Simulation of small-amplitude frequency-dispersive transient waves by means of the mild-slope equation

A numerical model based on the mild-slope equation is applied to reproduce the propagation of small-amplitude transient waves. The model makes use of the Fourier Transform to convert the time-dependent hyperbolic equation into a set of elliptic equations in the frequency domain. The results of two available experimental studies on tsunamis generated by landslides are used to validate the model, which appears to be able of carefully reproducing the effects of the frequency dispersion. An example application of tsunamis propagating around the Stromboli island is also presented to show the applicability of the present approach to real life scenarios. It is finally discussed how this model could be applied as support to a tsunami early warning system.     

港域波浪数学模型的改进与验证

通过物理模型对改进的港内波浪传播变形数学模型进行验证。该数学模型以推广的时变缓坡方程为控制方程,采用含松弛因子的ADI法求解,并对波浪反射和透射边界模拟方法进行改进。先通过物理模型试验确定斜向浪入射条件下抛石防波堤前的波浪反射系数,作为数学模型中部分反射边界模拟的依据。然后进行了一个典型港口内波浪折射、绕射和反射的模型试验,测量港内波浪分布。对比模型试验和数学模型计算的结果表明,数学模型可较好地模拟港内复杂地形和边界条件下规则波和不规则波的传播变形。     

一般曲线坐标系下波浪传播的数值模拟

在曲线坐标系下,建立了缓变水深水域波浪传播的数值模拟模型.模型适宜于复杂变化的边界形状,克服了各种代数坐标变换的局限性.在建立模型时,将原始的椭圆型缓坡方程的近似型式——依赖时间变化的抛物型方程,作为控制方程,既克服了一般抛物近似方法的缺点,又便利了方程的求解;从开边界条件、不同反射特性的固壁边界条件相统一的表达式出发,对边界条件进行处理;用ADI法数值求解控制方程.对模型的验证表明,数值解与物模实验值吻合良好,模型对于具有复杂边界的工程实际有较强的适应性.     

Assessment of open boundary conditions on the elliptic formulation of the mild-slope equation

The performance of open boundaries in a finite differences scheme of the elliptic mild-slope equation is assessed. The wave propagation results show that lowest order parabolic radiation boundary conditions, unlike sponge layers combined with first order radiation boundary conditions, are an efficient alternative to first order radiation boundary conditions in order to improve the accuracy of the numerical solution of the problem.     

Transient response of harbours to long waves under resonance conditions

This paper presents the results of a study aimed at quantifying the time–response of harbour basins to long waves under resonance conditions. On the basis of numerical simulations reproducing long waves in the yacht harbour of Rome (Ostia, Italy), it shows that the results valid for periodic forcing waves, acting for an infinitely long time, as those provided by models based on elliptic equations like the Helmoltz and the mild-slope equations, can be misleading with respect to the more realistic ones that can be obtained using time-varying wave equations. Taking advantage of the similarity between the processes studied here and a simple one-dimensional resonator, a method is also proposed to roughly estimate a time–response parameter of each mode of the harbour, using results from steady-state numerical model results, commonly applied for studying harbour resonance in engineering practice. On the basis of further numerical simulations, aimed at reproducing schematic harbour layouts, the effect on resonance of the position of the entrance and of an outer harbour is studied. The results indicate that the effects of design solutions to reduce resonance, by placing the entrance at the middle of the harbour, or using the outer harbour as a resonator, can be correctly evaluated only when considering the time needed for the oscillations to fully develop.     

近岸波浪在刚性植被区域传播的数值模型

基于扩展型Boussinesq水波方程,建立了波浪在刚性植被覆盖的近岸海域传播的数值模型。通过在动量方程源项中引入拖曳阻力项考虑植被对波浪的衰减作用。控制方程采用有限差分和有限体积混合格式求解,模型稳定性强,具备间断捕捉能力,能有效模拟近岸区域波浪的传播变形、破碎和处理海岸动边界问题。利用所建立模型对典型物理模型实验进行模拟,计算结果与实验结果吻合良好,表明模型可用于波浪在刚性植被覆盖海域的数值计算。     

A finite difference method for effective treatment of mild-slope wave equation subject to non-reflecting boundary conditions

