NWF: Propagation of Tsunami and its Interaction with Continental Shelf and Vertical Wall

In this article, tsunamis represented as solitary waves was simulated using the fully nonlinear free surface waves based on Finite Element method developed by Sriram et al. (2006). The split up of solitary wave while it propagates over the uneven bottom topography is successfully established. Wave transmission and reflection over a vertical step introduced in the bottom topography is in good agreement with the experimental results from Seabra-Santos et al. (1987). The wave transformation over a continental shelf with different smooth slopes reveals that the solitary wave reflection increases while the continental slope varies from flat to steep. The interaction of the solitary wave with a vertical wall for different wave steepness has been analysed. The reflected shape of the profile is in good agreement with the observation made by Fenton and Rienecker (1982) and an increase in wave celerity is observed.     

陆架斜坡对内孤立波的动力响应特性试验研究

针对内孤立波在行进过程中遇到海底斜坡会对海底产生力的作用,不同坡度斜坡对内孤立波的动力响应应该存在差异。本文通过水槽中制造内波,对不同角度的斜坡对内孤立波的动力响应过程进行了研究。结果表明,内孤立波通过陆架斜坡上方,会造成斜坡沉积物超孔隙水压力的积累;在相同振幅条件下,缓坡沉积物动力响应的幅度比陡坡沉积物大;随着振幅的增加,缓坡发生动力破坏程度大于陡坡;在斜坡沉积物稳定性受到破坏之前,超孔隙水压力的积累和释放同时存在,内孤立波振幅的增大会加剧超孔隙水压力的释放。该结果对于斜坡沉积物在内孤立波作用下失稳破坏的动力学研究和斜坡稳定性分析将起到指导作用。     

强非线性和色散性Boussinesq方程数值模型检验

采用同位网格有限差分法,建立了强非线性和色散性Boussinesq方程数值计算模型。以稳恒波Fourier近似解给定入射波边界条件,对均匀水深深水和浅水域不同非线性的行进波、缓坡地形上深水至浅水域的浅水变形波、以及缓坡和陡坡地形上的波浪水槽实验进行了数值计算,并将计算结果与解析解、解析数值解以及实验值进行了较为详细的比较,从而检验了模型的色散性、非线性以及不同底坡下非线性波的浅水变形性能。     

Internal tide and nonlinear internal wave behavior at the continental slope in the northern south China Sea

A field program to measure acoustic propagation characteristics and physical oceanography was undertaken in April and May 2001 in the northern South China Sea. Fluctuating ocean properties were measured with 21 moorings in water of 350- to 71-m depth near the continental slope. The sea floor at the site is gradually sloped at depths less than 90 m, but the deeper area is steppy, having gradual slopes over large areas that are near critical for diurnal internal waves and steep steps between those areas that account for much of the depth change. Large-amplitude nonlinear internal gravity waves incident on the site from the east were observed to change amplitude, horizontal length scale, and energy when shoaling. Beginning as relatively narrow solitary waves of depression, these waves continued onto the shelf much broadened in horizontal scale, where they were trailed by numerous waves of elevation (alternatively described as oscillations) that first appeared in the continental slope region. Internal gravity waves of both diurnal and semidiurnal tidal frequencies (internal tides) were also observed to propagate into shallow water from deeper water, with the diurnal waves dominating. The internal tides were at times sufficiently nonlinear to break down into bores and groups of high-frequency nonlinear internal waves.     

Wave propagation in a fully nonlinear numerical wave tank: A desingularized method

The problem of wave propagation in a fully nonlinear numerical wave tank is studied using desingularized boundary integral equation method coupled with mixed Eulerian–Lagrangian formulation. The present method is employed to solve the potential flow boundary value problem at each time step. The fourth-order predictor–corrector Adams–Bashforth–Moulton scheme is used for the time-stepping integration of the free surface boundary conditions. A damping layer near the end-wall of wave tank is added to absorb the outgoing waves with as little wave reflection back into the wave tank as possible. The saw-tooth instability is overcome via a five-point Chebyshev smoothing scheme. The model is applied to several wave propagations including solitary, irregular and random incident waves.     

