开孔沉箱与斜向波作用的理论研究和实验验证

应用透空壁内流体速度与壁两侧的压力差成正比的线性模型,研究了无限多个开孔沉箱在斜向波作用下的反射问题。整个流域被分成无限多个子域,在每个子域内应用特征函数展开法对速度势进行展开。对于沉箱内的波浪运动,根据沉箱位置引入相位差概念。在构造反射波模型时,考虑了结构物几何形状周期性的影响。结果表明,当孔隙系数无限大时,开孔墙前后的速度非常接近,反射系数符合能量守恒定律。在低频入射波作用下,沉箱越短,其反射系数越小,反射系数随着角度的变大而减小。     

开孔沉箱在斜向入射波作用下受力研究

应用透空壁内流体速度与壁两侧的压力差成正比的线性模型,研究了斜向波与无限多个开孔沉箱的相互作用.依照结构物的几何形状,把整个流域分成无限多个子域,在每个子域内应用特征函数展开法对速度势进行展开.对于沉箱内的波浪运动,引入相位差概念;在构造反射波模型时,考虑了结构物的几何形状影响.列举出物理模型实验结果与数值实验结果的比较,可以看出两者吻合较好.进一步的数值计算验证表明,当孔隙系数无限大时,开孔墙前后的速度非常接近.在低频入射波作用下,垂直于沉箱的水平力随角度的变大而减小,平行于沉箱排列方向的力则变大.     

The reflection of oblique waves by an infinite number of partially perforated caissons

This study examines the reflection of obliquely incident waves by an infinite array of partially perforated caissons. Based on the linear potential theory, an analytical solution of the present problem was developed by means of the matched eigenfunction expansion method. The solution was obtained in a single strip consisting of the semi-infinite narrow region in front of a caisson and the fluid domain inside this caisson. It was then extended to the whole fluid domain by using the periodicities of the structure and the incident waves along the length of the caissons. The present model was validated by comparing the reflection coefficients of several limiting cases with the corresponding results obtained by previous researchers. Numerical experiments were also conducted to examine the variations of the reflection coefficient versus its main effect factors. The numerical results indicate the differences between the present model and the previous limiting cases, and some helpful results are recommended for practical engineering.     

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.     

Wave motion over a breakwater system of a horizontal plate and a vertical porous wall

A two-dimensional analytical solution is presented to study the reflection and transmission of linear water waves propagating past a submerged horizontal plate and through a vertical porous wall. The velocity potential in each fluid domain is formulated using three sets of orthogonal eigenfunctions and the unknown coefficients are determined from the matching conditions. Wave elevations and hydrodynamic forces acting on the porous wall are computed. Reflection and transmission coefficients are presented to examine the performance of the breakwater system. The present analytical solutions are found in fairly good agreement with the available laboratory data. The results indicate that the plate length, the porous-effect, the gap between plate and porous wall, and the submerged depth of the plate all show a significant influence on the reflected and transmitted wave fields. It is also interesting to note that the submerged plate plays an important role in reducing the transmitted wave height, especially for long incident waves.     

Hydroelastic interaction between obliquely incident waves and a semi-infinite elastic plate on a two-layer fluid

The hydroelastic response of a semi-infinite thin elastic plate floating on a two-layer fluid of finite depth due to obliquely incident waves is investigated. The upper and lower fluids with different densities separated by a sharp and stable interface are assumed to be inviscid and incompressible and the motion to be irrotational. Simply time-harmonic incident waves of the surface and interfacial wave modes with a given angular frequency are considered within the framework of linear potential flow theory. With the aid of the methods of matched eigenfunction expansion and the inner product of the two-layer fluid, a closed system of simultaneous linear equations is derived for the reflection and transmission coefficients of the series solutions. Based on the dispersion relations for the gravity waves and the flexural–gravity waves in a two-layer fluid and Snell’s law for refraction, we obtain a critical angle for the incident waves of the surface wave mode and three critical angles for the incident waves of the interfacial wave mode, which are related to the existence of the propagating waves. Graphical representations of the series solutions show the interaction between the water waves and the plate. The effects of several physical parameters, including the density and depth ratios of the fluid and the thickness of the plate, on the wave scattering and the hydroelastic response of the plate are studied. It is found that the variation of the thickness of the plate may change the wave numbers and the critical angles. The density ratio is the main factor to influence the wave numbers of the interfacial wave modes. Finally, the stress state is considered.     

