Nonlinear Gravity Waves in a Thin Sheet of Viscous Fluid
Nonlinear Gravity Waves in a Thin Sheet of Viscous Fluid
复制标题
粘性流体薄片中的非线性重力波
DOI：
10.1002/sapm1966451266
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发表时间：
1966
期刊：
影响因子：
--
通讯作者：
C. Mei
中科院分区：
文献类型：
--
作者：
C. Mei
在有限振幅重力长波的研究中，
现有理论的主要部分是建立在简化的假设上的，即粘度要么完全可以忽略不计，要么由一个
经验法则到目前为止，很少出现基于Navier-Stokes运动方程的粘性效应的系统说明。因此在
对于河流中洪水波的重要问题，Chezy公式和各种水力学经验定律已被用来代替粘性应力项，
这是大多数明渠水流水力研究所采用的方法。在沿着这条路线的理论贡献中，可以提到
Stoker的书（1957），Dressler的作品（1949），以及Lighthill和Whitham的作品（1955，I）。德雷斯勒发展了一套严格的滚波理论。特别是
他在振幅相对较大的情况下获得了不连续的周期解，在振幅较小的情况下获得了连续的周期（椭圆曲线）解
振幅Lighthill和Whitham（1955，I）曾将长河中的洪水运动作为一种运动波进行过研究。他们的
具有不连续性的大振幅波浪瞬态运动的预测方法
(or冲击）尤其值得注意。
In the study of long gravity waves of finite amplitude, the
main body of the existing theories has been built upon the simplifying assumption that the viscosity is either totally negligible, or adequately described by an
empirical law. To date very little systematic account of the viscosity effect has appeared that is based on the Navier-Stokes' equations of motion. Thus, in the
important problems of flood waves in rivers, Chezy's formula and a variety of empirical laws of hydraulics have been used to replace the viscous stress terms,
and this is the approach taken in most of the hydraulic studies on open channel flows. Among theoretical contributions along this line, one may mention the
book by Stoker (1957), the works of Dressler (1949), and of Lighthill and Whitham (1955, I). Dressler developed a rigorous theory of roll waves. In particular
he obtained a discontinuous periodic solution in the case of relatively large amplitudes and a continuous periodic (cnoidal) solution in the case of small
amplitudes. General flood movement in long rivers has been masterfully investigated by Lighthill and Whitham (1955, I), as a type of kinematic waves. Their
method of predicting the transient motion of large amplitude waves with discontinuities
(or shocks) is especially noteworthy.