Linear stability of plane couette flow of an upper convected maxwell fluid |
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| Institution: | 1. Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA;2. Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA;1. Aeronautics Institute of Technology – IEFM/ITA, 12228-900 São José dos Campos, SP, Brazil;2. National Institute for Space Research – DGE/INPE and World Institute for Space Environment Research – WISER, P.O. Box 515, 12227-010 São José dos Campos, SP, Brazil;1. Faculty of Mathematics, Physics, and Computation, Schmid College of Science and Technology, Chapman University, One University Drive Orange, CA 92866, USA;2. Politecnico di Milano, Dipartimento di Matematica, Via E. Bonardi, 9, 20133 Milano, Italy;3. School of electrical and computer engineering Ben-Gurion University of the Negev, P.O.B. 653, Beer-Sheva, 84105, Israel;1. Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, PR China;2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;3. Department of Mathematics, Quaid-i-Azam University, 45320, Islamabad 44000, Pakistan;4. School of Mathematics, Shanghai University of Finance and Economics, Shanghai 200433, PR China |
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| Abstract: | We 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 1] and Lee and Finlayson 2], but contradicts “proofs” of instability by Gorodtsov and Leonov 3] and Akbay and Frischmann 4,5]. The errors in those arguments are pointed out. We also find that the numerical discretization can generate artificial instabilities (see also 1,6]). The qualitative behavior of the eigenvalue spectrum as well as the artificial instabilities is discussed. |
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