波浪传播数值模型波向角计算

波浪传播变形数值模型的抛物型近似在近海工程大范围水域的波浪推算中应用十分广泛，本文就抛物型缓坡方程（PMSE）数值计算中波浪方向的计算作了分析。首先从椭圆型缓坡方程（MSE）推导了波向角的计算方法；然后介绍大范围水域波浪折射绕射传播变形缓坡方程的抛物型近似法以及波向角的计算；最后，利用抛物型缓坡方程和椭圆型缓坡方程法分别对Berkhoff实验室地形条件下波浪场进行计算，比较两种方法计算得到的波向线图。比较结果显示抛物型缓坡方程法计算波向角结果与椭圆型缓坡方程法计算结果是一致的，抛物型近似法计算波向角是可行的。     

计算域中存在直立岛式结构物时波浪传播的数值模拟

针对计算域中存在直立岛式结构物的复连通区域，提出了岛体边界条件，利用缓坡方程建立了在计算域中存在直立岛式结构物时波浪传播的数值模拟模型。模型适用于变水深水域问题，克服了解析解只能适用于等水深水域的不足。直立圆柱和无穷小厚度岛式防波堤周围波浪传播的数值算例表明，数值解与解析解吻合良好，说明所建立的数值模拟模型能有效地模拟复连通区域内的波浪传播。矩形固定式防波堤周围波浪场的数值模拟说明该模型对工程实际有较强的适应性。     

波浪在双滩地形上的传播

使用抛物型缓坡方程和修改抛物型缓坡方程研究了双圆形浅滩地形的波浪折射绕射。并与单圆形浅滩的波浪折射绕射进行了比较，进而对多圆形浅滩进行数值模拟，从中模拟了陷波现象。     

基于抛物型缓坡方程模拟近岸波流场

波浪向近岸传播的过程中由波浪破碎等效应所形成的近岸波流场是近岸缓坡区域重要的环境动力因素之一。本文基于近岸波浪传播的缓坡模型对近岸波浪场及近岸波浪斜向入射破碎后所产生的沿岸波流场进行了数值模拟。考虑到波浪向近岸传播中局部复杂区域波向不易确定，计算时直接从波浪辐射应力定义出发，采用抛物型缓坡方程所给出的辐射应力公式来计算波浪产生的辐射应力，在此基础上耦合近岸波流场数学模型对近岸波浪破碎形成的波流场进行了数值模拟研究，结果表明本文的数值模型是有效的。     

一种扩展型缓坡方程的时域计算模式

该文通过引入有效波面函数,把考虑海底摩擦、波浪破碎、陡变和快变地形等因素影响的扩展型缓坡方程,化为最简形式的时间双曲型缓坡方程.基于此方程和非线性振幅频散关系,建立了波浪传播的数值模拟模型,并对数值格式进行了误差分析,结果表明由于耗散项的引入,数值格式的稳定性较文献[1]得到了提高.数值解与物理模型实验值和解析解吻合良好,表明模型可以对近岸波浪传播过程中折射、绕射、反射、浅水变形、海底摩擦、波浪破碎和弱非线性等因素的影响进行较好地预测.     

不规则波抛物型缓底坡波动方程

使用Kubo近似，导出了不规则波抛物型缓底坡波动方程的折射绕射联合模型。对不规则波抛物型缓底坡波动方程进行数值模拟，并对结与实验进行比较。不规则波抛物型缓底坡波动方程能很好地描述波浪传播过程中的变化，由此，可以预测波浪在传播过程中受到地形及波浪间相互用作而发生的变化。     

波—流在摩阻地形上的综合传播

本文采用波浪缓坡方程抛物型近似方法，研究了缓变地形上波－流共存情况下的传播问题。文章首先提出了包含摩阻项在内的抛物型控制方程，然后结合波－流作用守恒方程和文献（８）的成果，给出了波能衰减率的简便形式。算例表明，本文提出的计算方法可用于大型水域实际工程设计中波浪要素的计算。     

近岸波浪及沿岸流数值模拟研究

利用抛物型缓坡方程计算波浪场,并以波浪辐射应力为近岸动力因素,建立深度平均的二维近岸流的控制方程。运用该近岸流方程,对美国Santa Barbara Leadbetter海岸波浪斜向入射所产生的波浪场及波浪破碎所形成的沿岸流进了数值模拟,其中抛物型缓坡模型采用Crank-Nicolson格式进行数值离散,近岸流方程采用ADI差分格式离散。与现场实测资料的对比表明,无论考虑或不考虑波浪非线性因子,模拟结果与实测结果均吻合良好。     

新抛物型缓底坡波动方程

应用变分原理导出修改抛物型缓底坡方程和扩展抛物型缓底坡方程。通过数值模拟方法数值求解具体地形上的波浪折射绕射，同Kirby抛物型缓坡方程的线性方程和非线性方程进行比较。结果表明新的抛物型缓底坡方程具有适用性。提供了一种模拟波浪折射绕射的新方法     

直立岛式结构物周围波浪传播的数值模拟

针对计算域中存在直立岛式结构物的复连通区域,基于时间关联型缓坡方程和相应的边界条件,建立了在计算域中存在直立岛式结构物时波浪传播的数值模拟模型.该模型不仅适用于变水深问题,而且适用于模拟线性波浪的时间和空间演化过程.对直立岛式防波堤及直立方柱周围波浪传播变形的数值模拟表明,所建立的模型能够有效地模拟计算域内存在直立岛式结构物的波浪绕射和反射问题.     

