两层流体界面内波的色散和非线性特征研究

IOCAS-IR > 海洋环流与波动重点实验室

	两层流体界面内波的色散和非线性特征研究
其他题名	Study on Characteristics of Dispersion and Nonlinearity for Interfacial Waves in Two layer Fluid
	杨红丽
学位类型	博士
	2008-06-10
学位授予单位	中国科学院海洋研究所
学位授予地点	海洋研究所
关键词	界面内波色散性非线性高阶boussinesq方程改进的方程
摘要	色散和非线性是两层流体界面内波的两个重要特性，对其的研究，不仅有助于揭示两层流体界面内波的生成、演化、衰减、消亡机理，而且对水底及沿岸工程具有现实的指导意义。通过引入描述非线性和色散的两个小参数，考虑了无旋、无粘、不可压两层流体的界面内波。首先，分别用未扰动面速度、任意水深处速度和平均速度推导出两层流体界面波的高阶Boussinesq方程，所得到的方程不仅包括了前人关于两层流体界面波的结果，而且可以退化到表面波的许多情况。随后，分析了用任意水深处速度表示的方程的色散性、非线性特征和浅化因子。结果表明，通过选择适当的和位置有关的无量纲参数，尽管刻画色散性小参数量阶保留到低阶，所获得的结果足可与原始方程的色散性、非线性特征和浅化系数保持很好的吻合。接着，对用平均速度表示的方程和用任意水深处速度表示的方程进行了改进，改进后方程的色散性有了很大的提高。最后建立了包括均匀流、均匀剪切流和泊肃叶流等背景流下的界面波运动的高阶Boussinesq方程，求得了均匀流和剪切流情况下方程的二阶Stokes解，揭示了波流之间和界面波之间的非线性相互作用特性。
其他摘要	Dispersion and nonlinearity are two important characteristics of the interfacial waves in two layer fluid, and the research on them not only helps to uncover the mechanisms of their formation, evolvement and attenuation, but also can guide the ocean and coastal engineering in reality. By introducing the two small parameters, nonlinearity and dispersion, we consider the interfacial waves propagating along the interface between a two fluid system, and the fluid in each layer is homogeneous, irrotational, inviscid and incompressible. First, we derive the higher-order Boussinesq equations for the interfacial waves in terms of the velocities at the still water level, the velocities at arbitrary locations and the depth-averaged velocities, respectively. The derived equations not only include the results before for the interfacial waves in a two fluid system, but also can be reduced to the many cases for the surface waves. Then, we analyze the characteristics of dispersion, nonlinearity and shoaling coefficients of the equations in terms of the velocities at arbitrary locations, the results demonstrate that they can fit well with the dispersion, nonlinearity and shoaling coefficients of the original equations when we choose the suitable nondimensional parameters and keep up to lower order. Subsequently, we improve the equations in terms of the depth averaged velocities and the velocities at arbitrary locations, the dispersion relations of the improved equations are much better. Finally we consider the higher order Boussinesq equations with background flows including uniform basic flows, uniform shear flows and Poiseuille flows, and present the second order asymptotic solutions of the velocities and the second-order Stokes solutions of the associated elevations of the interfacial waves in the cases of uniform basic flows and uniform shear flows as well, which reveal the nonlinear interactions between waves and flows and among the interfacial waves.
页数	114
语种	中文
文献类型	学位论文
条目标识符	http://ir.qdio.ac.cn/handle/337002/731
专题	海洋环流与波动重点实验室
推荐引用方式 GB/T 7714	杨红丽. 两层流体界面内波的色散和非线性特征研究[D]. 海洋研究所. 中国科学院海洋研究所,2008.

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