Boussinesq方程的二阶椭圆余弦驻波解

等深浅水域中的流体运动可由Boussinesq方程描述.众所周知,该方程有行进波解(孤立波及椭圆余弦波).本文则以Boussinesq方程为控制方程,利用渐近匹配法对椭圆余弦波在直墙上反射进行研究,给出了反射过程中内、外场波形及速度变化的解析表达,从而得到了Boussinesq方程的二阶椭圆余弦驻波型的解析解,并讨论了这类驻波的若干性质.当波长无限增大时,所得解析解收敛于孤立波的情况.这些解析结果不仅有助于揭示岸坡对非线性浅水波影响的力学机理,在海岸防护和开发和岸壁附近结构物的设计条件等工程领域中也具有现实的指导意义.

An analytical solution of the Boussinesq equations for the second-order cnoidal standing waves

It is well know that the Boussinesq equations, which govern the fluid motion in shallow-waters of constant depth, have analytical solutions of both cnoidal waves and solitary waves.By using the Boussinesq equations as the governing equations and the method of asymptotic matching expansions, an analytical solution of the second-order cnoidal standing waves is obtained for the reflection of a train of progressive cnoidal waves on a vertical rigid wall, and the variations of the wave pattern and particle veloc...