Stabilité linéaire de l'écoulement de Poiseuille en conduite cylindrique viscoélastique

The stability of Hagen-Poiseuille flow in a viscoelastic tube is determined using a linear stability analysis. It is found that such a flow is unstable, while the Hagen-Poiseuille flow is stable, as is well known. In this paper, we study the instability arising from an axisymmetric disturbance. The neutrality curves in several planes formed by the physical parameters of the problem are plotted. In particular, the effect of the Reynolds number, which was neglected in previous work, is examined. Particular attention is payed to the effect of the viscosity of the viscoelastic tube.