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.

The force of oblique incident wave on the breakwater with a partially perforated wall

Wave forces induced by the interaction between the oblique incident wave and the breakwater with a partially perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigen-function expansion method is applied to expanding 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 other theories and a good agreement can be found between them. Experimental data have been compared with the present theoretical results. The effect of the traverse wall on wave forces has been discussed in detail. On the basis of the linear wave theory, it is shown that in the range Of engineering practice, the incident angle of wave has small influence on wave forces on the unit length of perforated caisson.

A Method to Determine the Incident Wave Boundary Conditions and Its Application

When studying the harbor water tranquility, cases are often confronted as that the verification point is not located on the generation line or that the angle between the generation line and the isobath is so large that the differences of the wave climates along the generation line can not be ignored. For these cases, the incident boundary conditions are difficult to evaluate. In order to solve this problem, a combined wave model is developed in the present paper based on the Boussinesq equation and the wave action balance equation. Instead of the one-line wave generation method, a multi-line generation method is proposed for the combined model. Application of this method is given to a case that the harbor is designed with two entrances and the angle between the generation line and the isobath is large and the results are shown reasonable. We suggest that the wave generation method on multi-lines might also be introduced to the wave physical model as the replacement for the one-line generation method.

Laboratory Study on the Interaction Between Regular Obliquely Incident Waves and Vertical Walls

The characteristics of wave forces are studied based on physical model tests with regular waves. The ratio of obliquely incident wave forces to normally incident wave forces on unit length of a vertical wall is related with various factors. A linear reduction of the mean force of obliquely incident waves is confirmed with an increase in the relative caisson length. Also the characteristics of reflection coefficient of diagonal waves are discussed.

2.5-dimension soil seismic response to oblique incident waves based on exact free-field solution

With the three dimensional(3D)oblique incident waves exactly determined for the free field,the soil seismic responses in both frequency and time domains are studied by the 2.5 dimension(2.5D)finite/infinite element method.First,the free-field responses in frequency domain are solved exactly for 3D arbitrary incident P and SV waves,which requires no coordinate conversion or extra effort for SV waves with super-critical incident angles.Next,the earthquake spectra are incorporated by the concept of equivalent seismic forces on the near-field boundary,based only on the displacements input derived for unit ground accelerations of each frequency using the 2.5D approach.For the asymmetric 2.5D finite/infinite element model adopted,the procedure for soil seismic analysis is presented.The solutions computed by the proposed method are verified against those of Wolf’s and de Barros and Luco’s and for inversely calculated ground motions.Of interest is that abrupt variation in soil response occurs around the critical angle on the wave propagation plane for SV waves.In addition,the horizontal displacements attenuate with increasing horizontal incident angle,while the longitudinal ones increase inversely for 3D incident P and SV waves.

Seismic stability of jointed rock slopes under obliquely incident earthquake waves

Seismic stability of slopes has been traditionally analyzed with vertically propagated earthquake waves.However,for rock slopes,the earthquake waves might approach the outcrop still with a evidently oblique direction.To investigate the impact of obliquely incident earthquake excitations,the input method for SV and P waves with arbitrary incident angles is conducted,respectively,by adopting the equivalent nodal force method together with a viscous-spring boundary.Then,the input method is introduced within the framework of ABAQUS software and verified by a numerical example.Both SV and P waves input are considered herein for a 2 D jointed rock slope.For the jointed rock mass,the jointed material model in ABAQUS software is employed to simulate its behavior as a continuum.Results of the study show that the earthquake incident angles have significance on the seismic stability of jointed rock slopes.The larger the incident angle,the greater the risk of slope instability.Furthermore,the stability of the jointed rock slopes also is affected by wave types of earthquakes heavily.P waves induce weaker responses and SV waves are shown to be more critical.

REFLECTION OF OBLIQUE INCIDENT WAVES BY PERFORATED CAISSONS WITH TRAVERSE WALL

The interaction of oblique incident waves with infinite number of perforated caissons is investigated. The fluid domain is divided into infinite sub-domains by the caissons, and eigen-function expansion is applied to expand velocity potentials in each domain. A phase relation is introduced for wave oscillation in each caisson, and the structure geometry is considered in constructing the models of reflection waves. The reflected waves with the present analysis include all of the waves traveling in different directions when incident wave period is short. Numerical examinations show that velocities at the inner and outer sides of the front walls of caissons ase close to each other, and reflection coefficients satisfy the energy conservation relation very well when porous effect parameter is infinite. Numerical results show that the reflection coefficients of oblique incident waves are smaller for shorter caissons at low frequency, and decrease with the increase of wave incident angle.

Soil seismic analysis for 2D oblique incident waves using exact free-field responses by frequency-based finite/infinite element method

The seismic analysis of a viscoelastic half-space under two-dimensional(2D)oblique incident waves is carried out by the finite/infinite element method(FIEM).First,the frequency-domain exact solutions for the displacements and stresses of the free field are derived in general form for arbitrary incident P and SV waves.With the present formulation,no distinction needs to be made for SV waves with over-critical incident angles that make the reflected P waves disappear,while no critical angle exists for P waves.Next,the equivalent seismic forces of the earthquake(Taft Earthquake 1952)imposed on the near-field boundary are generated by combining the solutions for unit ground accelerations with the earthquake spectrum.Based on the asymmetric finite/infinite element model,the frequency-domain motion equations for seismic analysis are presented with the key parameters selected.The results obtained in frequency and time domain are verified against those of Wolf’s,Luco and de Barros’and for inversely computed ground motions.The parametric study indicated that distinct phase difference exists between the horizontal and vertical responses for SV waves with over-critical incident angles,but not for under-critical incident angles.Other observations were also made for the numerical results inside the text.

