|Non-modal instability in plane Couette flow of a power-law fluid|
|Liu R(刘荣); Liu QS(刘秋生); Liu, R (reprint author), Chinese Acad Sci, Key Lab Micrograv, Natl Micrograv Lab, Inst Mech, Beijing 100190, Peoples R China
|Source Publication||Journal of Fluid Mechanics
|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 epsilon-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.|
Transition To Turbulence
; CHANNEL FLOWS
; POISEUILLE FLOW
; ENERGY AMPLIFICATION
|WOS Research Area||Mechanics
; Physics, Fluids & Plasmas
|Funding Organization||The authors thank the National foundation of China for financial support for this research (50890182, 11072249 and 10772185). The authors also gratefully acknowledge the referees for their many helpful comments.
|Corresponding Author||Liu, R (reprint author), Chinese Acad Sci, Key Lab Micrograv, Natl Micrograv Lab, Inst Mech, Beijing 100190, Peoples R China|
Liu R,Liu QS,Liu, R . Non-modal instability in plane Couette flow of a power-law fluid[J]. Journal of Fluid Mechanics,2011,676:145-171.
刘荣,刘秋生,&Liu, R .(2011).Non-modal instability in plane Couette flow of a power-law fluid.Journal of Fluid Mechanics,676,145-171.
刘荣,et al."Non-modal instability in plane Couette flow of a power-law fluid".Journal of Fluid Mechanics 676(2011):145-171.