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

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1986
Accession Number
ADA167927

Entities

People

  • Michael Renardy
  • Yuriko Renardy

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Abstracts
  • Chebyshev Polynomials
  • Continuous Spectra
  • Couette Flow
  • Differential Equations
  • Eigenvalues
  • Elastic Properties
  • Equations
  • Flow
  • Mathematics
  • Numerical Analysis
  • Reynolds Number
  • Shear Flow
  • Shear Stresses
  • Spectra
  • Steady Flow
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Fluid Dynamics.
  • Plasma Physics / Magnetohydrodynamics