A numerical model for coastal water wave motion that includes an effective method for treatment of non-reflecting boundaries is presented. The second-order one-way wave equation to approximate the non-reflecting boundary condition is found to be excellent and it ensures a very low level of reflection for waves approaching the boundary at a fairly wide range of the incidence angle. If the Newman approximation is adopted, the resulting boundary condition has a unique property to allow the free propagation of wave components along the boundary. The study is also based on a newly derived mild-slope wave equation system that can be easily made compatible to the one-way wave equation. The equation system is theoretically more accurate than the previous equations in terms of the mild-slope assumption. The finite difference method defined on a staggered grid is employed to solve the basic equations and to implement the non-reflecting boundary condition. For verification, the numerical model is then applied to three coastal water wave problems including the classical problem of plane wave diffraction by a vertical circular cylinder, the problem of combined wave diffraction and refraction over a submerged hump in the open sea, and the wave deformation around a detached breakwater. In all cases, the numerical results are demonstrated to agree very well with the relevant analytical solutions or with experimental data. It is thus concluded that the numerical model proposed in this study is effective and advantageous.     

一个二维数值波浪水槽的改进

对Drimer,Agnon及Segre研发的数值波浪水槽(简称DAS),首先通过修正DAS中某些积分计算的错误,建立了第一个修正模型(MDAS1),使得模型更加准确稳定。其次,将DAS模型自由表面线性元近似替换为更为合理准确的三阶元近似,建立了第二个修正模型(MDAS2),使得模型计算的波面更合理可靠。平底水槽中波群的生成及传播算例表明:与DAS结果相比,MDAS1对波面没有显著影响,而采用三阶元的MDAS2对波面有显著影响。与Hansen和Svendsen的实测资料相比较证实了两个修正模型的有效性。     

海浪特性及其传播变形研究新进展

综述第27届国家海岸工程会议（ICCE2000）上有关海浪特性及其传播变形研究的新进展，内容包括海浪的时域特性，海浪的特征，海浪的传播变形和波浪的破碎，反射等四部分。     

不规则区域海浪嵌套模式设计及其应用实例

本研究针对第三代MASNUM海浪模式的并行设计特点,设计实现了并行化不规则嵌套计算,从而提高了海浪模式嵌套模拟的灵活性和时效性.选取浙江舟山、宁波附近海域,利用201 1年的NCEP再分析风场作为强迫,采用大、中、小网格并利用该嵌套模式进行了三重嵌套应用.其中大、中区域实验均采用规则矩形方式设置开边界,大区域的模拟结果为中区域嵌套实验提供开边界条件,同时中区域嵌套输出小区域嵌套实验在不规则开边界上的边界条件.中区域的实验结果与卫星观测资料的对比表明:嵌套实验比无嵌套实验的误差小30％左右,二者在开边界附近的有效波高差异较大,达到0.5m以上.8月份中区域的无嵌套实验所得有效波高平均为0.7m,最大值为3.6m,嵌套实验结果则分别为1.0、7.1m,后者更接近以往观测资料所显示的平均波高1.5～2.0 m和最大波高5.0 ～10.0 m的结果,表明该常规嵌套方式的可行性.小区域实验也包含嵌套和无嵌套2个实验,开边界均采用不规则形状.实验结果表明:在5～8月期间,嵌套实验的波向与无嵌套的波向差异较明显,主要表现为外海传入;在6～7月份,嵌套实验与无嵌套实验有效波高的差值达1.0m以上;嵌套实验的周期普遍大于无嵌套的模拟结果,其最大差异为8 s.上述实验结果表明,该嵌套模式可实现规则开边界区域和不规则区域的嵌套模拟,可应用于复杂近岸区域的海浪数值模拟和预报,有效提高对关注区域海浪的模拟能力.     

Numerical modelling of deformation of multi-directional random waves over a varying topography

Two numerical formulations of the breaking phenomenon were implemented in a numerical model for random wave propagation based on the elliptic formulation of the mild-slope equation. The randomness of the wave field was simulated based on a spectral component method, in which the 3-D spectrum is discretised in components of equal energy. One of the breaking process formulations is based on the concept of breaking each independent spectral component. The other is based on the distribution of the local amount of energy dissipated through the independent spectral components. The model based on the concept of breaking each independent spectral component produces the best estimates of the wave field, when the numerical results are compared with laboratory data.     

