Two-dimensional instability of flow in a rough channel

Physics of Fluids

Volumn 17, Issue 4, 2005, Pages

  Floryan, J M ^a  

^a UNIVERSITY OF WESTERN ONTARIO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; GEOMETRY; REYNOLDS NUMBER; STABILITY; SURFACE ROUGHNESS;

LINEAR STABILITY; TRAVELING WAVES; TWO-DIMENSIONAL INSTABILITY; WAVE NUMBERS;

CHANNEL FLOW;

CHANNEL FLOW; SURFACE ROUGHNESS;

EID: 17444407054     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1865252     Document Type: Article

References (46)

1. O. Reynolds, "An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the wall of resistance in parallel channels," Philos. Trans. R. Soc. London PTRSAV 0370-2316 174, 935 (1883).
2. J. Nikuradse, "Strömungsgesetze in Rauhen Rohren," VDI-Forschungscheft Report No. 36, 1933; J. Nikuradse, NACA TM Report No. 1292, 1950.
3. C. F. Colebrook, "Turbulent flow in pipes, with particular reference to the transition region between smooth and rough pipes," J. Inst. Civ. Eng. London ZZZZZZ 0307-8353 11, 133 (1939).
4. L. F. Moody, "Friction factors for pipe flow," Trans. ASMETASMAV 0097-6822 66, 671 (1944).
5. P. Bradshaw, "A note on critical roughness and transitional roughness," Phys. Fluids PHFLE6 1070-6631 10.1063/1.870410 12, 1611 (2000).
6. D. R. Waigh and R. Kind, "Improved aerodynamic characterization of regular three-dimensional roughness," AIAA J. AIAJAH 0001-1452 36, 1117 (1998).
7. A. Fage, "The smallest size of span wise surface corrugation which affects boundary layer transition on an airfoil," Br. Aero. Res. Council Report No. 2120, 1943.
8. B. H. Carmichael, "Surface waviness criteria for swept and unswept laminar suction wings," Northrop Aircraft Report No. NOR-59-438 (BLC123), 1957.
9. H. Schlichting, Boundary Layer Theory, 7th ed. (McGraw-Hill, New York, (1979).
10. I. Tani, "Effect of two dimensional and isolated roughness elements," in Boundary Layer and Flow Control, edited by G. V. Lachman (Pergamon, New York 1961), Vol. 2, p. 637.
11. A. E. Doenhoff and A. L. Braslow, "The effect of distributed surface roughness on laminar airfoil," in Boundary Layer and Flow Control, edited by G. V. Lachman (Pergamon, New York, 1961), Vol. 2, p. 657.
12. M. V. Morkovin, "On roughness-induced transition: Facts, views and speculations," in Instability and Transition, ICASE/NASA LARC Series Vol. 1, edited by M. Y. Hussaini and R. G. Voigt (Springer, Berlin, 1990), p. 281.
13. P. S. Klebanoff and K. D. Tidstrom, "Mechanism by which a two-dimensional roughness element induces boundary layer transition," Phys. Fluids PFLDAS 0031-9171 10.1063/1.1693047 15, 1172 (1972).
14. A. H. Nayfeh, S. A. Ragab, and A. A. Al-Maaitah, "Effect of bulges on the stability of boundary layers," Phys. Fluids PFLDAS 0031-9171 10.1063/1.866815 31, 796 (1988).
15. J. A. Masad and V. Iyer, "Transition prediction and control in subsonic flow over a hump," Phys. Fluids PHFLE6 1070-6631 10.1063/ 1.868086 6, 313 (1994).
16. J. M. Floryan, "On the Görtler instability of boundary layers," Prog. Aerosp. Sci. PAESD6 0376-0421 10.1016/ 0376-0421(91)90006-P 28, 235 (1991).
17. R. H. Radeztsky, M. S. Reibert, and W. S. Saric, "Effect of isolated micron-sized roughness on transition in swept-wing flows," AIAA J. AIAJAH 0001-1452 37, 1370 (1999).
18. E. Reshotko, "Disturbances in a laminar boundary layer due to distributed surface roughness," in Turbulence and Chaotic Phenomena, Proceedings of IUTAM Symposium, edited by T. T. Tatsumi (Elsevier, New York, 1984), p. 39.
19. T. C. Corke, A. Bar Sever, and M. V. Morkovin, "Experiments on transition enhancements by distributed roughness," Phys. Fluids PFLDAS 0031-9171 10.1063/1.865838 29, 3199 (1986).
20. J. M. Floryan, "Stability of wall-bounded shear layers in the presence of simulated distributed roughness," J. Fluid Mech. JFLSA7 0022-1120 335, 29 (1997).
21. T. Cabal, J. Szumbarski, and J. M. Floryan, "Stability of flow in a wavy channel," J. Fluid Mech. JFLSA7 0022-1120 10.1017/ S0022112001007546 457, 191 (2002).
