近岸波浪传播变形数学模型的研究与进展

对近岸波浪传播变形的各种数学模型进行了归纳评述和总结,以期对本研究方向的发展起到一定的引导和促进作用。     

考虑波能耗散的近岸波浪传播数学模型

基于考虑能耗的定常缓坡方程，推导得出包含波能耗散的近岸水域波浪传播变形数学模型，并用所得模型对浅水中波浪的传播进行了计算，将计算结构与Berkhoff的实验数据进行比较，表明二者吻合很好。该数学模型能较好地解决波浪在浅水中的传播变形问题。     

Boussinesq方程波浪数学模型的应用

介绍了Ｂｏｕｓｓｉｎｅｓｑ 方程的推导过程和发展过程,基于深水和缓变地形的色散关系,建立了Ｂｏｕｓｓｉｎｅｓｑ方程的波浪数学模型。该模型可以产生波浪,模拟吸收边界和不同反射率的反射边界。该模型可用于研究深水和浅水地区波浪的浅水变形、折射、绕射和反射     

波浪变形的数学模型

本文给出一个在复杂水深地形条件下计算包括折射和绕射效应的线性波浪变形数学模型。该模型用差分方法进行求解,并应用于兴化湾江阴岛码头及航道的波浪要素计算,所得结果与其他方法的结果进行比较。通过实际应用说明它是计算开阔海域波浪变形的有力工具。     

考虑非线性弥散影响的波浪变形数学模型

提出了逼近Kirby和Dalrymple的非线性弥散关系的显式非线性弥散关系的表达式,该显式表达式与他们的非线性弥散关系的精度几乎完全相同.采用显式非线性弥散关系,结合含弱非线性效应的缓坡方程,得到考虑非线性弥散影响的波浪变形数学模型,并对该数学模型进行了数值验证.结果表明,考虑非线性弥散影响的波浪变形数学模型更为精确.     

关于波浪缓坡方程的研究

缓坡方程（ｍｉｌｄ－ｓｌｏｐｅ ｅｑｕａｔｉｏｎ）是基于线性波浪理论研究波浪在近岸传播变形（折射绕射）的基础和被广泛应用的方程。从缓坡方程问世到现在,人们对它进行了大量的理论和应用研究,包括求解该方法、简化近似和改进。本文对有关波浪缓坡方程的研究成果进行了较为系统的归纳总结和评述,以期对本学科的发展起到一定的引导和促进作用。     

基于改进缓坡方程的波浪传播数值模拟

用变分原理导出考虑底坡一阶导数平方项和二阶曲率项影响的缓坡方程,对传统缓坡方程作了改进,提高波浪在海底地形变化剧烈、水深较浅时数值模拟精度。数值计算与已有实验室试验资料比较表明,该模型可以较好地模拟有剧烈变化的海底地形的波浪传播,比传统缓坡方程模型计算结果在精度上有明显提高。     

波浪谱形对不规则波数值模拟的影响

通过数值模拟分析了波浪谱形对不规则波浪数值模拟结果的影响.采用不同参数的JONSWAP谱模拟入射波要素,基于抛物型缓坡方程模拟不规则波浪的传播,分析了波浪谱形状对波浪数值模拟结果的影响.结果表明,采用抛物型缓坡方程模拟不规则波浪时,入射波浪谱形对模拟结果影响不明显;但由于模型中非线性项的影响,采用不规则波模拟的波高分布和采用规则波模拟的结果略有差别.     

Boussinesq方程与抛物型缓坡方程2种波浪模型的比较分析

波浪破碎的模拟对于波浪模拟的准确性十分重要。为了解波浪破碎模型的问题,本文对抛物型缓坡方程和Boussinesq方程这2种波浪模型所采用的破碎方法进行比较和分析。运用基于Boussinesq方程的Funwave模型和基于抛物型缓坡方程的REF/DIF模型,分别对特拉华大学的未破碎圆形浅滩试验和作者于实验水槽进行的Undertow试验这2个物理模型进行波高模拟、比较与分析。模拟结果表明:Funwave和REF/DIF这2种波浪模型都能准确的模拟出波高随水深的变化情况,但对于波浪破碎后的情况,REF/DIF模型模拟的更为精确一些。     

近岸波浪破碎区不规则波浪的数值模拟

基于近岸不规则波浪传播的抛物型缓坡方程和两类波浪破碎能量损耗因子,对近岸波浪破碎区不规则波浪的波高分布进行了数值模拟,并结合实验结果对数值模拟结果进行了验证分析,结果表明采用两类波浪破碎能量损耗因子所模拟的破碎区波高与实测值均吻合良好,波浪破碎能量损耗因子及波浪破碎指标对破碎区波浪波高分布影响较明显。     

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.     

