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

Journal of Chongqing Jiaotong University(Natural Science) ›› 1998, Vol. 17 ›› Issue (2): 131-134.

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

Feng Chun¹

1. Department of Computer and Information Engineering, Chongqing Jiaotong Institute, Chongqing 400074, P. R. China

Received:1997-05-27 Revised:1997-09-19 Online:1998-06-20 Published:2016-07-13

流体线性稳定性分析Orr-Sommerfeld方程求解的一点补充

冯春¹

1. 重庆交通学院计算机及信息工程系, 重庆 400074

作者简介:冯春(1963-), 女, 讲师

Abstract

Abstract: In this paper, a new solution Bk(z) of Airy equation related with the Orr-Sommerfeld equation is presented by modifying the laplaces method, and the generalization of Bk(z) is just the function Bk(z,p,q). Thus, it shows complementarily why the Bk(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 .

Key words: fluid, hydrodynamic stability, asymptotic, turning-point, related equation

摘要： 通过对Laplace积分解法的改进, 求得Orr-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Orr-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.

关键词: 流体, 稳定性, 渐近解, 转点, 相关方程

CLC Number:

O351

Feng Chun. A Complement of Extracting Solutions on Orr-Sommerfeld Equation about the Analysis of Hydrodynamic Stability[J]. Journal of Chongqing Jiaotong University(Natural Science), 1998, 17(2): 131-134.

冯春. 流体线性稳定性分析Orr-Sommerfeld方程求解的一点补充[J]. 重庆交通大学学报（自然科学版）, 1998, 17(2): 131-134.

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