Wave Transformation and Breaking in Diagonal Opposing Current

- When waves propagate into diagonal opposing current from non-current area, not only the wave parameters but also the direction of wave propagation will change, that is, wave refraction will occur. The authors have calculated the changes of wave parameters, including wave refraction, by Linear Wave Theory, and have also done systematic study on wave transformation and breaking in opposing current by means of experimental analysis and theoretical calculation. In order to know the effect of wave refraction, computation is done in this paper about wave transformation and breaking on gentle slopes in diagonal opposing current.     

Interactions of nonlinear gravity waves and uniform current in Lagrangian system

The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an EulerLagrange transformation. The thirdorder asymptotic solution is a periodic bounded function of Lagrangian labels and time, which imply that the entire solution is uniformlyvalid. The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form. The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian. The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.     

Particle trajectories of nonlinear gravity waves in deep water

The paper presents a numerical method for calculating the particle trajectories of nonlinear gravity waves in deep water. Particle trajectories, mass-transport velocity and Lagrangian wave period can be accurately determined by the proposed method. The high success rate of the proposed method is examined by comparing the present results with those of (a) Longuet-Higgins, M.S., 1986, 1987. Eulerian and Lagrangian aspects of surface waves. Journal of Fluid Mechanics 173, 683-707 and (b) Lagrangian moments and mass transport in Stokes waves. Journal of Fluid Mechanics 179, 547-555. It is shown that the dimensionless mass-transport velocity can exceed 10% for large waves, and the Lagrangian wave period is much larger than the Eulerian wave period for large waves.     

Wave Breaker Indices in Finite Water Depth

Based on the analysis and comparison of wave breaker indices defined by geometric, kinetic as well as dynamic stabilities and verified by observation, the value a, which is equal to H / Lthkd by Miche's result and may be modified by Goda's results, is" suggested as the wave breaking criteria. The applicable values of a for pure waves or wave-current co-existing field are given in this paper. They are smaller than Miche's result (0.142), and they have been verified by model tests.     

Nonlinear Dispersion Effect on Wave Transformation

—A new nonlinear dispersion relation is given in this paper.which can overcome the limitationof the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple(1986).and which has a better approximation to Hedges'empirical relation than the modified relations by Hedges(1987).Kirby and Dalrymple(1987)for shallow waters.The new dispersion relation is simple in form.thusit can be used easily in practice.Meanwhile,a general explicit approximation to the new dispersion rela-tion and other nonlinear dispersion relations is given.By use of the explicit approximation to the newdispersion relation along with the mild slope equation taking into account weakly nonlinear effect.amathematical model is obtained,and it is applied to laboratory data.The results show that the model de-veloped with the new dispersion relation predicts wave transformation over complicated topography quitewell.     

Nonlinear Wave Force on Pier Group in Shallow Water

Based on the 1st order cnoidal wave theory, the wave diffraction around the pier group inshallow water is studied in this paper. The formulas for calculating the nonlinear wave forces are also presented here. In order to verify the theoretical results, model tests are conducted in the wave flume in The State Key Laboratory of Coastal and Offshore Engineering located in Dalian University of Technology. The range of the wave parameters in the experiments is characteristic wave period T g/d~(1/2) = 8.08- 22.86, characteristic wave height H/ d= 0.1 ~ 0.45. The results obtained from the experiments agree with the theoretical results quite well. It is shown that, in shallow water the nonlinear wave forces acting on a pier group are greater than those calculated by linear wave theory, the value of increment in wave force increases with the increases of the nonlinearity of the wave. In the wave range studied in this paper, the nonlinear wave force can reach over 4 times the force calculatecd by linear wave theory. Thus, it is suggested that, when Tg / d~(1/2)> 8, the wave force on the piers in the pier group in shallow water should be calculated by using the cnoidal wave theory.     

