连续分层流体中内波传播的李群分析法

Lie group analysis of internal wave propagation in continuous stratified fluids

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.