Reflection of irregular waves from perforated-wall caisson breakwaters

An analytical model has been developed that predicts the reflection of irregular waves normally incident upon a perforated-wall caisson breakwater. To examine the predictability of the developed model, laboratory experiments have been conducted for the reflection of irregular waves of various significant wave heights and periods impinging upon breakwaters having various wave chamber widths. For frequency-averaged reflection coefficients, though the overall agreement is fairly good between measurement and calculation, the model somewhat over-predicts the reflection coefficients at larger values, and under-predicts at smaller values. The model also underestimates the energy loss coefficients as wave reflection becomes larger. These differences occur because the model neglects the evanescent waves near the breakwater, which increase the energy loss at the perforated wall. The frequency-averaged reflection coefficient shows a minimum when the wave chamber width is approximately 0.2 times the significant wavelength, and it decreases with increasing wave steepness. Finally, it is shown that the reflection of irregular waves from a perforated-wall caisson breakwater depends on the wave frequency, so that the reflected wave spectrum shows a frequency dependent oscillatory behavior.     

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

1 IntroductionRecently breakwaters with perforated front wallshave been widely used. The use of perforated break-waters mainly has two advantages. Firstly, wave forcesacting on the whole structure can be divided into twoparts on two different walls with a phase difference.To select the distance between the two plates suitably,the total wave force on the whole structure can bemaintained at a low level. Secondly, waves will dissi-pate when they transmit over a porous medium. Thus,the reflection…     

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 poten-tials 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.     

Interaction of linear waves with an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth

The linear water wave scattering and radiation by an array of infinitely long horizontal circular cylinders in a two-layer fluid of infinite depth is investigated by use of the multipole expansion method. The diffracted and radiated potentials are expressed as a linear combination of infinite multipoles placed at the centre of each cylinder with unknown coefficients to be determined by the cylinder boundary conditions. Analytical expressions for wave forces, hydrodynamic coefficients, reflection and transmission coefficients and energies are derived. Comparisons are made between the present analytical results and those obtained by the boundary element method, and some examples are presented to illustrate the hydrodynamic behavior of multiple horizontal circular cylinders in a two-layer fluid. It is found that for two submerged circular cylinders the influence of the fluid density ratio on internal-mode wave forces is more appreciable than surface-mode wave forces, and the periodic oscillations of hydrodynamic results occur with the increase of the distance between two cylinders; for four submerged circular cylinders the influence of adding two cylinders on the wave forces of the former cylinders is small in low and high wave frequencies, but the influence is appreciable in intermediate wave frequencies.     

不规则波作用下大尺度方形群墩结构的相互影响

本文用谱分析方法对方柱群墩结构在不规则波作用下的相互影响进行了计算。研究了在不同入射波向时每个方墩的群墩影响系数随墩距变化的规律并与折算圆墩的结果进行了比较。入射波谱采用Ｂｒｅｔｓｃｈｎｅｉｄｅｒ谱。计算结果表明方柱墩群与折算圆柱墩群的群墩影响系数较为接近且随着墩间距的增加趋近于孤立墩情形。     

双层局部开孔板沉箱对波浪反射的理论研究

提出了一种用于研究由双层开孔板和一个不透水后板的开孔结构对斜向波反射率的理论分析方法。整个流域被分成三个子域，在每个子域内应用特征函数展开法以得到该域内包含未知展开系数的势函数的表达式，在速度势的展开中，考虑了非传播模态波浪的影响。通过匹配开孔板处的边界条件可以求解待定的展开系数，继而求解双层开孔板防波堤结构对斜向波的反射率。数值计算结果与试验结果进行了比较，符合较好。并进一步讨论了几个重要因素对反射系数的影响。     

波浪反射系数谱的特征分析

应用斜向不规则波反射系数的改进两点法(MTPM),用模型试验研究了混凝土护面堤和块石护面堤波浪反射系数的频率谱和方向谱,结果表明,分析的反射系数随入射波频率的增加、结构坡度的减小和入射角的加大而减小.给出了波浪反射系数频率谱及其随Iribarren数变化的规律,提出了反射系数三维谱的经验公式,由此可定量地描述斜向不规则波的反射系数随无量纲特征参数Iribarren数和入射波角度的变化规律.     

