Linear Stability of Plane Couette Flow of an Upper Convected Maxwell Fluid

摘要

This document investigate the linear stability of plane Couette flow of an upper convected Maxwell fluid using a spectral method to compute the eigenvalues. No instabilities are found. This is in agreement with the results of Ho and Denn and Lee and Finlayson, but contradicts proofs of instability given by Gorodtsov and Leonov and Akbay and Frischmann. The errors in those arguments are pointed out. The authors also find that the numerical discretization can generate artificial instabilities. The qualitative behavior of the eigenvalue spectrum as well as the artificial instabilities is discussed. Keywords: Parallel shear flow; and Shear stresses.