均匀剪切流场中的强非线性波及其色散关系

Strongly nonlinear long waves with uniform shear flows and their dispersion relationship

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。

Long surface waves of finite amplitude with uniform shear flows are considered under the only assumption that the aspect ratio 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.