Numerical observations on the continuous spectrum of the linearized viscoelastic operator in shear dominated complex flows

The eigenspectrum of the viscoelastic operator of the upper convected Maxwe ll (UCM) model in two-dimensional mixed-kinematic flows without internal st agnation points is contained on a line with real part given by -1/De, where De denotes the Deborah number [9]. We examine the manifestation of this co ntinuous spectrum in numerical simulations of viscoelastic journal hearing and eccentric Dean hows using a pseudo-spectral Chebyshev-Fourier collocati on technique. Our numerical results show that for a given set of geometric parameters the maximum imaginary Dart of the continuous spectrum increases with the largest wavenumber that can be accommodated by the mesh. Hence, in creasing azimuthal resolution for a given eccentricity introduces higher wa venumbers leading to an overall convergence that is poorer than that obtain ed for a coarser mesh. The eigenfunctions exhibit singular behavior in both the wall-normal and azimuthal directions. The locations of these singulari ties depend on the imaginary part of the eigenvalue. (C) 2000 Elsevier Scie nce B.V. All rights reserved.