%0 Journal Article %1 renardy1986linear %A Renardy, Michael %A Renardy, Yuriko %D 1986 %J Journal of Non-Newtonian Fluid Mechanics %K 76a10-viscoelastic-fluids 76e05-parallel-shear-flows %N 1 %P 23-33 %R https://doi.org/10.1016/0377-0257(86)80002-7 %T Linear stability of plane couette flow of an upper convected maxwell fluid %U https://www.sciencedirect.com/science/article/pii/0377025786800027 %V 22 %X 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.

@article{renardy1986linear, 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.}, added-at = {2021-09-01T04:02:54.000+0200}, author = {Renardy, Michael and Renardy, Yuriko}, biburl = {https://www.bibsonomy.org/bibtex/2502e0794c38e73bb8af0c88098c2f3eb/gdmcbain}, doi = {https://doi.org/10.1016/0377-0257(86)80002-7}, interhash = {b6dea97c82382d6e96b28d2a7c722c5a}, intrahash = {502e0794c38e73bb8af0c88098c2f3eb}, issn = {0377-0257}, journal = {Journal of Non-Newtonian Fluid Mechanics}, keywords = {76a10-viscoelastic-fluids 76e05-parallel-shear-flows}, number = 1, pages = {23-33}, timestamp = {2021-09-01T04:02:54.000+0200}, title = {Linear stability of plane couette flow of an upper convected maxwell fluid}, url = {https://www.sciencedirect.com/science/article/pii/0377025786800027}, volume = 22, year = 1986 }