Instability of Hagen-Poiseuille flow for axisymmetric mode (Q1114515)

An investigation is described for the 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.