock train phenomenon inside the shock tube. For the present study a computational fluid dynamics （CFD） analysis has been performed on a two dimensional axi-symmetric model of a shock tube using unsteady, compressible Navier-Stokes equations. In order to investigate the detailed characteristics of shock train, parametric studies have been performed by varying different parameters such as the shock tube length, diameter, pressure ratio used inside the shock tube.

Theoretical Calculation of Floating Breakwater Performance

In this paper, the theoretical calculation of floating breakwater performance in regular waves with arbitrary wave direction is discussed. Under the hypothesis of linearized system and applying the strip theory, we can solve the boundary condition problems of diffraction potential and radiation potential. Introducing the asymptotic expression of the wave velocity potential at infinity and using wave energy conservation, we can separately calculate the transmitted waves generated by the sway, heave and roll motion of the floating breakwater and by the fixed breakwater. Finally, we define the amplitude ratio of the transmitted wave to the incident wave as the transmitted wave coefficient CT which describes the floating breakwater effectiveness. Two examples are given and the theoretical results obtained by the present method agree well with experimental results.

Effect of High-Frequency Electric Field on Propagation of Electrostatic Wave in a Non-Uniform Relativistic Plasma Waveguide

The effect of a high frequency （HF） electric field on the propagation of electrostatic wave in a 2D non-uniform relativistic plasma waveguide is investigated. A variable separation method is applied to the two-fluid plasma model. An analytical study of the reflection of electrostatic wave propagation along a magnetized non-uniform relativistic plasma slab subjected to an intense HF electric field is presented and compared with the case of a non relativistic plasma. It is found that, when the frequency of the incident wave is close to the relativistic electron plasma frequency, the plasma is less reflective due to the presence of both an HF field and the effect of relativistic electrons. On the other hand, for a low-frequency incident wave the reflection coefficient is directly proportional to the amplitude of the HF field. Also, it is shown that the relativistic electron plasma leads to a decrease in the value of reflection coefficient in comparison with the case of the non relativistic plasma.

基于波场分离的不规则地形下地震波输入方法

不规则地形条件下斜入射地震波场求解难度较大,以往的方法在计算精度和适用范围方面仍有不足。该文结合解析推导和有限元模拟,提出了一种基于波场分离技术的不规则地形条件下地震波输入方法,将地震P波和SV波在不同边界下进行波场分离:垂直入射时在侧面边界上分离为自由波场和散射波场,底部边界上分离为入射波场和边界外行场;斜入射时将输入侧对面的边界改为分离成入射波场和边界外行场;并充分考虑局部地形条件的影响,还基于改进的波动方法以便捷地输入节点力。同时对比了多组不同地震入射角度下规则场地和不规则场地的振动反应。结果表明:该方法在多类地形条件下计算精度与效率均较高,适用范围广且易于推广至复杂场地条件,并发现地震波入射角度和局部场地条件对地表位移响应影响较大。该研究可为不规则地形条件下的振动响应分析提供有效的手段。

Negative reflection and negative surface wave conversion from obliquely incident electromagnetic waves

Complete control of spatially propagating waves(PWs)and surface waves(SWs)is an ultimate goal that scientists and engineers seek for,in which negative reflection of PW and negative surface wave are two exotic phenomena.Here,we experimentally demonstrate an anisotropic digital coding metasurface capable of controlling both PWs and SWs with a single coding pattern.On the basis of the digital description of coding metasurfaces,a simple coding method is proposed to allow dual functionalities(either PW or SW manipulations)under two orthogonal polarizations at arbitrarily oblique incidences,thus improving the adaptability of digital coding metasurfaces in more practical circumstances.With elaborately designed ellipse-shaped coding particles,we experimentally demonstrate various functions under oblique incidences,including the negative reflection of PW,negative SW,anomalous reflection and their arbitrary combinations,all having good agreements with theoretical and numerical predictions.We believe that the proposed method may enable the digital coding metasurfaces to have broad applications in radar detections,wireless communications and imaging.