海洋内波垂向结构求解的几种数学方法

Several Mathematical Methods Used in Solving the Vertical Structure of Ocean Internal Waves

海洋内波垂向结构的求解有不同的数学方法.首先,简述了利用两次Sturm变换,将内波控制方程转化为Sturm-liouville标准型的主要过程.其次,给出了由一般二阶变系数常微分方程的通用变换方法,将内波控制方程转化为Sturm-liouville标准型的方法.随后,通过直接差分法,给出了将内波控制方程离散化为矩阵特征值问题的一般过程.最后,详述了Thomson-Haskell方法求解内波垂向结构的过程.

There are several different mathematical methods used in salving the vertical structure of ocean internal waves. First, it simply depicts the method of twice-Sturm transformations, and gives the main procedure to obtain the standard Sturm-Liouville equation. Second, it gives another transformation method to get the standard Sturm-Liouville equation based on the theory of second order ODE with variable coefficients. Third, it gives the common procedure on how to transform the control equation to matrix eigenvalue problem with directly finite differential method. And at last, it thoroughly discusses the Thomson-Haskell method widely used in solving the vertical structure of ocean internal waves.