经过修正的层次流流动的流动稳定性问题(Ⅱ)——经过修正的平行剪切流的线性稳定性研究

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On the Stability of Distorted Laminar Flow(Ⅱ)——The Linear Stability Analysis of Distorted Parallel Shear Flow

摘要: 本文根据文[1]给出的经过修正的层流流动的流动稳定性理论及平行剪切流中平均速度的一类修正剖面,研究了平行剪切流的线性稳定性性质,对于平面Couette流动和圆管Poiseuill流动,首次得到了二维扰动和轴对称扰动也能造成失稳的结果,并给出了这两种流动在某种定义下的中性曲线.

Abstract: Based on the hydrodynamic stability theory of distorted laminar flow and the kind of distortion profiles on the mean velocity in parallel shear flow given in paper [1], this paper investigates the linear stability behaviour of parallel shear flow, presents unstable results of plane Couette flow and pipe Poiseuille flow to two-dimensional or axisymmetric disturbances for the first time, and obtains neutral curves of these two motions under certain definition.

[1]	周哲玮,经过修正的层流流动的流动稳定性问题(I)—基本概念和理论,应用数学和力学,10,2(1989).
[2]	周哲玮,圆管Poiseuille流动中平均速度的一种修正剖面及其稳定性研究,应用数学和力学,9,1(1988).
[3]	Gill,A.E.,A mechanism for instability of plane Couette flow and of Poiseuille flow in a pipe,J.Fluid Mech.,21(1962),503.
[4]	Orszag,S.A.,Accurate solution of the Orr-Sommerfeld stability equation,J.Fluid Mech.,50(1971),689.
[5]	Deardoff J.W.,On the stability of viscous plane Couette flow,J.Fluid Mech.,15(1963),623.