Run-up of long solitary waves of different polarities on a plane beach

We study the run-up of long solitary waves of different polarities on a beach in the case of composite bottom topography: a plane sloping beach transforms into a region of constant depth. We confirm that nonlinear wave deformation of positive polarity (wave crest) resulting in an increase in the wave steepness leads to a significant increase in the run-up height. It is shown that nonlinear effects are most strongly pronounced for the run-up of a wave with negative polarity (wave trough). In the latter case, the run-up height of such waves increases with their steepness and can exceed the amplitude of the incident wave.     

Breaking of Solitary Waves on Uniform Slopes

The propagation,shoaling and breaking of solitary waves on mild slopes are simulated byboundary element method.In this paper,the criterion of breaking solitary waves on mild slopes is discussed.The criterion is that the ratio of horizontal velocity of water particles on the wave crest to wave celerity equalsone.However,the case that the ratio of horizontal velocity of water particles on the wave crest to wave ce-lerity is below one but the front face of wave profile becomes vertical is also considered as a breaking criteri-on.According to the above criteria,the breaking index for slopes 1:10 to 1:25 is studied.The result is com-pared to other researchers'.The deformation of solitary waves on slopes is discussed and the distribution offluid velocities at breaking is shown.     

Nonlinear progressive waves in water of finite depth — an analytic approximation

An analytical solution using homotopy analysis method is developed to describe the nonlinear progressive waves in water of finite depth. The velocity potential of the wave is expressed by Fourier series and the nonlinear free surface boundary conditions are satisfied by continuous mapping. Unlike the perturbation method, the present approach is not dependent on small parameters. Thus solutions are possible for steep waves. Furthermore, a significant improvement of the convergence rate and region is achieved by applying Homotopy-Padé Approximants. The calculated wave characteristics of the present solution agree well with previous numerical and experimental results.     

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.     

基于高阶边界元的三维数值波浪港池--波浪破碎的模拟

在势流理论的框架内,采用高阶边界元方法和混合欧拉-拉格朗日法,实现了对三维波浪破碎过程的数值模拟.数值模型使用可调节时间步长的基于二阶显式泰勒展开的混合欧拉-拉格郎日时间步进来求解自由表面的演化过程.在所使用的边界元方法中,采用16节点三次滑移四边形单元来表示,这种单元在单元内具有高阶的精度同时在单元之间具有良好的连续性.给出了孤立波的传播和周期性非线性波浪沿缓坡传播的计算结果,表明数值模型具有良好的稳定性.     

Experimental study of long wave generation on sloping bottoms

Low-frequency waves generated on steep (1:10) and mild (1:40) slopes by six series of bichromatic wave groups are studied experimentally. The shorelines for both slopes are replaced by horizontal reaches of small depth. This reduces the reflection of long waves near the shoreline significantly, which for the first time makes possible the explicit observation of outgoing breakpoint forced long waves. The breakpoint and released bound long wave mechanisms on the different slopes are compared. Generally, the breakpoint forced long waves dominate the low-frequency wave field on the steep slope, while the released bound long waves are found to be more significant on the mild slope. Two parameters indexing the effectiveness of the breakpoint mechanism are compared and the normalized slope tends to give more realistic results. Shoaling of bound long waves is analyzed and the shallow-water equilibrium limit ~ h^−5/2 exhibits a good prediction of the variation of the bound long waves on both slopes.     

