On the instability of pipe Poiseuille flow

Physics of Fluids

Volumn 8, Issue 11, 1996, Pages 2923-2932

  Zikanov, Oleg Yu ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000088852     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869071     Document Type: Article

References (28)

1. O. Reynolds, "An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuos and of the law of resistance in parallel channels," Proc. R. Soc. London 35, 84 (1883).
2. E. R. Lindgren, "The transition process and other phenomena in viscous flows," Ark. Phys. 12, 1 (1958).
3. R. J. Leite, "An experimental investigation of the stability of Poiseuille flow," J. Fluid Mech. 5, 81 (1959).
4. I. J. Wygnanski and F. H. Champagne, "On transition in a pipe. Part I. The origin of puffs and slugs and the flow in a turbulent slug," J. Fluid Mech. 59, 281 (1973).
5. Y. Rubin, I. J. Wygnanski, and J. H. Haritonidis, "Further observations on transition in a pipe," in Laminar-Turbulent Transition; Proceedings of the IUTAM Symposium Stuttgart, edited by R. Eppler and F. Hussein (Springer-Verlag, Berlin, 1980), p. 19.
6. A. G. Darbyshire and T. Mullin, "Transition to turbulence in constant-mass-flux pipe flow," J. Fluid Mech. 289, 83 (1995).
7. W. Pfenniger, "Transition in the inlet length of tubes at high Reynolds numbers," in Boundary Layer and Flow Control, edited by G. V. Lachman (Pergamon, New York, 1961), p. 970.
8. I. J. Wygnanski, M. Sokolov, and D. Friedman, "On transition in a pipe. Part 2. The equilibrium puff," J. Fluid Mech. 69, 283 (1975).
9. T. Sarpkaya, "A note on the stability of developing laminar pipe flow subjected to axisymmetric and non-axisymmetric disturbances," J. Fluid Mech. 68, 345 (1975).
10. T. Tatsumi, "Stability of the laminar inlet-flow prior to the formation of Poiseuille regime. II." J. Phys. Soc. Jpn. 7, 495 (1952).
11. P. Drasin and W. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1981).
12. J. T. Stuart, "Instability and transitions in pipes and channels," in Transition and Turbulence; Proceedings of the Symposium at the Mathematics Research Center, University of Wisconsin - Madison (Academic, New York, 1981), p. 77.
13. M. Lessen, G. S. Sadler, and T.-Y. Liu, "Stability of pipe Poiseuille flow," Phys. Fluids 11, 1404 (1968).
14. H. Salwen, F. W. Cotton, and C. E. Grosch, "Linear stability of Poiseuille flow in a circular pipe," J. Fluid Mech. 98, 273 (1980).
15. V. K. Garg and W. T. Rouleau, "Linear spatial stability of pipe Poiseuille flow," J. Fluid Mech. 54, 113 (1972)
16. F. T. Smith and R. J. Bodonyi, "Amplitude-dependent neutral modes in the Hagen-Poiseuille flow through a circular pipe," Proc. R. Soc. London, Ser. A 384, 463 (1982).
17. L. Boberg and U. Brosa, "Onset of turbulence in a pipe," Z. Naturforsch. 43a, 697 (1988).
18. L. Bergström, "Initial algebraic growth of small angular dependent disturbances in pipe Poiseuille flow," Stud. Appl. Math. 87, 61 (1992).
19. L. Bergström, "Optimal growth of small disturbances in pipe Poiseuille flow," Phys. Fluids A 5, 2710 (1993).
20. P. J. Schmid and D. S. Henningson, "Optimal energy density growth in Hagen-Poiseuille flow," J. Fluid Mech. 277, 197 (1994).
21. L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, "Hydrodynamic stability without eigenvalues," Science 261, 578 (1993).
22. F. Waleffe, "Transition in shear flows. Nonlinear normality versus non-normal linearity," Phys. Fluids 7, 3060 (1995).
23. N. V. Nikitin, "Direct numerical modeling of three-dimensional turbulent flows in pipes of circular cross section," Fluid Dyn. 6, 749 (1994).
24. B. Klingmann and P. H. Alfredsson, "Experiments on the evolution of a pointlike disturbance in plane Poiseuille flow into a turbulent spot," in Advances in Turbulence 3 (Springer-Verlag, Berlin, 1991).
25. S. A. Orszag and A. T. Patera, "Secondary instability of wall-bounded shear flows," J. Fluid Mech. 128, 347 (1983).
26. M. R. Khorrami, M. R. Malik, and R. L. Ash, "Application of spectral collocation techniques to the stability of swirling flows," J. Comput. Phys. 81, 206 (1989).
27. S. K. Godunov and V. S. Ryabenki. Theory of Difference Schemes (North-Holland, Amsterdam, 1964), pp. 146-154.
28. S. C. Reddy, P. J. Schmid, and J. S. Baggett, "On stability of streamwise streaks and transition to turbulence in plane channel flows," submitted to J. Fluid Mech. (1996).