轴对称模型的Hagen-Poiseuille流的运动不稳定性

Instability of Hagen-Poiseuille Flow for Axisymmetric Mode

摘要: 本文讨论流体通过圆管的运动不稳定性问题。作为流体运动所受的干扰波,我们考虑了一个非线性轴对称模型。它对应的相关振幅函数满足扩散方程,且由于复杂的分子运动和流体粘性的相互作用,当流体的雷诺数增大时其扩散系数会出现负值。如负扩散现象出现,在流体运动中出现的湍流段内会引起流体的能量集中,并扮演减少阻尼的角色。

Abstract: An investigation is described for instability problem of flow through a pipe of circular cross section.As a disturbance motion,we consider an axisymmetric nonlinear mode.An associated amplitude or modulation equation has been derived for this perturbation.This equation belongs to the diffusion type.The coefficient of it can be negative with Reynolds number increasing,because of the complex interaction between molecular diffusion and convection.The negative diffusion,when it occurs,causes a concentration and focusing of energy within the decaying slug,acting as a role of reversing natural decays.

[1]	Cloes,D.,In Mecanique ala Turbulence,Ed.A.Favre,C.N.R.S.,Paris(1962),229-250.
[2]	Davey,A.and H.P.F.Nguyen,Finite-amplitude stability of pipe flow,J Fluid Mech.,45(1971),701-720.
[3]	Davey,A.,On Iton's finite amplitude stability theory for pipe flow,J Fluid Mech.,82(1978),695-703.
[4]	Iton,N.,Nonlinear stability of parallel flows with subcritical Reynolds number,Part 1:An asymptotic theory valid for small amplitude disturbances,Part 2:Stability of pipe Poiseuille flow to finite axisymmetric disturbances,J.Fluid Mech.,82(1977),455-479.
[5]	Stuart,J.T.,On the nonlinear mechanics of wave disturbance in stable and unstable parallel flow,Part 1:The basic behaviour in plane Poiseuille flow,J.Flvid Mech.,9(1960),353-370.
[6]	Stuart,J.T.,Laminar Turbulent Transition,ed.R.Eppler And H.Fasel,Springer-Verlag-Berlin-Heidelberg Press(1980).
[7]	Stuart,J.T.,Laminar and turbulence transition in channel and pipe,Transition and Turbulence,Academic Press Inc.(1981),77-94.
[8]	Smith,F.T.and R.J.Bodonyi,Amplitude-dependent neutral modes in the Hagen-Poiseuille flow through a circular pipe,Proc.Roy.Soc.,A 384(1982),463-489.
[9]	Watson,J.,On the nonlinear mechanics of wave disturbance in stable and unstable parallel flow,Part 2:The development of a solution for plane Poiseuille flow and for plane Couette flow,J Fluid Mech.,9(1960),371-389.