摘要
对于密度连续分层海洋流体中的内波传播,从绝热Boussinesq近似方程组出发,得出了考虑变密度的非线性控制方程。应用李群分析方法,推导出了系统偏微分方程组的多组允许无穷小对称性、守恒矢量以及群不变解,对不变解的有关性质进行了说明,给出了系统精确解析解表达式。本文的李群分析解析解与已有文献中内波传播过程密度和垂向速度随时间变化的数值模拟计算结果基本一致,密度和垂向速度随时间呈正弦振荡,并且李群分析解析解也可推导出内波色散关系具有各向异性特征。
For the internal wave propagation in densely stratified oceanic fluids, the adiabatic Boussinesqapproximation equations are used to derive a nonlinear governing equation with variable density. The permissible infinitesimal symmetries, conserved vectors and group invariant solutions of partial differential equations are derived by using Lie group analysis method. More importantly, their detailed analytical expressions and properties are discussed. The numerical simulations of the density and vertical velocity with time of internal wave propagation are basically consistent with the analytical solution of Lie group analysis. Similarly, the analytical solution of Lie group analysis can also deduce that the dispersion relation of internal wave has anisotropic characteristics.
作者
郑明亮
冯鲜
Zheng Mingliang;Feng Xian(School of Mechanical and Electrical engineering,Taihu University of Wuxi,214064,Wuxi,China)
出处
《应用力学学报》
CAS
CSCD
北大核心
2019年第6期1294-1299,I0003,I0004,共8页
Chinese Journal of Applied Mechanics
基金
江苏省高等学校自然科学基金(18KJB460027)
关键词
连续分层海内波
李群分析
守恒矢量
不变解
continuous stratified internal waves
Lie group analysis
conserved vectors
invariant solutions