22. K. Sing and J. L. Lumley, "Effect of roughness on the velocity profile of a laminar boundary layer," Appl. Sci. Res. ASRHAU 0003-6994 24, 168 (1972).
23. M. Lessen and S. T. Gangwani, "Effect of small amplitude wall waviness upon the stability of the laminar boundary layer," Phys. Fluids PFLDAS 0031-9171 10.1063/1.861515 19, 510 (1976).
24. J. M. Kendall, "Laminar boundary layer velocity distortion by surface roughness: Effect upon stability," AIAA Paper 81-0195, Proceedings of the AIAA 19th Aerospace Sciences Meeting, 1981.
25. C. L. Merkle, K. T-S. Tzou, and T. Kubota, "An analytical study of the effect of surface roughness on boundary layer stability," Dynamics Technology Inc. Report No. DT-7606-4, 1977.
26. E. Reshotko and A. Tumin, "Investigation of the role of transient growth in roughness induced transition," AIAA Paper 2002-2850, Proceedings of 32nd AIAA Fluid Dynamics Conference, St. Louis, 2002.
27. J. M. Floryan, J. Szumbarski, and Y. Wu, "Stability of flow in a channel with vibrating walls," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1511545 14, 3927 (2002).
28. J. M. Floryan, "Centrifugal instability of Couette flow over a wavy wall," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1416185 14, 312 (2002).
29. J. M. Floryan, "Vortex instability in a converging-diverging channel," J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112003003987 482, 17 (2003).
30. W. M. Orr, "The stability or instability of the steady motions of a perfect liquid and a viscous liquid," Proc. R. Ir. Acad., Sect. A PRIAAK 0035-8975 27, 27 (1907); 27, 69 (1907).
31. A. Sommerfeld, "Ein Beitrag zur hydrodynamishen Erklärung der turbulenten Flüssigkeitsbewegung," in the Proceedings of the 4th International Congress of Mathematicians, III, Roma, 116 (1908).
32. W. Tollmien, "Ein allgemeines Kriterium der Instabilität laminarer Geschwindigkeitsverteilungen," Nachr. Ges. Wiss. Goettingen, Math.-Phys. Kl. NWGAAN 0369-6650 1, 79 (1935)
33. "General instability criterion of laminar velocity distributions," National Advisory Committee for Aeronautics, Washington, Technical Memorandum No. 792 (1936).
34. H. Schlichting, "Berechnung der Anfachung kleiner Störungen bei der Plattenströmung," Z. Angew. Math. Mech. ZAMMAX 0044-2267 13, 171 (1933).
35. T. Herbert, "Finite amplitude stability of plane parallel flows," AGARD Conf. Proc. AGCPAV 0549-7191 224, 3.1 (1977).
36. U. Ehrenstein and W. Koch, "Three-dimensional wavelike equilibrium states in plane Poiseuille flow," J. Fluid Mech. JFLSA7 0022-1120 228, 111 (1991).
37. J. Jimenez, "Transition to turbulence in two-dimensional Poiseuille flow," J. Fluid Mech. JFLSA7 0022-1120 218, 265 (1990).
38. S. A. Orszag and A. T. Patera, "Secondary instability of wall-bounded shear flows," J. Fluid Mech. JFLSA7 0022-1120 128, 347 (1983).
39. T. Herbert, "Secondary instability of boundary layers," Annu. Rev. Fluid Mech. ARVFA3 0066-4189 20, 487 (1988).
40. R. R. Kerswell, "Elliptical instability," Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/annurev.fluid.34.081701.171829 34, 83 (2002).
41. M. Nishioka and M. Asai, "Some observations of the subcritical transition in plane Poiseuille flow," J. Fluid Mech. JFLSA7 0022-1120 150, 441 (1985).
42. S. C. Reddy, P. J. Schmid, and D. S. Henningson, "Pseudospectra of the Orr-Sommerfeld operator," SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/0153002 53, 15 (1993).
43. L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, "Hydrodynamic stability without eigenvalues," Science SCIEAS 0036-8075 261, 577 (1993).
44. J. T. Stuart, "On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows. Part 1. The basic behavior in plane Poiseuille flow," J. Fluid Mech. JFLSA7 0022-1120 9, 353 (1960).
45. K. M. Butler and B. F. Farrell, "Three-dimensional optimal perturbations in viscous shear flow," Phys. Fluids APFADEB 0899-8213 10.1063/1.858386, 4 1637 (1992).
46. P. J. Schmid and D. S. Henningson, in Stability and Transition in Shear Flows, Applied Mathematical Sciences, Vol. 142 (Springer, Berlin, 2001).