SWAN模型模拟风浪场侧边界失真范围研究

鉴于SWAN模型存在着不能有效地模拟固壁边界附近风浪场的缺点,即在边界附近所模拟的波要素存在失真的现象,研究了在不同水深、风速和风向情况下模型侧边界附近波要素的失真范围,并对计算结果进行了详细的分析。结果表明水深、风速和风向对于侧边界附近波要素的失真范围具有不同的影响,即在风速一定的情况下,失真范围随着水深的增大而增大;水深一定的情况下,失真范围随着风速的增大而减小、随着风向的增大而增大。在利用SWAN模型模拟计算近岸或内陆湖泊风浪场时,必须采取适当的措施以减少实际计算域侧边界附近计算结果的失真范围。     

一种基本Boussinesq方程的近岸区破碎波模型

基于文献「１」Ｂｏｓｓｉｎｅｓｑ方程的近岸区破碎波模型基础,将数值模型中的波高衰减规律由假设改进为Ｄａｌｌｙ的解析公式,使近岸区破碎波模型的应用性更强。并将数值模型计算结果与现场实验资料进行对比,取得了满意的结果。     

聚焦波浪在浅堤上传播变形高精度数值模拟研究

基于开源程序REEF3D,通过建立高精度二维数值波浪水槽,系统研究了聚焦波浪在浅堤上传播变形的规律,着重分析了聚焦波浪通过浅堤的水动力过程及能量变化规律,讨论了不同波浪要素对聚焦波浪传播特性的影响。除此之外,还考虑了双浅堤布置对聚焦波浪传播变形的影响。研究结果表明:极端波浪通过浅堤时,堤顶水深越小,波浪主频能量衰减越显著。在给定堤顶水深条件下,聚焦点与浅堤的相对位置对聚焦波浪能量的衰减影响较小。在双浅堤布置条件下,随着浅堤间距的增加,上下游浅堤的相互影响逐渐减弱,高频段的波浪能量也随之减小。     

波浪产生和运动的二阶计算模型

在快速模拟波浪运动的谱方法基础上,引入造波边界,建立了模拟波浪产生和运动的二阶计算模型。采用摄动展开方法简化了带有造波边界的水波运动问题,将速度势分解,得到了满足造波边界和自由面边界的速度势的一般解,运用快速Fourier变换和时间积分,建立了模拟波浪产生和运动的数学模型。基于该模型,采用不同的数值造波条件,模拟了波浪的产生问题;考虑了波浪的初始运动问题;通过把数值结果与物理实验的比较,验证了波浪计算模型的有效性。     

网衣对波浪传播影响的三维数值模拟

为研究网衣对波浪传播的影响,采用多孔介质模型模拟网衣,建立了模拟网衣与波浪相互作用的三维数值波浪水槽模型。基于该数值模型研究了波浪经过网衣作用后波高衰减的变化规律,并与物理模型试验结果进行比较。通过对比数值模拟和物理模型试验的结果,证明了该三维数值模型模拟网衣对波浪传播影响的可行性。     

Linear and nonlinear irregular waves and forces in a numerical wave tank

A time-domain higher-order boundary element scheme was utilized to simulate the linear and nonlinear irregular waves and diffractions due to a structure. Upon the second-order irregular waves with four Airy wave components being fed through the inflow boundary, the fully nonlinear boundary problem was solved in a time-marching scheme. The open boundary was modeled by combining an absorbing beach and the stretching technique. The proposed numerical scheme was verified by simulating the linear regular and irregular waves. The scheme was further applied to compute the linear and nonlinear irregular wave diffraction forces acting on a vertical truncated circular cylinder. The nonlinear results were also verified by checking the accuracy of the nonlinear simulation.     

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.     

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.     

On the nudging terms at open boundaries in regional ocean models

For open boundary conditions (OBCs) in regional models, a nudging term added to radiative and/or advective conditions during the wave or flow propagation outward from the model domain of interest is widely used, to prevent the predicted boundary values from evolving to become quite different from the external data, especially for a long-term integration. However, nudging time scales are basically unknown, leading to many empirical selections. In this paper, a method for objectively estimating nudging time scales during outward propagation is proposed, by using internal model dynamics near the boundary. We tested this method and other several commonly used OBCs for cases of both an idealized model domain and a realistic configuration, and model results demonstrated that the proposed method improves the model solutions. Many similarities are found between the nudging and mixing time scales, in magnitude, spatial and temporal variations, since the nudging mainly replaces the effect of the mixing terms in this study. However, the mixing time scale is not an intrinsic property of the nudging term because in other studies the nudging term might replace terms other than the mixing terms and, thus, should reflect other characteristic time scales.