【作者】 张扬；

【导师】 李瑞杰；

【作者基本信息】 河海大学 ， 物理海洋学， 2004， 硕士

【摘要】 波浪由深海向海岸传播过程中，由于地形和水工建筑物等因素的影响，将发生浅水变形、折射、绕射、反射、破碎以及能量耗散等波浪变形现象。Boussinesq型方程包含了非线性和色散性，能够模拟近岸浅水中的各种波浪传播变形。但经典Boussinesq方程(Peregrine)只具有弱非线性和弱色散性，限制了其仅适用于浅水区域和弱非线性效应情况。本文在总结概述前人关于Boussinesq方程波浪数学模型研究进展的基础上，主要做了以下几点工作： 从质量守恒方程和Euler方程出发，以某一水层处水平速度矢量作为独立变量，推导出包含底摩擦耗能、波浪破碎效应和子网格湍流效应的改进型Boussinesq方程。改进后的方程同经典Boussinesq方程相比明显改善了方程的色散性能和非线性性能，拓宽了方程的适用范围。 采用改进的窄缝法，假设岸滩上存在“窄缝”的同时，保证了水体的质量守恒，能够更加准确地处理动边界问题。采用“海绵层”技术，可以有效地处理消波边界问题。 推导了正交曲线坐标系下的改进型Boussinesq方程，以Poission方程变换为基础，建立拟合正交曲线坐标系下正交曲线网格的生成方法，进而建立正交曲线坐标系下的二维波浪模型，提高了模型对复杂地形的适用性。 采用四阶精度的ABM预测-校正差分格式，基本满足了高阶Boussinesq方程对数值格式的要求。在数值计算中，采用了数值过滤技术，有效地除去了由于非线性效应的相互作用而产生的极小波长谐波，保证了数值计算的准确性。 用多个实验地形对本文模型进行了验证，计算结果与实测数据吻合很好，反映了本文模型可以较好地模拟波浪传播过程中的浅水变形、折射、绕射和反射等波浪变形现象。 对波浪增减水现象、波浪破碎现象以及波浪破碎引起的环流进行了模拟，数值模拟结果与实测资料验证的结果表明本文模型的计算结果是合理、有效的。 此外，本文还采用线性缓坡方程和在缓坡方程中引入Li(2003)的改进色散关系而建立的非线性模型对Berkhoff经典试验进行了模拟，并对其模拟结果同本文模型进行了对比，结果显示本文模型的具有较高的计算精度。另外还证实了在缓坡方程中引入非线性色散关系可以明显改善缓坡方程模型的计算结果。更多还原

【Abstract】 As surface waves propagate from deep to shallow water, the wave will take series of transformation including shoaling, refraction, diffraction, reflection, breaking and energy dissipation due to the effect of topography and various hydraulic structures. Boussinesq-type equations, which include the effect of the lowest order effects of nonlinear and frequency, has been shown to provide an accurate description of wave transformation in coastal regions. However, owing to the assumptions of weak dispersion and weak nonlinearity, the standard Boussinesq equations derived by Peregrine are restricted to shallow water areas and to small nonlinear. In this paper, based on summarizing previous numerical studies on wave transformations, several works are documented:Based on the mass conservation equation and Euler’s equation, the extended form of Boussinesq equations is derived by using the velocity at an arbitrary water depth as the independent variable, and several terms are added into governing equations to model the effects of bottom friction, wave breaking and subgrid turbulent mixing. Compared with the standard Boussinesq equations (Peregrine), the new alternative form of equation significantly improves the dispersion and nonlinearity properties of equations, making them applicable to a wider range of water depths.The improved slot technique, which maintains mass conservation in the presence of artificial slots, is used to treat the problem of moving shoreline. The improved technique can simulate the wave runup more accurately. The absorbing boundary condition is tackled easily and properly by using sponge layer technique.The expression of the improved Boussinesq equations in curvilinear orthogonal coordinate system is derived. On the basis of Poission equation conversion, the methods to generate curvilinear orthogonal grids are introduced, and then the two-dimensional numerical wave model under curvilinear orthogonal coordinate system is established.A composite 4-th order Adams-Bashforth-Moulton scheme is used to solve the equations. With this higher-order scheme, the accuracy of numerical computation results is well ensured. Furthermore, a numerical filter method is applied to eliminate some undesired short waves generated as the program runs, which prevents the computed results of the numerical model from distortions.The numerical model is tested by computing wave field for several examples of laboratory experiment, and agreement between model results and availableexperimental data is found to be quite reasonable, which demonstrates the model’s ability to simulate wave shoaling, refraction, diffraction and reflection.The model is also applied to study the wave set-up, wave breaking and wave-induced current, and the computed results indicate are well agree with measured data.In addition, numerical simulations of the Berkhoff classical laboratory experiment using linear mild-slop model and nonlinear mild-slop model which is developed by introducing Li’s improved nonlinear dispersion relation (2003) into the mild-slop equation are undertaken, and computed results are used to compare with those of the model established in the paper. Comparison results indicate that the new model can give considerably accurate computed results. Moreover, it is confirmed that more desired results could be obtained by utilizing the Li’s new dispersion relation (2003) instead of the linear form.更多还原