椭圆余弦波爬坡与反射的解析研究

本文应用渐近匹配法对椭圆余弦波在中等陡度的岸坡上的爬高和反射进行了解析研究。给出了反射过程中内、外场波形及速度变化的解析表达,得到了坡面上水波最大和最小爬高的规律及它们出现的时间,并进而探讨了坡陡的影响。当波长无限增大时,该解析解收敛于孤立波的情况。这些新的解析结果不仅有助于揭示岸坡对非线性浅水波影响的力学机理,在海岸防护和开发等工程领域中也具有现实的指导意义。     

两层模式下内波K-dv方程的频散关系

为了更好地了解内孤立波的特性,分别利用椭圆余弦波方法和摄动展开方法,对两层模型下内孤立波K-dv方程的频散关系进行了推导。结果显示：利用后一种方法得到的两层模式下内孤立波K-dv方程的频散关系是一种方便、实用的解析式。据此解析式可进一步得到内孤立波半波宽度与内波波数间的关系,从而可将内孤立波理论与内波合成孔径雷达（SAR）图像联系起来。用此解析式计算得到的内孤立波频率和相速度与实测结果具有很好的一致性,因而为进一步进行分析和利用数据估计内孤立波的部分参数提供了理论依据。对解析式中频散项和非线性项量级的进一步分析认为,非线性项的作用在从SAR图像中提取内波振幅等参数时最好不予忽略。     

关于非线性浅水波理论中的孤立波解

本文在[1]的基础上,详尽地得到了Boussinesq方程和KdV方程的孤立波解,并对波高和波形进行了细致的分析。为了更好地比较,本文还给出了高阶摄动的孤立波解。     

二维孤立波的透射与反射

本文应用渐近匹配方法探讨了孤立波遇到二维柱体时的透射与反射问题。远场解由Boussinesq方程制约,用差分方法数值地求解;内场解则从Laplace方程着手,对矩形柱体,分区域按本征函数的展开来表示;内外解经过匹配迭代求解。作为算例,给出了透射和反射的波形以及作用力和力矩随时间变化的曲线。     

Boussinesq方程的永形波的级数解

对于用层平均速度势(或速度)与波高给出的非线性等水深Boussinesq方程,与KdV方程一样,存在两类永形波—孤立波和周期波。不同的是,对于Boussinesq方程,孤立波和周期波一样,是以反函数的积分形式给出的,这在使用上是不方便的。本文对这两类波,分别给出了相应的级数形式的正函数解。对于孤立波,级数的收敛速度是十分快的,且文中还给出了一个具有高精度的十分简单的近似解,对于周期波,只要有关参数选得合适,解的收敛速度也是相当快的。这就有效地克服了反函数形式解在使用上的不方便。     

椭圆余弦波对透空直立防波堤波浪力解析计算

根据椭圆余弦波理论与水波绕射理论,应用特征函数展开法,推导了浅水区水波对透空防波堤的波浪作用,并取得了满足椭圆余弦波一阶分量边值问题提法的反射和透射波势的数学解。由此得出作用于直立透空防波堤的水平波浪力和力矩算式,并与浅水条件下的Airy波理论加以比较,说明浅水条件下椭圆余弦波理论更能反映非线性因素变化对波浪力及力矩的影响。     

关于振荡型的界面孤立波

当计及表面张力时,对于二流体系统中两层流体深度比的一种临界情形,界面孤立波可用推广的KdV方程来描述,这一方程难以解析地求出孤立波解。本文采用作者提出的推广的PLK方法求得了三阶近似孤立波解,并采用Lindstedt-Poincare方法对所得的结果作了验证,从而首次解析地证实了振荡型界面孤立波的存在性。     

浅水波与圆弧型贯底式防波堤的相互作用

该文基于椭圆余弦波绕射理论,应用特征函数展开法,推导了浅水波对圆弧型贯底式多孔介质防波堤绕射的波势解,并据此解析计算了作用于防波堤的水平波浪载荷与浅水波波面分布。计算结果表明:浅水波入射角与非线性影响参数、海况条件以及防波堤几何条件等因素的相对变化对波浪作用均存在一定的影响,结构透空可以明显减弱防波堤所受波浪作用。与微幅波理论对比可知:在一定浅水条件下采用椭圆余弦波一阶分量模型所计算的最大无量纲波浪力、力矩和波面分布值均明显高于微幅波理论的对应估值,反映了水波非线性因素的影响效应。     

有限深两层流体中内孤立波传播演化理论模型研究

该文对Choi和Camassa给出的一个内孤立波方程模型中的系数进行了修正,并给出了基于方程的内孤立波定态解表达式,将其称为内孤立波me Kd V理论解,进而采用有限体积/有限差分混合方法数值求解内孤立波的三类(Kd V、e Kd V和me Kd V型)非线性传播演化方程,分别以内孤立波的Kd V、e Kd V、MCC和me Kd V定态解作为初始输入波,研究其非线性传播演化特性,并获得其适用性条件。结果表明,三类非线性传播演化方程,只适合于相应内孤立波定态解初始波的定态传播,而对其他定态解初始波将发生波形变形、分裂等非线性现象。在此基础上,定量地给出了三类非线性传播演化方程的适用性条件,为采用何种非线性方程来研究实际海洋中内孤立波的传播演化问题提供了理论依据。     

VOF方法模拟波浪槽中二维非线性波

造波板运动生成非线性波问题是研究物体与波浪非线性相互作用的典型例子。本文研究了用ＶＯＦ方法模拟波浪水槽生成非线性波（孤立波和椭圆余弦波）的问题，为实现造波板在计算中可以做穿越网格的大幅值运动，本文采用在压力迭代中调整造波板邻近单元中压力来满足造波板上流体运动条件。对开路边界条件和自由表面与物面交点处边界条件也提出了处理方法，计算结果与实验结果和解析结果进行了对比。     

NUMERICAL MODELING OF WAVE EVOLUTION AND RUNUP IN SHALLOW WATER

Based on the Navier-Stokes (N-S) equations for viscous, incompressible fluid and the VOF method, 2-D and 3-D Numerical Wave Tanks (NWT) for nonlinear shallow water waves are built. The dynamic mesh technique is applied, which can save computational resources dramatically for the simulation of solitary wave propagating at a constant depth. Higher order approximation for cnoidal wave is employed to generate high quality waves. Shoaling and breaking of solitary waves over different slopes are simulated and analyzed systematically. Wave runup on structures is also investigated. The results agree very well with experimental data or analytical solutions.     

