Effects of the Reynolds and Weissenberg’s Numbers on the Stability of Linear Pipe Flow of Viscous Fluid

Abstract

A Fourier-Chebyshev Petrov-Galerkin spectral method is described for high accuracy computation of linearized dynamics for flow in a circular pipe. The code used here is based on solenoidal velocity variables and is written in FORTRAN. Systematic studies are presented of the dependence of eigenval-ues and other quantities on the axial and azimuthal wave numbers; the Reyn-olds’ number of up to 107 and the Weissenberg’s number that is considered lower here. The flow will be considered stable if all the real parts of the ei-genvalues obtained are negative and unstable if only one of these values is positive.