Analytical Method for the Wave Diffraction of Asymmetrically Arranged Breakwaters

The layout forms of several breakwater structures can be generalized as asymmetrical arrangements in actual engineering.However,the problem of wave diffraction around asymmetrically arranged breakwaters has not been adequately investigated.In this study,we propose an analytical method of wave diffraction for regular waves passing through asymmetrically arranged breakwaters,and we use the Nyström method to obtain the analytical solution numerically.We compared the results of this method with those of previous analytical solutions and with numerical results to demonstrate the validity of our approach.We also provided diffraction coefficient diagrams of breakwaters with different layout forms.Moreover,we described the analytical expression for the problem of diffraction through long-wave incident breakwaters and presented an analysis of the relationship between the diffraction coefficients and the widths of breakwater gates.The analytical method presented in this study contributes to the limited literature on the theory of wave diffraction through asymmetrically arranged breakwaters.

Wave Diffraction on Arc-Shaped Floating Perforated Breakwaters

An analytical method is developed to study the sheltering effects on arc-shaped floating perforated breakwaters. In the process of analysis, the tloating breakwater is assumed to be rigid, thin, vertical, and immovable and located in water with constant depth. The fluid domain is divided into two regions by imaginary interface. The velocity potential in each region is expanded by eigenfunction in the context of linear theory. By satisfying continuity of pressure and normal velocity across the imaginary fluid interface, a set of linear algebraic equations can be obtained to determine the unknown coefficients for eigenfunction expansions. The accuracy of the present model was verified by a comparison with existing results for the case of arc-shaped floating breakwater. Numerical results, in the form of contour maps of the non-dimensional wave amplitude around the breakwater and diffracted wave amplitude at typical sections, are presented for a range of wave and breakwater parameters. Results show that the sheltering effects on the arc-shaped floating perforated breakwater are closely related to the incident wavelength, the draft and the porosity of the breakwater.

Numerical Study of Wave Diffraction Effect Introduced in the SWAN Model

New version of SWAN model includes the wave diffraction effect which is the main improvement compared with the previous versions. Experimental data collected in the wave basin of the University of Delaware were used to test its performance. Wave heights were compared in the four cases （with different wave energies and directional spreading spectra）. The results agreed well with the measurements, especially for the broad directional spectra cases. The effect of wave diffraction was analyzed by switching on/off the corresponding tenn. By introducing the diffraction term, the distributions of wave height and wave direction were smoothed, especially obvious for the narrow spectrum cases. Compared with the calculations without diffraction, the model with diffraction effect gave better results.

A composite numerical model for wave diffraction in a harbor with varying water depth

A composite numerical model is presented for computing the wave field in a harbor. The mild slope equation is discretized by a finite element method in the domain concerned. Out of the computational domain, the water depth is assumed to be constant. The boundary element method is applied to the outer boundary for dealing with the infinite boundary condition. Because the model satisfies strictly the infinite boundary condition, more accurate results can be obtained. The model is firstly applied to compute the wave diffraction in a narrow rectangular bay and the wave diffraction from a porous cylinder. The numerical results are compared with the analytical solution, experimental data and other numerical results. Good agreements are obtained. Then the model is applied to computing the wave diffraction in a square harbor with varying water depth. The effects of the water depth in the harbor and the incoming wave direction on the wave height distribution are discussed.

Analytical Research on Wave Diffraction on Arc-Shaped Bottom-Mounted Perforated Breakwaters

An analytical method is developed to study wave diffraction on arc-shaped and bottom-mounted perforated breakwaters. The breakwater is assumed to be rigid, thin, vertical, immovable and located in water of constant depth. The fluid domain is divided into two regions by imaginary interface. The velocity potential in each region is expanded by eigenfunctions. By satisfying the continuity of pressure and normal velocity across the imaginary fluid interface, a set of linear algebraic equations can be obtained to determine the unknown coefficients of eigenfunctions. Numerical results, in the form of contour maps of the relative wave amplitude around the breakwater, are presented for a range of wave and breakwater parameters. Results show that the wave diffraction on the arc-shaped and bottom-mounted perforated breakwater is related to the incident wavelength and the porosity of the breakwater. The porosity of the perforated breakwater may have great effect on the diffracted field.

Evaluation of Diffraction Predictability in Two Phase Averaged Wave Models

Two different methods for incorporating diffraction effect into wave action balance equation based coastal spectral wave models, WABED and SWAN, are discussed and evaluated with respect to their formulations, numerical implementations, and modeling capabilities. Both models were nm to simulate the wave transformation through a gap between two infinitely long breakwaters and that across an elliptical shoal observed in laboratory studies, with the emphasis laid on the diffraction induced by either obstacles or wave amplitude variations. Calculations of WABED were compared with Sommerfeld＇s analytical solutions, experimental observations and SWAN simulations. It is shown that both methods can predict reasonably wave diffraction for the two eases studied herein, and a fairly better performance is provided by WABED for stronger diffraction ease.

