期刊
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS
卷 127, 期 2-3, 页码 169-190出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.jnnfm.2005.03.002
关键词
Couette flow; Oldroyd-B model; linear stability; generalized functions; non-normal operators; stress diffusion
类别
It is well known that plane Couette flow for an Oldroyd-B fluid is linearly stable, yet, most numerical methods predict spurious instabilities at sufficiently high Weissenberg number. In this paper we examine the reasons which cause this qualitative discrepancy. We identify a family of distribution-valued eigenfunctions, which have been overlooked by previous analyses. These singular eigenfunctions span a family of nonmodal stress perturbations which are divergence-free, and therefore do not couple back into the velocity field. Although these perturbations decay eventually, they exhibit transient amplification during which their passive transport by shearing streamlines generates large cross-stream gradients. This filamentation process produces numerical under-resolution, accompanied with a growth of truncation errors. We believe that the unphysical behavior has to be addressed by fine-scale modelling, such as artificial stress diffusivity, or other non-local couplings. (c) 2005 Elsevier B.V. All rights reserved.
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