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Linear stability of plane creeping Couette flow for Burgers fluid

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Abstract

It is well known that plane creeping Couette flow of UCM and Oldroy-B fluids are linearly stable. However, for Burges fluid, which includes UCM and Oldroyd-B fluids as special cases, unstable modes are detected in the present work. The wave speed, critical parameters and perturbation mode are studied for neutral waves. Energy analysis shows that the sustaining of perturbation energy in Poiseuille flow and Couette flow is completely different. At low Reynolds number limit, analytical solutions are obtained for simplified perturbation equations. The essential difference between Burgers fluid and Oldroyd-B fluid is revealed to be the fact that neutral mode exists only in the former.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Tsinghua University, 100084, Beijing, China

    Kai-Xin Hu, Jie Peng & Ke-Qin Zhu

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  1. Kai-Xin Hu
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  2. Jie Peng
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  3. Ke-Qin Zhu
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Correspondence to Kai-Xin Hu.

Additional information

The project was supported by the National Natural Science Foundation of China (11172152).

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Hu, KX., Peng, J. & Zhu, KQ. Linear stability of plane creeping Couette flow for Burgers fluid. Acta Mech Sin 29, 12–23 (2013). https://doi.org/10.1007/s10409-013-0007-4

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  • DOI: https://doi.org/10.1007/s10409-013-0007-4

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