流体线性稳定性分析 Orr-Sommerfeld 方程求解的一点补充

A Complement of Extracting Solutions on Orr Sommerfeld Equation about the Analysis of Hydrodynamic Stability

通过对Ｌａｐｌａｃｅ积分解法的改进，求得ＯｒＳｏｍｍｅｒｆｅｌｄ方程的相关方程Ａｉｒｙ方程的一个新解Ｂｋ（ｚ），推广后得展开函数族Ｂｋ（ｚ，ｐ，ｑ），从而从理论上补充说明为什么可用该函数族Ｂｋ（ｚ，ｐ，ｑ）得到ＯｒＳｏｍｍｅｒｆｅｌｄ方程奇异无粘解的一致有效渐近展开式，由此使流体线性稳定性分析ＯｒｒＳｏｍｍｅｒｆｅｌｄ方程的求解得到圆满解决．

In this paper,a new solution B k(z) of Airy equation related with the Orr Sommerfeld equation is presented by modifying the laplaces method,and the generalization of B k(z) is just the function B k(z,p,q) .Thus,it shows complementarily why the B k(z,p,q) can expand the Orr Sommerfeld equation for the uniformly valid asymptotic expansion of its two singular inviscial solutions in theory and complete extracting solutions on the Orr Sommerfeld equation about the analysis of hydrodynamic stability.