Applied Mathematics and Mechanics

, Volume 8, Issue 11, pp 1037–1044

# Instability of hagen-poiseuille flow for axisymmetric mode

• Wang F. M.
• J. T. Stuart
Article

## 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, cause a concentration and focusing of energy within the decaying slug, acting as a role of reversing natural decays.

## Keywords

Reynolds Number Nonlinear Stability Poiseuille Flow Critical Reynolds Number Amplitude Function
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