轴对称模型的Hagen-Poiseuille流的运动不稳定性

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。

Instability of Hagen-Poiseuille Flow for Axisymmetric Mode

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.