Numerical study of edge waves using extended Boussinesq equations

An edge wave numerical model was developed based on extended Boussinesq equations with the internal wave-generation method. The form of edge waves near a seawall was chosen as the input signal in order to avoid treatment of the moving shoreline on a sloping beach. As there was an energy transfer between different edge wave modes, not only the target mode but also other modes appeared in the simulations. Due to the nonlinear effect, the simulation results for mode-0 edge waves were slightly modulated by mode-1 and mode-2 waves. As the magnitudes of these higher-mode waves are not significantly related to those of the target mode, the internal wave-generation method in Boussinesq equations can produce high-quality edge waves. The numerical model was used to investigate the nonlinear properties of standing edge waves, and the numerical results were in strong agreement with theory.     

TESTS AND APPLICATIONS OF A BOUSSINESQ MODEL WITH AMBIENT CURRENT

A new type Boussinesq model is proposed and applied for wave propagation in a wave flume of uniform depth and over a submerged bar with current present or absent, respectively. Firstly, for the propagation of monochromatic incident wave with current absent, the Boussinesq model is tested in its complete form, and in a form without the introduction of utility velocity variables. It is validated that the introduction of utility velocity variables can improve the characteristics of velocity field, dispersion and nonlinearity. Both versions of the Boussinesq models are of higher accuracy than the fully-nonlinear fourth-order model, which is one of the best forms among the existing traditional Boussinesq models that do not incorporate breaking mechanism in one dimension. Secondly, the Boussinesq model in its complete form is applied to simulating the propagation of bichromatic incident waves with current present or absent, respectively, and the modeled results are compared to the analytical ones or the experimental ones. The modeled results are reasonable in the case of inputting bichromatic incident waves with the strong opposing current present.     

A THIRD-ORDER BOUSSINESQ MODEL APPLIED TO NONLINEAR EVOLUTION OF SHALLOW-WATER WAVES

1.　INTRODUCTIONIncoastalandoceanengineering,thepredictionofwaverun-upwithadesirableaccuracyisoftenofparamountinterest.Previously,thesecond-orderBoussinesqmodel,whichassumesthatnonlinearanddispersiveeffectsarebothweakandofthesameorderofmagnitude,hasbeenextensivelyusedtostudytheevolutionofwavesinshallowwater(Peregrine,1967;MeiandUnliiata,1972etc.).Recently,theconventionalBoussinesqmodelhasalsobeenextendedtomodelwavesoveranintermediateorevenlargedepth,withinthescopeofasecond-ordertheory(wi…     

BOUSSINESQ MODELLING OF NEARSHORE WAVES UNDER BODY FITTED COORDINATE

A set of nonlinear Boussinesq equations with fully nonlinearity property is solved numerically in generalized coordinates,to develop a Boussinesq-type wave model in dealing with irregular computation boundaries in complex nearshore regions and to facilitate the grid refinements in simulations.The governing equations expressed in contravariant components of velocity vectors under curvilinear coordinates are derived and a high order finite difference scheme on a staggered grid is employed for the numerical implementation.The developed model is used to simulate nearshore wave propagations under curvilinear coordinates,the numerical results are compared against analytical or experimental data with a good agreement.     

NUMERICAL STUDY OF SOLITARY WAVE FISSION OVER AN UNDERWATER STEP

Solitary wave fission over an underwater step is numerically investigated. The numerical model is based on the enhanced Boussinesq equations, which appropriately represent both the nonlinearity and dispersivity of surface water waves. The finite difference method defined on the staggered grid in space with an implicit scheme for time stepping is employed for the numerical solution of the governing equations. It is demonstrated that Boussinesq type equations, though they are vertically integrated, can describe the details of the solitary wave fission process with very good accuracy. Numerical results of the reflected and transmitting wave heights, the number of solitons emitted from the transmitting wave and their amplitudes all agree very well with the analytical solution derived from KdV equation by virtue of a linear long wave approximation in the vicinity of the underwater step.     

分层流体中的椭圆余弦波

本文采用Friedrichs展开法导出了椭圆余弦波在分层流体中传播问题的解答,精度为σ的一次方。所得的结果表明:同分层流体中线性波传播一样,分层流体中的椭圆余弦波存在着两种可能的模态—快模态和慢模态,流体波动的水平流速与z无关,垂直流速为零,压力服从静压分布规律。另外,由本文结果还可求得两种极限情形—微幅波和孤立波在分层流体中传播的解答。     

数值计算域内产生波浪的方法

解决入射边界域内反射波浪吸收问题的方法之一是在域内产生所需的波浪，而在边界处采用其它方法来吸收域内反射波浪，本文采用源函数的方法。给出了Bossinesq方程计算域内产生波浪的方法，典型波浪的数值模拟计算结果表明，该方法可以在域内生产所期望的波浪。     

EVOLUTION EQUATIONS FOR NONLINEAR WAVES IN A THREELAYER FLUID MODEL

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