Nonlinear Dispersion Relation in Wave Transformation

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The Nonlinear Wave Force on a Circular Cylinder in Shallow Water

Based on the 1st order cnoidal wave theory, the nonlinear wave diffraction around a circular cylinder in shallow water is studied in this paper. The equation of the wave surface around the cylinder is formulated and by using this formula the wave surface elevation on the cylinder surface can be obtained. In this paper, the formula for calculating the cnoidal wave force on a circular cylinder is also derived. For the wave conditions which are often encountered in practical engineering designs, the ratios of the nonlinear wave forces to the linear wave forces are calculated, and the results are plotted in this paper for design purposes. In order to verify the theoretical results, model tests are conducted. After comparing the test results with the theoretical ones, it is concluded that, in shallow water, for the case of T g / d~(1/2) > 8-10 and H / d > 0.3, the cnoidal wave theory should be used to calculate the wave action on a cylindrical pier.     

Nonlinear Analysis of Nearshore Wave Height Variation Due to Shoaling

Wave formulae derived from the dispersion relation for cnoidal waves are used to find an analytical solution to the problem of nearshore wave height variation on a simple topography, i. e., with an incrementally constant slope. The solution accounts for shoaling, frictional dissipation and will be sufficiently accurate for practical purposes considering the simplified assumptions which are necessary for the treatment of this problem by any method.     

Nonlinear Effect of Wave Propagation in Shallow Water

—In this paper,a nonlinear model is presented to describe wave transformation in shallow wat-er with the zero-vorticity equation of wave-number vector and energy conservation equation.Thenonlinear effect due to an empirical dispersion relation(by Hedges)is compared with that of Dalrymple＇sdispersion relation.The model is tested against the laboratory measurements for the case of a submergedelliptical shoal on a slope beach,where both refraction and diffraction are significant.The computation re-sults,compared with those obtained through linear dispersion relation.show that the nonlinear effect ofwave transformation in shallow water is important.And the empirical dispersion relation is suitable for re-searching the nonlinearity of wave in shallow water.     

波流组合作用下SPAR平台垂荡-纵摇耦合运动研究

探讨SPAR平台在波流组合作用下的运动响应机理。运用Matlab程序分析了SPAR平台产生内共振的运动过程,运用刚体动力学理论建立了平台垂荡-纵摇耦合方程,对波流共同作用下Spar平台的垂荡、纵摇运动进行数值模拟,结果表明:流的加入对于内共振的影响并不明显;同时采用AQWA软件研究了流的加入对于纵荡二阶慢漂力的影响,研究发现,当波流同向时能大大增加Spar平台的纵荡运动,而波流反向时却能明显削弱纵荡运动。本文研究成果对于指导深海浮式结构设计开发具有一定的理论借鉴作用。     

波流水槽模拟波浪技术的研究

介绍了实验室的造波机系统和造波特性及其在模型试验中的应用,并讨论了实验室内模拟海浪的检验标准及其方法。并对造波机应用前景进行讨论,对不规则波造波机进行物模试验具有一定的现实意义。     

Numerical Modeling of Wave Diffraction-Refraction in Water of Varying Current and Topography

—A numerical model for wave diffraction-refraction in water of varying current and topogra-phy is proposed,and time-dependent wave mild-slope equation with a dissipation term and correspondingequivalent governing equations are presented.Two different expressions of parabolic approximations forthe case of the absence of current are also given and analyzed.The influence of current on the results ofsimulation of waves is discussed.Some examples show that the present model is better than others in simu-lating wave transformation in large water areas.And they also show that the influence of current shouldbe taken into account,on numerical modeling of wave propagation in water of strong current and coastalareas,otherwise the modeling results will be largely distorted.     

