Orr-Sommerfeld方程的Green函数和积分方程解法

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名

邮箱

手机号码

标题

留言内容

验证码

Green Function and Integral Equation Method for the Orr-Sommerfeld Equation

摘要: 本文提出了一种求解线性稳定性理论Orr-Sommerfeld方程的方法.我们首先定义了该方程的Green函数,并将它表达成矩阵形式;然后证明了Green函数的互易性;最后导出了等价于原方程的线性积分方程.该方法适用于两固壁间任意Reynolds数下各种主流速度分布的情况.

Abstract: In this paper, an alternative method has been presented to solve the Orr-Sommerfeld equation in the linear theory of stability. To begin with, we define a Green function which is expressed in terms of matrix. Subsequently, its reciprocity has been shown. Finally, a linear integral equation equivalent to the original Orr-Sommerfeld equation is derived. The method is applied to the cases with two solid walls and any velocity distribution of the main flow at any Reynolds number.

[1]	Lin, C. C., The Theorg of Hydrodynamic Stability, Cam. Uni. Press, (1955).
[2]	Lakin, W. D., Ng, B. S. and Reid, W. H., Approximation to the eigenvalue relation for the Orr-Sommerfeld problem. Phi. Trans. Roy. Soc. Lon. 289,No. 1360, (1978).
[3]	李家春,流体运动稳定性和渐近方法,力学与实践,3,4. (1981).
[4]	Thomas, L. H., The stability of plane Poiseuille flow. Phys. Rev. 91,(1953), 780.
[5]	Dolph, C. L. and Lewis, D. C., On the application of finite systems of ordinary differential equations to perturbations of plane Poiseuille flow,Quar. Appl. Math. 16, (1958),97.
[6]	Gallagher, A. P. and Mercer, A. M., On the behaviour of small disturtances in plane Couette flow. Jour. Fluid Mech. 13, (1962),91.
[7]	Grosch, C. E. and Salwen, H., The stability of steadg and time-dependent plane Poiseuille flow. Jour. Fluid Mech. 34, (1968), 177.
[8]	Orszag, S. A., Accurate solution of the Orr-Sommerfeld stability equation,Jour. Fluid Mech. 50, (1971), 689.

点击查看大图