Scattering of obliquely incident water waves by partially reflecting non-transmitting breakwaters

In the present paper, analytic solutions are derived for scattering of water waves obliquely incident to a partially reflecting semi-infinite breakwater or breakwater gap. In order to examine the correctness of the derived solutions, they are compared with the solutions derived by McIver (1999) and Bowen and McIver (2002) for a semi-infinite breakwater and a breakwater gap, respectively, in the case of perfect reflection. The derived analytic solutions are used to investigate the effect of reflection coefficient of the breakwater and wave incident angle upon the tranquility at harbor entrance. The tranquility is deteriorated by the reflected waves as the reflection coefficient increases and as waves are incident more obliquely.     

Bragg reflection of water waves by multiple submerged semi-circular breakwaters

This study examines the Bragg reflection of water waves by multiple submerged semi-circular breakwaters. The multipole expansions combined with the shift of polar coordinates are used to develop full linear potential solutions of the problem. In the full solutions, the obliquely and normally incident waves are independently considered. Experimental tests are carried out to measure the reflection and transmission coefficients of the breakwaters at different wave periods and body spacings. The analytical results are in reasonable agreement with the experimental data. The peak reflection coefficient of multiple submerged semi-circular breakwaters and the bandwidth of Bragg reflection are carefully examined by numerical examples. Some significant results for practical application are discussed.     

Experimental determination of wavelengths in the presence of a mean current

This paper describes a simple method for determining the wavelength of small amplitude waves under laboratory conditions where reflected wave components are present both with and without a mean current flow superimposed. It assumes a locally horizontal bed but requires no a priori assumption concerning the form of the dispersion relation with a coexisting current. Synchronous measurements of the water surface recorded along any straight line are analysed to yield Fourier coefficients at each location. It is then shown that for all practical conditions excluding a perfect standing wave, the average rate of change of wave phase in the chosen direction can be related directly to the component of incident wave number in that direction, irrespective of reflection coefficient or relative current strength. The technique has been applied to regular and bichromatic waves in a flume with an absorbing wave generator, and can also be applied in 3-D wave basins where waves and currents intersect at arbitrary angles. In combined wave–current experiments, by assuming the linear dispersion relation, it is also possible to estimate the effective current velocity.     

Generalized boussinesq model for periodic non-linear shallow-water waves

This paper presents the development of a generalized Boussinesq (gB) model for the periodic non-linear shallow-water waves. An incident cnoidal wave solution for the gB model is derived and applied to the wave simulation. A set of radiation boundary conditions is also established to transmit effectively the cnoidal waves out of the computational domain. The classical solutions of the second-order cnoidal waves are discussed within the content of the KdV equation and the generalized Boussinesq equations. An Euler's predictor-corrector finite-difference algorithm is used for numerical computation. The propagation of normally incident cnoidal waves in a channel is studied. The simulated wave profiles agree well with the analytical results. The temporal and spatial evolution of an obliquely incident cnoidal wave is also modelled. The phenomenon of Mach reflection is discussed.     

Numerical simulation of non-linear regular and focused waves in an infinite water-depth

Inviscid three-dimensional free surface wave motions are simulated using a novel quadratic higher order boundary element model (HOBEM) based on potential theory for irrotational, incompressible fluid flow in an infinite water-depth. The free surface boundary conditions are fully non-linear. Based on the use of images, a channel Green function is developed and applied to the present model so that two lateral surfaces of an infinite-depth wave tank can be excluded from the calculation domain. In order to generate incident waves and dissipate outgoing waves, a non-reflective wave generator, composed of a series of vertically aligned point sources in the computational domain, is used in conjunction with upstream and downstream damping layers. Numerical experiments are carried out, with linear and fully non-linear, regular and focused waves. It can be seen from the results that the present approach is effective in generating a specified wave profile in an infinite water-depth without reflection at the open boundaries, and fully non-linear numerical simulations compare well with theoretical solutions. The present numerical technique is aimed at efficient modelling of the non-linear wave interactions with ocean structures in deep water.     

An Efficient Model for Transient Surface Waves in Both Finite and Infinite Water Depth

A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Eulerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The boundary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.     

Wave reflection from perforated-wall caisson breakwaters

Analytical models for predicting wave reflection from a perforated-wall caisson breakwater have been developed. Most of the existing models deal with the case in which the waves are normally incident to the caisson lying on a flat sea bottom. In the present paper, using the Galerkin-eigenfunction method, an analytical model is developed that can predict the reflection coefficient of a perforatedwall caisson mounted on a rubble mound foundation when waves are obliquely incident to the breakwater at an arbitrary angle. The developed model is compared with other theoretical results and hydraulic experimental data.