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Non-modal instability in plane Couette flow of a power-law fluid

Published online by Cambridge University Press:  26 April 2011

R. LIU  and
Q. S. LIU
R. LIU*
Affiliation:
Key Laboratory of Microgravity (National Microgravity Laboratory), Institute of Mechanics, Chinese Academy Of Sciences, Beijing, China100190
Q. S. LIU
Affiliation:
Key Laboratory of Microgravity (National Microgravity Laboratory), Institute of Mechanics, Chinese Academy Of Sciences, Beijing, China100190
*
†Email address for correspondence: liurong@imech/ac.cn, liu@imech.ac.cn
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Abstract

In this paper, we study the linear stability of a plane Couette flow of a power-law fluid. The influence of shear-thinning effect on the stability is investigated using the classical eigenvalue analysis, the energy method and the non-modal stability theory. For the plane Couette flow, there is no stratification of viscosity. Thus, for the stability problem the stress tensor is anisotropic aligned with the strain rate perturbation. The results of the eigenvalue analysis and the energy method show that the shear-thinning effect is destabilizing. We focus on the effect of non-Newtonian viscosity on the transition from laminar flow towards turbulence in the framework of non-modal stability theory. Response to external excitations and initial conditions has been studied by examining the ε-pseudospectrum and the transient energy growth. For both Newtonian and non-Newtonian fluids, it is found that there can be a rather large transient growth even though the linear operator of the Couette flow has no unstable eigenvalue. The results show that shear-thinning significantly increases the amplitude of response to external excitations and initial conditions.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 676 , 10 June 2011 , pp. 145 - 171
Copyright
Copyright © Cambridge University Press 2011

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