Nonlinear equilibrium solutions for the channel flow of fluid with temperature-dependent viscosity

Journal of Fluid Mechanics

Volumn 406, Issue , 2000, Pages 1-26

  Wall, D P ^a,b   Nagata, M ^a,c  

^a UNIVERSITY OF BIRMINGHAM   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CHANNEL FLOW; EQUILIBRIUM; MATHEMATICAL ANALYSIS; TEMPERATURE EFFECT; VISCOSITY;

EID: 0033912521     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S002211209900748X     Document Type: Article

References (29)

1. BAYLY, B. J., ORSZAG, S. A. & HERBERT, T. 1988 Instability mechanisms in shear-flow transition. Ann. Rev. Fluid Mech. 20, 359-391.
2. DAVIES, S. J. & WHITE, C. M. 1928 An experimental study of the flow of water pipes of rectangular section. Proc. R. Soc. Lond. A 119, 92-107.
3. EHRENSTEIN, U. & KOCH, W. 1989 Nonlinear bifurcation study of plane Poiseuille flow. DLR Res. Rep. FB 89-42.
4. EHRENSTEIN, U. & KOCH, W. 1991 Three-dimensional wavelike equilibrium states in plane Poiseuille flow. J. Fluid Mech. 228, 111-148.
5. ELOFSSON, P. A. & ALFREDSSON, P. H. 1998 An experimental study of oblique transition in plane Poiseuille flow. J. Fluid Mech. 358, 177-202.
6. GROHNE, D. 1969 Die Stabilität der ebenen Kanalströmung gegenüber dreidimensionalen Strörungen von endlicher Amplitude. AVA Göttingen, Rep. 69 A 30.
7. HERBERT, T. 1981 A secondary instability mechanism in plane Poiseuille flow. Bull. Am. Phys. Soc. 26, 1257.
8. HERBERT, T. 1983 On perturbation methods in nonlinear stability theory. J. Fluid Mech. 126, 167-186.
9. KLEBANOFF, P. S., TIDSTROM, K. D. & SARGENT, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 1-34.
10. KOZLOV, V. V. & RAMAZANOV, M. P. 1984 Development of finite-amplitude disturbances in Poiseuille flow. J. Fluid Mech. 147, 149-157.
11. MEKSYN, D. 1964 Stability of laminar flow between parallel planes for two-and three-dimensional finite disturbances. Z. Physik 178, 159-172.
12. MEKSYN, D. & STUART, J. T. 1951 Stability of viscous motion between parallel planes for finite disturbances. Proc. Soc. Lond. A 208, 517-526.
13. MORKOVIN, M. V. 1969 On the many faces of transition. In Viscous Drag Reduction. (ed. C. S. Wells), pp. 1-31. Plenum.
14. NISHIOKA, M., IIDA, S. & ICHIKAWA, Y. 1975 An experimental investigation of the stability of plane Poiseuille flow. J. Fluid Mech. 72, 731-751.
15. NISHIOKA, M., IIDA, S. & KANBAYASHI, S. 1978 An experimental investigation on the subcritical instability in plane Poiseuille flow. In Proc. 10th Turbulence Symp., Inst. Space Aaron. Sci., Tokyo University, pp. 55-62 (in Japanese).
16. ORSZAG, S. A. 1971 Accurate solution of the Orr-Sommerfeld stability equation. J. Fluid Mech. 50, 689-703.
17. ORSZAG, S. A. & KELLS, L. C. 1980 Transition to turbulence in plane Poiseuille and plane Couette flow. J. Fluid Mech. 96, 159-205.
18. ORSZAG, S. A. & PATERA, A. T. 1980 Subcritical transition to turbulence in plane parallel flows. Phys. Rev. Lett. 45, 989-993.
19. ORSZAG, S. A. & PATERA, A. T. 1983 Secondary instability of wall bounded shear flows. J. Fluid Mech. 128, 347-385.
20. PEKERIS, C. L. & SHKOLLER, B. 1969 The neutral curves for periodic perturbations of finite amplitude of plane Poisuille flow. J. Fluid Mech. 39, 629-639.
21. POTTER, M. C. & GRABER, E. 1972 Stability of plane Poiseuille flow with heat transfer. Phys. Fluids 15, 387-391.
22. POTTER, M. C. & SMITH, M. C. 1968 Stability of an unsymmetrical plane flow. Phys. Fluids 11, 2763-2764.
23. PUGH, J. D. & SAFFMAN, P. G. 1988 Two-dimensional superharmonic stability of finite amplitude waves in plane Poiseuille flow. J. Fluid Mech. 194, 295-307.
24. ROZHDESTVENSKY, B. L. & SIMAKIN, I. N. 1984 Secondary flows in a plane channel: their relationship and comparison with turbulent flows. J. Fluid Mech. 147, 261-289.
25. SCHÄFER, P. & HERWIG, H. 1993 Stability of plane Poiseuille flow with temperature dependent viscosity. Intl J. Heat Mass Transfer 36, 2441-2448.
26. STUART, J. T. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. J. Fluid Mech. 9, 353-370.
27. WALL, D. P. 1996 Thermal effects in fluid flow. PhD thesis, University of Strathclyde, Glasgow, UK.
28. WALL, D. P. & WILSON, S. K. 1996 The linear stability of channel flow of fluid with temperature-dependent viscosity. J. Fluid Mech. 323, 107-132.
29. WATSON, J. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. Part 2. The development of a solution for plane Poiseuille flow and for plane Couette flow. J. Fluid Mech. 9, 371-389.