Time domain three-dimensional fully nonlinear computations of steady body–wave interaction problem

Three-dimensional fully nonlinear waves generated by moving disturbances with steady forward speed without motions are solved using a mixed Eulerian–Lagrangian method in terms of an indirect boundary integral method and a Runge–Kutta time marching approach which integrates the fully nonlinear free surface boundary conditions with respect to time.A moving computational window is used in the computations by truncating the fluid domain (the free surface) into a computational domain. The computational window maintains the computational domain and tracks the free surface profile by a node-shifting scheme applied within it. An implicit implement of far field condition is enforced automatically at the truncation boundary of the computational window.Numerical computations are applied to free surface waves generated by Wigley and Series 60 hulls for the steady problem. The present numerical results are presented and compared with existing linear theory, experimental measurements, and other numerical nonlinear computations. The comparisons show satisfactory agreements for these hydrodynamic problems.     

Gerris在海洋大振幅内孤立波数值模拟中的应用

本文运用基于自适应网格的流体动力学开源软件Gerris,来建立基于Boussinesq近似下的二维不可压缩Euler方程组的数值模型,以模拟不同层化条件下稳定状态的完全非线性大振幅内孤立波。文中比较了完全非线性的用Gerris实现的Euler模型与弱非线性的KdV理论模型在刻画大振幅内孤立波结构及特征参数上的差异,说明在模拟大振幅内孤立波时,高阶非线性不应忽略。Euler模型模拟结果表明,完全非线性大振幅内孤立波的等密度面半宽度随深度变化,这使得基于KdV方程解析解、利用卫星SAR(Synthetic Aperture Radar)图像提取内孤立波极值间距来反演内波振幅的可行性存疑,需要重新评估。此外,本文用两组实测数据验证了用Gerris实现的Euler模型模拟大振幅内波的有效性。     

Numerical study of vegetation damping effects on solitary wave run-up using the nonlinear shallow water equations

Vegetation damping effects on propagating water waves have been investigated by many researchers. This paper investigates the effects of damping due to vegetation on solitary water wave run-up via numerical simulation. The numerical model is based on an implementation of Morison's formulation for vegetation induced inertia and drag stresses in the nonlinear shallow water equations. The numerical model is solved via a finite volume method on a Cartesian cut cell mesh. The accuracy of the numerical scheme and the effects of the vegetation terms in the present model are validated by comparison with experiment results. The model is then applied to simulate a solitary wave propagating on a plane slope with vegetation. The sensitivity of solitary wave run-up to plant height, diameter and stem density is investigated by comparison of the numerical results for different patterns of vegetation. The numerical results show that vegetation can effectively reduce solitary wave propagation velocity and that solitary wave run-up is decreased with increase of plant height in water and also diameter and stem density.     

Numerical Study on Breaking Criteria for Solitary Waves

Studies of the breaking criteria for solitary waves on a slope are presented in this paper. The boundary element method is used to model the processes of shoaling and breaking of solitary waves on various slopes. Empirical formulae that can be used to characterize the breaking of solitary waves are presented. These include the breaking index, the wave height, the water depth, and the maximum particle velocity at the point of breaking. Comparisons with the results of other researches are given.     

孤立波与带窄缝双箱相互作用模拟研究

针对孤立波与带窄缝双箱的作用问题,应用时域高阶边界元方法建立了二维数值水槽。其中,自由水面满足完全非线性运动学和动力学边界条件,对瞬时自由表面流体质点采用混合欧拉-拉格朗日法追踪,采用四阶龙格库塔法对下一时刻的自由水面的速度势和波面升高进行更新。采用加速度势法求解物体湿表面的瞬时波浪力。采用推板方法生成孤立波。通过模拟孤立波在直墙上的爬高以及施加在直墙上的波浪力,并与已发表的实验和数值结果对比,验证本数值模型的准确性。通过数值模拟计算研究了窄缝宽度、方箱尺寸对波浪在箱体迎浪侧爬高,窄缝内波面升高,箱体背浪侧透射波高及箱体受波浪荷载的影响。同时研究了有一定时间间隔的双孤立波与带窄缝双箱系统作用问题。