Verification of A Numerical Harbour Wave Model

A numerical model for wave propagation in a harbour is verified by use of physical models.The extended time-dependent mild slope equation is employed as the governing equation,and the model is solved by use of ADI method containing the relaxation factor.Firstly,the reflection coefficient of waves in front of rubble-mound breakwaters under oblique incident waves is determined through physical model tests,and it is regarded as the basis for simulating partial reflection boundaries of the numerical model.Then model tests on refraction,diffraction and reflection of waves in a harbour are performed to measure wave height distribution.Comparative results between physical and numerical model tests show that the present numerical model can satisfactorily simulate the propagation of regular and irregular waves in a harbour with complex topography and boundary conditions.     

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。     

Improvement on open boundaries on a time dependent numerical model of wave propagation in the nearshore region

An improvement on the simulation of outgoing waves on a time dependent numerical model for water wave propagation in the nearshore region is presented. The governing equations consist of a system of first order partial differential equations (PDEs), the equation of continuity and the equation of motion. A comparative study of first order radiation boundary conditions (BCs) and first order radiation BCs combined with sponge layers is presented for cases where outgoing waves leave the numerical domain of calculation through the open boundary. A reduction of spurious reflections from the numerical open boundaries can be obtained with an irrelevant increase in terms of computational cost.     

Applications of sediment sudden deposition model based on the third-generation numerical model for shallow water wave

The existing numerical models for nearshore waves are briefly introduced, and the third-generation numerical model for shallow water wave, which makes use of the most advanced productions of wave research and has been adapted well to be used in the environment of seacoast, lake and estuary area, is particularly discussed. The applied model realizes the significant wave height distribution at different wind directions. To integrate the model into the coastal area sediment, sudden deposition mechanism, the distribution of average silt content and the change of sediment sudden deposition thickness over time in the nearshore area are simulated. The academic productions can give some theoretical guidance to the applications of sediment sudden deposition mechanism for stormy waves in the coastal area. And the advancing directions of sediment sudden deposition model are prospected.     

基于弱非线性RIDE模型的植物消浪数值模拟研究

通过基于考虑波浪非线性频散关系的椭圆型缓坡方程数学模型(RIDE),在原高阶的控制方程中添加植物阻力项,建立了模拟植物区波浪传播的数学模型(RIDE-VEG)。将计算结果与规则波在植物场中变形的水槽试验数据进行比较,验证良好,并分析了植物区特征参数对于波浪传播的影响。针对相对淹没度、植物密度和波浪周期等因素对波高衰减的影响进行敏感性分析,结果表明其三者对于消浪效果的影响是单调的,但消浪效果对于波浪周期的敏感程度则较其余二者为弱。与其他学者的研究相比,忽略流场效应的RIDE-VEG模型较其它的模型计算更为简便,且计算结果较为满意。     

基于双层Boussinesq方程的三维波浪数值模型及其验证

Liu等给出的最高导数为2的双层Boussinesq水波方程具有较好的色散性和非线性,基于该方程建立了有限差分法的三维波浪数值模型。在矩形网格上对方程进行了空间离散,采用高阶导数近似方程中的时、空项,时间积分采用混合4阶Adams-Bashforth-Moulton的预报—校正格式。模拟了深水条件下的规则波传播过程,计算波面与解析结果吻合较好,反映出数值模型能很好地刻画波面过程及波面处的速度变化;在kh=2π条件下可较为准确获得沿水深分布的水平和垂向速度,这与理论分析结果一致。最后,利用数值模型计算了规则波在三维特征地形上的传播变形,数值结果和试验数据吻合较好;高阶非线性项会对波浪数值结果产生一定的影响,当波浪非线性增强,水深减少将产生更多的高次谐波。建立的双层Boussinesq模型对强非线性波浪的演化具有较好的模拟精度。     

波浪非线性弥散关系及其应用

针对Hedges及Kirby等对Kirby和Dahymple的非线性弥散关系的修正关系,在小波陡时中等水深范围存在较大偏差的问题,给出了一个新的非线性弥散关系。比较可知,新的关系在小波陡时减小了中等水深范围内50％的误差,而在大波陡时能够保持其单调性,且形式上更为简练。将其应用于含弱非线性效应的缓坡方程进行数值验证,结果表明,采用新的非线性弥散关系得到的计算结果与实测结果更为吻合。