Stability of Poiseuille Flow in Elastic Tubes

Abstract

This paper presents a theoretical analysis of the temporal and spatial stability of Poiseuille flow in elastic tubes to infinitesimal axisymmetric disturbances. A cylindrical shell model which includes the effects of transverse shear and rotatory inertia is employed for the tube wall. The characteristic equation of the system is solved numerically and two sets of modes are obtained; one set has eigenvalues that are independent of the properties and dimensions of the tube wall, while the other set has eigenvalues that depend on the tube parameters. One mode of the “tube-dependent” set is shown to have a critical Reynolds number that depends on the elastic properties and dimensions of the tube and either wave number or frequency of the disturbance.