Stability of plane Couette - Poiseuille flow of shear-thinning fluid

Physics of Fluids

Volumn 21, Issue 6, 2009, Pages

  Nouar, Chérif ^a   Frigaard, Ian ^b  

^a NANCY UNIVERSITÉ   (France)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LINEAR STABILITY ANALYSIS; NEWTONIAN LIQUIDS; NON NEWTONIAN FLOW; REYNOLDS NUMBER; SHEAR THINNING; VELOCITY;

CHEBYSHEV COLLOCATION METHOD; COUETTE AND POISEUILLE FLOWS; CRITICAL REYNOLDS NUMBER; ORR-SOMMERFELD EQUATIONS; PLANE COUETTE-POISEUILLE FLOW; REYNOLDS STRESS DISTRIBUTION; TWO-DIMENSIONAL PERTURBATION; VISCOSITY STRATIFICATION;

SHEAR FLOW;

EID: 67650314932     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3152632     Document Type: Article

References (23)

1. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1985).
2. V. A. Romanov, "Stability of plane parallel Couette flow," Funct. Anal. Appl. FAAPBZ0016-2663 7, 137 (1973). 10.1007/BF01078886
3. M. C. Potter, "Stability of plane Couette-Poiseuille flow," J. Fluid Mech. JFLSA70022-1120 24, 609 (1966). 10.1017/S0022112066000855
4. F. D. Hains, "Stability of plane Couette-Poiseuille flow," Phys. Fluids PFLDAS0031-9171 10, 2079 (1967). 10.1063/1.1762411
5. S. Ozgen, Z. Dursunkaya, and A. A. Ebrinc, "Heat transfer effects on the stability of low speed plane Couette-Poiseuille flow," Heat Mass Transfer HMTRF80947-7411 43, 1317 (2007). 10.1007/s00231-006-0208-5
6. S. J. Cowley and F. T. Smith, "On the stability of Poiseuille-Couette flow: A bifurcation from infinity," J. Fluid Mech. JFLSA70022-1120 156, 83 (1985). 10.1017/S0022112085002002
7. L. B. Bergstrom, "Nonmodal growth of three-dimensional disturbances on plane Couette-Poiseuille flows," Phys. Fluids PHFLE61070-6631 17, 014105 (2005). 10.1063/1.1830511
8. R. Govindarajan, V. S. L'Vov, and I. Procaccia, "Retardation of the onset of turbulence by minor viscosity contrasts," Phys. Rev. Lett. PRLTAO0031-9007 87, 174501 (2001). 10.1103/PhysRevLett.87.174501
9. R. Govindarajan, V. S. L'Vov, I. Procaccia, and A. Sameen, "Stabilization of hydrodynamic flows by small viscosity variations," Phys. Rev. E PLEEE81063-651X 67, 026310 (2003). 10.1103/PhysRevE.67.026310
10. A. Pinarbasi and M. Imal, "Viscous heating effects on the linear stability of Poiseuille flow of an inelastic fluid," J. Non-Newtonian Fluid Mech. JNFMDI0377-0257 127, 67 (2005). 10.1016/ j.jnnfm.2005.02.004
11. N. T. M. Eldabe, M. F. El-Sabbagh, and M. A. S. El-Sayed, "The stability of plane Couette flow of a power-law fluid with viscous heating," Phys. Fluids PHFLE61070-6631 19, 094107 (2007). 10.1063/ 1.2778407
12. M. Renardy and Y. Renardy, "Linear stability of plane Couette flow of an upper convected Maxwell fluid," J. Non-Newtonian Fluid Mech. JNFMDI0377-0257 22, 23 (1986). 10.1016/0377-0257(86)80002-7
13. T. C. Ho and M. M. Denn, "Stability of plane Poiseuille flow of a highly elastic liquid," J. Non-Newtonian Fluid Mech. JNFMDI0377-0257 3, 179 (1977). 10.1016/0377-0257(77)80048-7
14. R. Sureshkumar and A. N. Beris, "Linear stability analysis of visco-elastic Pouiseuille flow using an Arnoldi-based algorithm," J. Non-Newtonian Fluid Mech. JNFMDI0377-0257 56, 151 (1995). 10.1016/ 0377-0257(94)01279-Q
15. R. B. Bird, R. Amstrong, and O. Hassager, Dynamics of Polymeric Liquids (Wiley-Interscience, New York, 1987).
16. V. Chikkadi, A. Sameen, and R. Govindarajan, "Preventing transition to turbulence: A viscosity stratification does not always help," Phys. Rev. Lett. PRLTAO0031-9007 95, 264504 (2005). 10.1103/ PhysRevLett.95.264504
17. C. Nouar, A. Bottaro, and J. P. Brancher, "Delaying transition to turbulence in channel flow: Revisiting the stability of shear-thinning fluids," J. Fluid Mech. JFLSA70022-1120 592, 177 (2007). 10.1017/ S0022112007008439
18. P. J. Schmid and D. S. Henningson, Stability and Transition in Shear Flows (Springer-Verlag, New York, 2001).
19. C. Nouar, N. Kabouya, J. Dusek, and M. Mamou, "Modal and non-modal linear stability of the plane Bingham Poiseuille flow," J. Fluid Mech. JFLSA70022-1120 577, 211 (2007). 10.1017/S0022112006004514
20. L. M. Mack, "A numerical study of the temporal eigenvalue problem of the Blasius boundary layer," J. Fluid Mech. JFLSA70022-1120 73, 497 (1976). 10.1017/S002211207600147X
21. K. M. Butler and B. F. Farrell, "Three-dimensional optimal perturbations in viscous shear flow," Phys. Fluids A PFADEB0899-8213 4, 1637 (1992). 10.1063/1.858386
22. E. Plaut, Y. Lebranchu, R. Simitev, and F. H. Busse, "Reynolds stresses and mean fields generated by pure waves: Applications to shear flows and convection in a rotating cell," J. Fluid Mech. JFLSA70022-1120 602, 303 (2008). 10.1017/S0022112008000840
23. V. M. Sadeghi and B. G. Higgins, "Stability of sliding Couette-Poiseuille flow in an annulus subject to axisymmetric and asymmetric disturbances," Phys. Fluids A PFADEB0899-8213 3, 2092 (1991). 10.1063/1.857892