A global spectral method is used to construct the steady-state flow and stability of a Criminale-Ericksen-Filbey fluid in a cylinder with a rotating lid. We extend the orthogonal collocation analysis of Nirschl and Stewart (J.P. Nirschl and W.E. Stewart, J. Non-Newtonian Fluid Mech., 16 (1984) 233) by locating the bifurcation loci in the Weissenberg-Reynolds parameter space and estimating the bifurcating solutions near the loci. Converging estimates of the steady flow field and the simple and Hopf bifurcation points are demonstrated. This is consistent with earlier speculations (A.N. Beris, R.C. Armstrong and R.A. Brown, J. Non-Newtonian Fluid Mech., 22 (1987) 129) that a global spectral method allows much higher resolution of viscoelastic fluids than the finite-element method. Reasonable agreement with Hill's measurements of flow fields and stability boundaries (C.T. Hill, Ph.D. Thesis, University of Wisconsin, Madison, 1969; C.T. Hill, Trans. Soc. Rheol., 16 (1972) 213) is also shown. Most interestingly, a region of chaotic (turbulent) flow, which has also been observed in the experiments, is predicted by our simulation and analysis. © 1990.