缓坡方程的有限分析数值模式

基于时间关联的双曲型缓坡方程,采用九点有限分析法,建立近岸波浪传播变形的数值模式,在对时间关联的双曲型缓坡方程数值离散时,空间导数采用九点有限分析法,时间导数仍采用有限差分法,再采用质量集中方法得到本文的数值模式。为了验证本模式的数值精度和有效性,分别对Berkhoff(1972)实验和突堤地形进行数值模拟,结果表明本模式的模拟值与物理模型试验值、解析解及有限差分模式的模拟值吻合良好,表明本模式可以对近岸波浪传播过程中折射、绕射、反射、浅水变形、波浪破碎和弱非线性等因素的影响进行较好的预测。     

非线性抛物型缓坡方程的数值模拟

参考Lo对MNLS方程中非线性项的处理方法,但不转换到频域求解,同时采用Li修正的非线性弥散关系,对非线性抛物型缓坡方程在复数域进行数值模拟,并分别在Berkhoff椭圆地形及淹没圆形浅滩地形验证了该模型,得到了较好的结果。此模型可以有效地模拟非线性波浪问题。此非线性项的处理方法使得数值计算过程中不需迭代求解,同时减少了边界周期性的限制,易于操作编程,提高了计算效率。     

Modeling of random wave transformation with strong wave-induced coastal currents

The propagation and transformation of multi-directional and uni-directional random waves over a coast with complicated bathymetric and geometric features are studied experimentally and numerically. Laboratory investigation indicates that wave energy convergence and divergence cause strong coastal currents to develop and inversely modify the wave fields. A coastal spectral wave model, based on the wave action balance equation with diffraction effect （WABED）, is used to simulate the transformation of random waves over the complicated bathymetry. The diffraction effect in the wave model is derived from a parabolic approximation of wave theory, and the mean energy dissipation rate per unit horizontal area due to wave breaking is parameterized by the bore-based formulation with a breaker index of 0.73. The numerically simulated wave field without considering coastal currents is different from that of experiments, whereas model results considering currents clearly reproduce the intensification of wave height in front of concave shorelines.     

NUMERICAL SIMULATION OF PROPAGATION AND BREAKING PROCESSES OF A FOCUSED WAVES GROUP

A two-dimensional numerical wave flume is developed to study the focused waves group propagation and the consequent breaking processes. The numerical model is based on the Reynolds-Averaged Navier-Stokes (RANS) equations, with the standard k-ε turbulence model to simulate the turbulence effects. To track the complicated and broken free-surface, the Volume Of Fluid (VOF) method is employed. The numerical model combines the "Partial Cell Treatment (PCT)" method with the "Locally Relative Stationary (LRS)" concept to treat the moving wave paddle so that various waves can be generated directly in a fixed Cartesian grid system. The theoretical results of the linear and nonlinear waves are used to validate the numerical wave flume firstly, and then a plunging breaking wave created by a focused waves group is simulated. The numerical results are compared to the experimental data and other simulation results, with very good agreements. The turbulence intensity, the flow field and the energy dissipation in the breaking processes are analyzed based on the numerical results. It is shown that the present numerical model is efficient and accurate for studying the waves group generation, the waves packet propagation, and the wave breaking processes.     

基于SWASH模型的近岸波浪传播变形数值模拟

SWASH模型是一种新型的非静压时域波浪模拟。为了探讨SWASH模型对于解决近岸波浪传播变形问题的适用性,在对其控制方程、边界条件、数值解法等进行介绍的基础上,采用该模型分别模拟了正向规则波、斜向规则波和斜向不规则波入射条件下L形防波堤附近水域的波浪场和波生流场,并与物理试验结果进行对比。结果表明,SWASH模型较好地复演了波浪在近岸区域所发生的浅水变形、折射、破碎,以及堤前反射、堤内绕射等物理现象,波高沿断面的定量分布与试验结果吻合良好,同时较好地模拟了不同波况下防波堤附近水域的波生流场,说明该模型适用于复杂岸线和地形条件下波浪传播变形的数值模拟。     

WATER WAVE SIMULATION IN CURVILINEAR COORDINATES USING A TIME-DEPENDENT MILD SLOPE EQUATION

The purpose of this article is to model the detailed progress of wave propagation in curvilinear coordinates with an effective time-dependent mild slope equation. This was achieved in the following approach, firstly deriving the numerical model of the equation, i.e., Copeland's hyperbolic mild-slope equation, in orthogonal curvilinear coordinates based on principal of coordinate transformation, and then finding the numerical solution of the transformed model by use of the Alternative Directions Implicit (ADI) method with a space-staggered grid. To test the curvilinear model, two cases of a channel with varying cross section and a semi-circular channel were studied with corresponding analytical solutions. The model was further investigated through a numerical simulation in Ponce de Leon Inlet, USA. Good agreement is reached and therefore, the use of the present model is valid to calculate the progress of wave propagation in areas with curved shorelines, nearshore breakwaters and other complicated geometries.     

Numerical solutions for two nonlinear wave equations

The split-step pseudo-spectral method is a useful method for solving nonlinear wave equations. However, it is not widely used because of the limitation of the periodic boundary condition. In this paper, the method is modified at its second step by avoiding transforming the wave height function into a frequency domain function. Thus, the periodic boundary condition is not required, and the new method is easy to implement. In order to validate its performance, the proposed method was used to solve the nonlinear parabolic mild-slope equation and the spatial modified nonlinear Schr dinger (MNLS) equation, which were used to model the wave propagation under different bathymetric conditions. Good agreement between the numerical and experimental results shows that the present method is effective and efficient in solving nonlinear wave equations.