Diffraction of SH-waves by topographic features in a layered transversely isotropic half-space

Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green＇s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green＇s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.

Wave Radiation and Diffraction by A Two-Dimensional Floating Body with An Opening Near A Side Wall

The radiation and diffraction problem of a two-dimensional rectangular body with an opening floating on a semi- infinite fluid domain of finite water depth is analysed based on the linearized velocity potential theory through an analytical solution procedure. The expressions for potentials are obtained by the method of variation separation, in which the unknown coefficients are determined by the boundary condition and matching requirement on the interface. The effects of the position of the hole and the gap between the body and side wall on hydrodynamic characteristics are investigated. Some resonance is observed like piston motion in a moon pool and sloshing in a closed tank because of the existence of restricted fluid domains.

A SECOND ORDER STATIONARY SOLUTION OF THE THREE DIMENSIONAL WAVE DIFFRACTION POTENTIAL

A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solu- tion of an initial value problem, and using Laplace transformation method and Tauberian theorem, the boundary value problems of stationary solution of the first and second order diffraction potential have been de- rived in this paper. Furthermore, the explicit solution of the second order stationary diffraction potential has been obtained with the method of the double Fourier transformation. It is found that the asymptotic behaviour of the second order stationary solution at far field is dependent on two wave systems, the first is 'free wave', travelling independently of the first order wave system, the other is 'phase locked waves', which accompany the first order waves. At the same time, the radiation conditions of the second order diffraction problems are derived. We also find that one can still pursue a steady state formulation with the inclusion of Rayleigh damping. Finally, as an example, the second order wave forces upon a fixed vertical cir- cular cylinder have been calculated, and the numerical results agree well with the experimental data.

A Fully Nonlinear HOBEM with the Domain Decomposition Method for Simulation of Wave Propagation and Diffraction

A higher-order boundary element method(HOBEM) for simulating the fully nonlinear regular wave propagation and diffraction around a fixed vertical circular cylinder is investigated. The domain decomposition method with continuity conditions enforced on the interfaces between the adjacent sub-domains is implemented for reducing the computational cost. By adjusting the algorithm of iterative procedure on the interfaces, four types of coupling strategies are established, that is, Dirchlet/Dirchlet-Neumman/Neumman(D/D-N/N), Dirchlet-Neumman(D-N),Neumman-Dirchlet(N-D) and Mixed Dirchlet-Neumman/Neumman-Dirchlet(Mixed D-N/N-D). Numerical simulations indicate that the domain decomposition methods can provide accurate results compared with that of the single domain method. According to the comparisons of computational efficiency, the D/D-N/N coupling strategy is recommended for the wave propagation problem. As for the wave-body interaction problem, the Mixed D-N/N-D coupling strategy can obtain the highest computational efficiency.

AN ANALYSIS FOR DIFFRACTION OF FLEXURAL WAVES AND DYNAMIC STRESS CONCENTRATIONS IN THICK PLATES WITH A CAVITY

By using the complex variable method and conformal mapping, the diffraction of flexural waves and dynamic stress concentrations in thick plates with a cavity have been studied. A general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of an arbitrary cavity is obtained. By employing the orthogonal function expansion technique, the dynamic stress problem can be reduced to the solution of an infinite algebraic equation series. As an example, the numerical results for the dynamic stress concentration factor in thick plates with a circular, elliptic cavity are graphically presented. The numerical results are discussed.

Analytical Study on Wave Diffraction from a Vertical Circular Cylinder in Front of Orthogonal Vertical Walls

In this paper, the principle of mirror image is used to transform the problem of wave diffraction from a circular cylinder in front of orthogonal vertical walls into the problem of diffraction of four symmetric incident waves from four symmetrically arranged circular cylinders, and then the eigenfunction expansion of velocity potential and Grafs addition theorem are used to give the analytical solution to the wave diffraction problem. The relation of the total wave force on cylinder to the distance between the cylinder and orthogonal vertical walls and the incidence angle of wave is also studied by numerical computation.

