流体线性稳定性分析中Orr-Sommerfeld方程求解的一点注记

A Note of the Orr-Sommerfeld Equation in the Analysis of Hydrodynamic Stability

通过对Laplace积分解法的改进，求出了Orr-Sommerfeld方程的相关方程Airy方程的一个新解Bk（Z），将其推广为展开函数族Bk（z,p，q）后，得到了Orr-Sommerfeld方程的奇异无粘解的一致有效渐近展开式，从而证明了Bk（z,p,q）实际上是一个广义Airy函数．

In this paper, a solution Bk(z) of Airy equation, related equation of theOrr-Sommerfeld equation is presented by modifying the Laplace's method, the generalization of which is just the function BK(z, p, q) used in [1], the Orr-Sonunerfeld, equation for the uniformly valid asymptotic expansion of its two singular inviscid solutions is given. Thus, the key step in the analysis of hydrodynamic stability from angle of mathematics, solving the Orr-Sommerfeld equation is resolved satisfactorily in theory.