【作者】 孙健；

【导师】 陶建华；

【作者基本信息】 天津大学 ， 流体力学， 2004， 硕士

【摘要】 本文讨论了二阶 Stokes 非线性波浪作用下流体微团的平动和变形对污染物输移及混合扩散的影响，推导了相关公式，得出了波浪场作用下污染物输移及混合扩散的基本规律，为进一步研究波浪场中的纵向离散系数提供了一定的理论依据。建立了基于有限元方法（FEM）的对流扩散数学模型，对理论推导的结果进行了验证。研究结果表明：在非线性波浪场中，污染物的混合扩散除了受漂移速度影响外，具有明显各向异性的特征。本文在高阶抛物缓坡方程的基础上，综合考虑了波浪长距离传播的底摩阻问题和风的影响，还考虑了近岸区波浪多次破碎问题以及弱非线性项对计算结果的影响，以扩大抛物缓坡方程在解决实际工程问题中的适用范围。此模型适用于没有建筑物的自然地形条件下的大面积波浪场的折、绕射推算。本文建立了一个基于普通贴体正交网格系统的抛物型缓坡方程模型，并给出了其在保角坐标系下的特殊形式，利用该模型研究了扩张防波堤和环形渠道内波浪的传播这两个典型算例。对每一个算例，首先采用解析的方法构造了普通正交网格系统和正交保角网格系统进行计算。计算结果表明，对相同的算例，在正交保角网格系统下得到的结果明显优于普通正交网格下得到的结果。为增强模型的实用性，本文将所建立的模型与一种保角网格系统的数值生成方法结合起来，并在数值网格系统上对上面的两个算例进行了重新计算。计算结果表明，将该数值网格生成技术形成的网格系统与本文所建立的缓坡方程模型相结合，能得到可靠的计算结果。用抛物缓坡方程模型进行了工程实例计算。模拟了东海大桥工程区域的波高分布，从而得到建筑物设计波高。更多还原

【Abstract】 In this paper the transport and diffusion of contaminants in nonlinear Stokeswater wave due to shift and rotation of the micro fluid mass is discussed, and somecharacters of the transport and diffusion of contaminants in wave field have beenobtained. A numerical transport-diffuse model based on Finite Element Method (FEM)is established to verify the theoretical results, and good agreements are obtained. Theresults show that in wave filed the transport and diffusion of contaminants isanisotropic, apart from being effected by drift velocity. Based on the extended parabolic mild-slope equation, the bottom friction andwind effect on the wave propagating through long distance are considered. Thisnumerical method can calculate the wave field after wave breaking more than once.The equation includes the weak nonlinear term and high order differential term thatcan forecast wave height distribution more accurately. In this numerical model, theapplication of the parabolic mild-slope equation is expanded in solving the practicalengineering problem. This refined model is suitable for calculating the waverefraction and diffraction in large water area without structures. In this paper a numerical model for simulating propagation and transform ofwater waves in coastal area is set up by using parabolic mild-slope equation inorthogonal coordinates, and the particular format of this equation in conformal systemis also set up. Two typical examples namely expanded breakwaters and circularchannel are studied to validate the model. At first the examples were studied by usingthe common orthogonal coordinates. Then the same examples were computed byusing the conformal system. The computational results show that much better resultcan be obtained by using the conformal coordinates than that by using the commonorthogonal system. A numerical technique for generating conformal grid is combinedwith the numerical model to improve the practicability of the model. And thiscombination has a good result. The applications of model of parabolic mild-slope equation in practicalengineering projects are carried out. The model is used in the Project of the DonghaiBridge to calculate the wave distribution in the project area.更多还原