任意水深变化水域非线性波数值模拟

为了较为准确地计算沙质海岸沿岸输沙率,基于网格模型建立沙质海岸波浪的传播变化模型,根据求得的波高和波向分布特征,并考虑辐射应力等,计算波生流的分布。并在此基础上通过波浪最大底部轨道速度和沿岸流的分布特点,建立估算破波带内各网格单元上沿岸输沙率的分布模型。     

Comparative Study of Different SPH Schemes on Simulating Violent Water Wave Impact Flows

Free surface flows are of significant interest in Computational Fluid Dynamics（CFD）. However, violent water wave impact simulation especially when free surface breaks or impacts on solid wall can be a big challenge for many CFD techniques. Smoothed Particle Hydrodynamics（SPH） has been reported as a robust and reliable method for simulating violent free surface flows. Weakly compressible SPH（WCSPH） uses an equation of state with a large sound speed, and the results of the WCSPH can induce a noisy pressure field and spurious oscillation of pressure in time history for wave impact problem simulation. As a remedy, the truly incompressible SPH（ISPH） technique was introduced, which uses a pressure Poisson equation to calculate the pressure. Although the pressure distribution in the whole field obtained by ISPH is smooth, the stability of the techniques is still an open discussion. In this paper, a new free surface identification scheme and solid boundary handling method are introduced to improve the accuracy of ISPH. This modified ISPH is used to study dam breaking flow and violent tank sloshing flows. On the comparative study of WCSPH and ISPH, the accuracy and efficiency are assessed and the results are compared with the experimental data.     

波浪与海流测量仪器测试装置

"波浪与海流测量仪器测试装置"依靠机械传动机构带动传感器作相对运动,模拟"波浪"和"海流"测量状态。测试装置为实现实验室内进行声学测波仪和声学矢量海流计的调机、考机、检测增添了有效可靠的技术手段。     

Numerical Modeling of Wave and Current Interaction in the Tidal Inlet Area

This paper investigates the phenomena of wave refraction and diffraction in the slowly varying topography, as well as the current deflection due to wave actions. A numerical model is developed based on depth integrated mean continuity equation and momentum equations, and a 3rd-order wave equation which governs the wave diffraction, refraction and interaction with current. Examples to examine the above model are given comparing with the laboratory data or the numerical results of other researchers. An example simulating the inlet area shows the interesting velocity field which may be used as a pioneer to further study on the nearshore hydrodynamics and sedimentation.     

High-Order Models of Nonlinear and Dispersive Wave in Water of Varying Depth with Arbitrary Sloping Bottom

High-order models with a dissipative term for nonlinear and dispersive wave in water of va-rying depth with an arbitrary sloping bottom are presented in this article.First,the formal derivations toany high order of μ(=h/λ,depth to deep-water wave length ratio)and ε(=α/h,wave amplitude todepth ratio)for velocity potential,particle velocity vector,pressure and the Boussinesq-type equations forsurface elevation η and horizontal velocity vector U at any given level in water are given.Then,the exactexplicit expressions to the fourth order of μ are derived.Finally,the linear solutions of η,U,C(phase ce-lerity)and C_g(group velocity)for a constant water depth are obtained.Compared with the Airy theory,excellent results can be found even for a water depth as large as the wave legnth.The present high-ordermodels are applicable to nonlinear regular and irregular waves in water of any varying depth(from shal-low to deep)and bottom slope(from mild to steep).     

Application of VOF in Calculating Wave Energy Loss due to Spilling Breaker

- A large amount of experimental analysis and systematical theoretical calculation has been done by the authors to solve the problem of wave transformation and breaking, considering the effect of both current and topography, but only the wave energy loss due to spilling breaker in the surf zone has been discussed in this paper. Based on test result analysis and calculation with the Stream Function Wave Theory, the wave velocity field at breaking points has been obtained, and it is used to calculate the wave heights after breaking by the VOF (Volume of Fluid) method, in which the governing equations are continuity equation and Navier-Stokes Equation for imcompressible fluids. In the present paper, the improved VOF technique is used to calculate the wave heights of stable regular waves after breaking. Results fit the test data well, which shows that the VOF method is suitable to numerical simulation of regular waves after breaking. Besides, the breaker coefficient B of regular waves in the bore model is a     

Study on Current-Random Wave Forces Acting on a Framework

—The forces of random wave plus current acting on a simplified offshore platform(jacket)mod-el have been studied numerically and experimentally.The numerical results are in good agreement withexperiments.The mean force can be approximated as a function of equivalent velocity parameter and theroot-mean-square force as a function of equivalent significant wave height parameter.