Theoretical solution for wave diffraction by wedge or corner with arbitrary reflection characteristics

An exact analytic solution for wave diffraction by wedge or corner with arbitrary angle (rπ) and reflection coefficients (R0 and Rr) is presented in this paper. It is expressed in two forms-series and integral representations, corresponding recurrence relation and asymptotic expressions are also derived. The solution is simplified for some special cases of rπ. For Rr= R0,r= 1/N and Rr≠R0,r = 1/2N, the solution can be reduced to linear superpositions of incident and partially reflected waves, hence a nonlinear solution of forth order for this problem can be obtained by using the author's theory of nonlinear interaction among gravity surface waves. The given solution is related to inhomogeneous Robin boundary conditions, which include the Neumann boundary conditions usually accepted in wave diffraction theory.

Ocean wave diffraction in near-shore regions observed by Synthetic Aperture Radar

Observation and analysis of ocean wave diffraction in near-shore and near-island region was performed with Synthetic Aperture Radar （SAR） data, using an optimized retrieval method named parameterized first-guess spectrum retrieval method. The results retrieved from ERS-SAR and ENVISAT-ASAR images showed that, in the region sheltered by land jut, the energy of long waves is reduced by 10%-20% and that the propagation direction of long waves is changed due to the effect of topography. In the shadow zone behind the island, ocean wave can propagate along the seashore instead of perpendicular to the coastline, as shown by SAR images.

Isolated attosecond electron wave packet diffraction

Wave-particle duality is one of the most fundamental and mysterious natures of matters. Here, we present an interesting scheme of isolated electron wave packet diffraction with a few-cycle laser pulse and an extreme ultraviolet （XUV） pulse. The diffraction fringes are clearly present in the laser dressed XUV photoelectron spectra, strongly resembling the Airy diffraction pattern of optical waves. This phenomenon suggests a great potential of attosecond diffractometry. According to this scheme we also propose a simple method to determine the XUV pulse duration from the photoelectron spectra with a rather high resolution.

Localized Effect of Light Diffraction by Capillary Wave

The localized effect of light diffracted by a capillary wave is discovered by changing the wave amplitude. The localized range is related to the wave number and the amplitude. The dependence of the half maximum localized angle on the wave number and amplitude is analytically derived. Meanwhile, the analytic angular distribution of the diffraction light in the localized range is obtained. Experiments are carried out to achieve diffraction patterns to confirm the localized effect and to measure the angular distribution of the diffraction light intensity as well as to determine the localized range scales corresponding to different wave amplitudes. Theoretical curves of the light intensity angular distribution and localized interval widths related to surface acoustic wave amplitudes are compared with the experimental data. The experimental results agree well with the theoretical prediction.

Combined refraction and diffraction models for sea waves over complicated topography and with currents in shallow water

-Combined refraction and diffraction models in the form of linear parabolic approximation are derived through smallparameter method. More strictly theoretical basis and more accuracy in the models than Lozano's (1980) are obtained. Some theoretical defects in Liu's model (1985) with consideration of current are not only found but also eliminated. More strict and accurate models are, therefore, presented in this paper.The calculation results and analysis in applying the models to actual wave field with consideration of bottom friction will be given in the following paper.

In-situ quantitative monitoring of fatigue crack using fastest time of flight diffraction method

Due to the cyclic loading and longtime exposure under extreme environment conditions, fatigue cracks often generate in the aircraft metal structures, i.e. wing skin, fuselage skin, strigners, pylons. These cracks could cause severe damages to the aircraft structures. Thus the position and size monitoring of fatigue cracks in the metal structures is very important to manufacturers as well as maintenance personnel for significantly improving the safety and reliability of aircraft. Much progress has been made for crack position monitoring in the past few years. However, the crack size monitoring is still very challenging. Fastest time of flight diffraction （FTOFD） method was developed to monitor both the position and size of a crack. FTOFD method uses an integrated sensor network to activate and receive ultrasonic waves in a structure. Diffraction waves will be generated when the ultrasonic waves pass a crack. These diffraction waves are received and analyzed to get the position and size of the crack. The experiment results show that the monitored size of the simulated crack is very close to the real size of the crack, and for frequencies of 350 and 400 kHz, the monitoring errors are both smaller than 5%.

Ware Diffraction from A Vertical Cylinder with Two Uniform Columns and Porous Outer Wall

Based on a linens model of the pressure difference between two sides of a porous wall and the fluid velocity inside it, an analytic solution is established for wave diffraction from a cylinder with an outer pore us column and an Inner solid column. Numerical experiments are carried out to examine the effects of the wave force on a porous low-column cylinder and the wave elevations outside and inside the cylinder due to the pore us character of the outer column and the ratio between the radii of the inner and outer columns. The numerical results show that the increase in the coefficient of porosity of the outer column of a double column cylinder will reduce the wave elevation around the cylinder and the wave load on it. The radius of the inner column does not affect too much the wave elevation around the cylinder and the total force on the cylinder.

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.