Instabilités absolue et convective de l'écoulement de Poiseuille en conduite viscoélastique

Abstract

The temporal stability of Poiseuille flow in viscoelastic tube has been studied by the author in a set of papers. In this paper the spatio-temporal stability of the foregoing system is examined. The method of orthnormalization is used in the numerical computation leading to an efficient algorithm to solve for an infinitesimal axisymmetric and nonaxisymmetric disturbances. Then a new method for eigenmodes search technique is founded which eliminates the need for the recurrence formula, developed previously by the author, in order to find the eigenmodes of the system. This new technique leads to more efficient and tractable algorithm to inspect the dispersion relation of the system in the complex wave number and frequency planes. The nature of the instabilities depends on the boundary conditions imposed at the outside tube surface. In the range of physical parameters taken into account in this paper, it is found that for a noncollapsible tube one of the two axisymmetric unstable modes represents an absolute instability. For collapsible tube, the absolute instability is induced by a set of nonaxisymmetric modes. The ratio of the frequency of these absolute unstable modes in their cusp points are in good agreement with the experimental finding. The absolute instability is introduced by solid-based mode. To cite this article: M. Hamadiche, C. R. Mecanique 330 (2002) 769–775.