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均匀剪切流场中的强非线性波及其色散关系
杨联贵1, 杨红丽2,3, 宋金宝2, 侯一筠2
1.内蒙古大学数学科学学院;2.中国科学院海洋研究所;3.中国科学院研究生院
摘要:
考虑了剪切流场中强非线性波,唯一的假设是水深与特征波长之比是小量,建立了基于任意水深处速度而不是通常所用的平均速度为速度变量的模型。不仅改进了色散关系,使模型的水深适用范围更大,而且由于整个推导过程对波的振幅没有做任何假设,因而所获得的模型可以用于任何振幅的波。
关键词:  剪切流  强非线性  色散关系
DOI：
分类号:
基金项目:中国科学院创新项目( KZCX2-YW-201) ;教育部留学回国人员科研启动基金和内蒙古自然科学基金资助项目
Strongly nonlinear long waves with uniform shear flows and their dispersion relationship
Abstract:
Long surface waves of finite amplitude with uniform shear flows are considered under the only assumption that the aspectratio between wavelength and water depth is small. A new model is derived using the velocity at an arbitrary distance from the still water level as the velocity variable instead of the commonly used depth-averaged velocity. This significantly improves the dispersion properties, making them applicable to a wider range of water depths. Since its derivation requires no assumption on wave amplitude, the model we got here can be used to describe arbitrary amplitude waves.
Key words:  uniform shear flows  strongly nonlinear  dispersion relation
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