Numerical study of fluid resonance of a two-dimensional heaving-free moonpool in a wide range of incident waves

The fluid resonance of a moonpool freely heaving in a beam sea is studied by an in-house constrained interpolation profile(CIP)code.Generally,the moonpool behaves as in the piston mode with a narrow opening.The numerical studies are carried out for a wide range of the incident waves,and a new secondary resonant region is identified in the low frequency region of the incident waves,besides the ordinary main resonant region.Numerical results demonstrate that the horizontal wave forces are significant in the secondary resonant region,although the resonant wave elevations are less remarkable than those of the main resonant region.It is concluded that the fluid resonance of the low frequency is excited mainly by the heave motion of the moonpool.Parameter studies of the moonpool draft and the gap width of the moonpool based on the fluid resonance are also performed.

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.

First-order approximate analytical expressions of oblique incident elastic wave at an interface of porous media saturated with a nonviscous fluid

The analysis technology of Amplitude Variation with Offset(AVO)is one of the important methods for oil and gas reservoir prediction.Zoeppritz equation and its approximations are the theoretical basis of AVO analysis,which assumes that the upper and lower media of a horizontal interface are single-phase media.Limited by this assumption,AVO analysis has limited prediction and identification accuracy for complex porous reservoirs.In view of this,the first-order approximate analytical expressions of oblique elastic wave at an interface of porous media are derived.Firstly,the incident and scattering characteristics of various waves at the interface of porous media are analyzed,and the displacement vectors generated by these elastic waves are described by exponential function.Secondly,the kinematic and dynamic boundary conditions at the interface of porous media are discussed.Thirdly,by substituting the displacement vectors of incident and scattered waves into boundary conditions,the exact analytical equation is derived.Then,considering the symmetry of scattering matrix in the equation,the exact analytical expressions of each scattered wave are obtained.Furthermore,under the assumptions of small incident angle,weak elasticity at an interface of porous media,and ignoring the second-and higherorder terms,the first-order approximate analytical expressions are derived.Establishing a model of sandstone porous media with different porosity in upper and lower media,the correctness of the approximate analytical expressions is verified,and the elastic wave response characteristics of lithology and pore fluids are analyzed.

Active control of interior noise within an irregular enclosure under the cooperation of point force and Incident wave

A new modeling method is developed for the active control of interior noise within an irregular three-dimensional cavity under the cooperation of point force and incident wave. The validity of this method is verified by a regular cuboid enclosure. With global and local performance functions, good results are obtained in the active control of noise within the irregular enclosure according to numerical investigations.

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.

Three-Dimensional Scattering of an Incident Plane Shear Horizontal Guided Wave by a Partly through-Thickness Hole in a Plate

We investigate the three-dimensional （3D） scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate, in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem. An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes, and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies. The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency. It is also found that the scattering patterns are different from those of the SO wave incidence. Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.

Approximate Calculation of Oblique Wave Transmission from A Single-Row of Rectangular Piles

Transmissions of oblique incident wave from a row of rectangular piles are analyzed theoretically. The incident angle of plane wave is taken as g = 90° , there then is the transmission coefficient ｜T｜ = 1 （This is a paradox）. In this paper, by means of the approximate relation between the transmitted and incident wave angle found from the shape of a slit, the paradoxical phenomenon is removed. On the basis of the continuality of the pressure and flux and the analysis of flow resistance at the row of rectangular piles, formulas of reflection and transmission coefficients are obtained. The transmission and reflection coefficients predicted by the present model quite agree with those of laboratory experiments in previous references

A SPECIAL SOLUTION OF WAVE DISSIPATION BY FINITE POROUS PLATES

The reflection and transmission of water waves caused by a small amplitude incident wave through finite fine porous plates with equal spacing and permeability in an infinitely long open channel of constant water depth and zero slope are studied. A special solution is obtained when the distance between the two neighbouring plates is an integral multiple of the half-wavelength of the incident wave. It is found that when the dimensionless porous-effect parameter G0 is equal to half the total plate number, the wave dissipation reaches a maximum, and only 50% of the incident wave energy remains in the reflected and transmitted waves. Meanwhile, the reflected and transmitted waves have the same amplitude.

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.

Long Waves Associated with Bichromatic Waves

A numerical model of low frequency waves is presented. The model is based on that of Roelvink (1993), but the numerical techniques used in the solution are based on the so-called Weighted- Average Flux (WAF) method with Time-Operator- Splitting JOS) used for the treatment of the source terms. This method allows a small number of computational points to be used, and is particularly efficient in modeling wave setup. The short wave (or primary wave) energy equation is solved with a traditional Lax-Wendroff technique. A nonlinear wave theory is introduced. The model described in this paper is found to be satisfactory in modeling low frequency waves associated with incident bichromatic waves.

Wave Forces Acting on Vertical Walls

Regular and irregular wave forces acting on vertical walls are studied by a previously developed numerical model. The computed wave forces are compared with the available experimental data to verify the numerical model, and satisfactory agreements are obtained. The variation of wave forces with incident angles and the shape of simultaneous pressure distribution are investigated, and the comparisons between numerical results and Goda＇ s predictions are also carried out. It is concluded that the maximum wave forces acting on the unit length of vertical wall is often induced by the obliquely incident waves instead of normally incident waves, while Goda＇ s formula may be inapplicable for oblique wave incidence. The shape of simultaneous pressure distribution is not significantly influenced by incident angles, and it can be favorably predicted by Goda＇ s formula. When regular wave heights are taken as the same as irregular wave height H1%, the irregular wave forces Ph. 1% are slightly larger than regular wave forces in most cases.

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.