Turbulence transition in pipe flow: Some open questions

Nonlinearity

Volumn 21, Issue 1, 2008, Pages

  Eckhardt, Bruno ^a  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38849090768     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/21/1/T01     Document Type: Article

References (105)

1. Barkley D and Tuckerman L S 2005 Phys. Rev. Lett. 94 014502
2. Ben-Dov G and Cohen J 2007 Phys. Rev. Lett. 98 064503
3. Boberg L and Brosa U 1988 Z. Naturf. a 43 697-726
4. Bottin S, Daviaud F, Manneville P and Dauchot O 1998 Europhys. Lett. 43 171-6
5. Braun R and Feudel F 1996 Phys. Rev. E 53 6562-5
6. Brosa U 1986 Z. Naturf. a 41 1141
7. Brosa U 1989 J. Stat. Phys. 55 1303-12
8. Brosa U and Grossmann S 1999 Eur. Phys. J. B 9 343-54
9. Chandrasekhar S 1961 Hydrodynamic and Hydromagnetic Stability (Oxford: Oxford University Press)
10. Clever R and Busse F H 1997 J. Fluid Mech. 344 137-53
11. Crutchfield J P and Kaneko K 1988 Phys. Rev. Lett. 60 2715-8
12. Cvitanovic P and Eckhardt B 1991 J. Phys. A: Math. Gen. 24 L237-41
13. Darbyshire A G and Mullin T 1995 J. Fluid Mech. 289 83-114
14. Dauchot O and Daviaud F 1994 Europhys. Lett. 28 225-30
15. Dauchot O and Daviaud F 1995 Phys. Fluids 7 335-43
16. Dauchot O and Vioujard N 2000 Eur. Phys. J. B 14 377
17. Doering C R and Gibbon J 1995 Applied Analysis of the Navier-Stokes Equation (Cambridge: Cambridge University Press)
18. Drazin P G and Reid W H 1981 Hydrodynamic Stability (Cambridge: Cambridge University Press)
19. Durst F and nsal B 2006 J. Fluid Mech. 560 449-64
20. Eckhardt B, Faisst H, Schmiegel A and Schneider T M 2008 Phil. Trans. R. Soc. (Lond.) at press (doi:10.1098/rsta.2007.2132)
21. Eckhardt B and Lathrop D P 2006 Nonlinear Phenom. Complex Syst. 9 133-40
22. Eckhardt B and Mersmann A 1999 Phys. Rev. E 60 509-17
23. Eckhardt B and Ott G 1994 Z. Phys. B 93 259-66
24. Eckhardt B, Schneider T M, Hof B and Westerweel J 2007 Annu. Rev. Fluid Mech. 39 447-68
25. Ehrenstein U and Koch W 1991 J. Fluid. Mech. 228 111-48
26. Faisst H and Eckhardt B 2000 Phys. Rev. E 61 7227-30
27. Faisst H and Eckhardt B 2003 Phys. Rev. Lett. 91 224502
28. Faisst H and Eckhardt B 2004 J. Fluid Mech. 504 343-52
29. Feffermann C L 2000 Existence and smoothness of the Navier-Stokes equation http://www.claymath.org/millennium/Navier-Stokes_Equations/ navierstokes.pdf
30. Gavarini M I, Bottaro A and Nieuwstadt F T M 2004 J. Fluid Mech. 517 131-65
31. Gibson J F, Halcrow J and Cvitanovic P 2007 Preprint 0705.3957 (31 pp)
32. Goren G, Eckmann J P and Procaccia I 1998 Phys. Rev. E 57 4106-134
33. Grebogi C, Ott E and Yorke J A 1983 Physica D 7 181-200
34. Grossmann S 2000 Rev. Mod. Phys. 72 603-18
35. Henningson D 1996 Phys. Fluids 8 2257-8
36. Hinrichsen D, Plischke E and Wirth F 2004 Unsolved Problems in Mathematical Systems Theory ed V D Blondel and A Megretski (Princeton, NJ: Princeton University Press) pp 197-202
37. Hof B 2004 IUTAM Symp. on Laminar-Turbulent Transition and Finite Amplitude Solutions (Dordrecht: Springer) pp 221-31 in Mullin T and Kerswell R R (ed) 2005
38. Hof B, Juel A and Mullin T 2003 Phys. Rev. Lett. 244502
39. Hof B, van Doorne C W H, Westerveel J, Nieuwstadt F T M, Faisst H, Eckhardt B, Wedin H, Kerswell R R and Waleffe F 2004 Science 305 1594-8
40. Hof B, Westerweel J, Schneider T and Eckhardt B 2007 Preprint 0707.2642 (p1)
41. Hof B, Westerweel J, Schneider T M and Eckhardt B 2006 Nature 443 60-4
42. Homsy G M et al 2004 Multi Media Fluid Mechanics (Cambridge: Cambridge University Press)
43. Hristova H, Roch S, Schmid P J and Tuckerman L S 2002 Phys. Fluids 14 3475-84
44. Itano T and Toh S 2001 J. Phys. Soc. Japan 70 703-16
45. Jachens A, Schumacher J, Eckhardt B, Knobloch K and Fernholz H H 2006 J. Fluid Mech. 547 55-64
46. Jackson D and Launder B 2007 Ann. Rev. Fluid Mech. 39 19-35
47. Joseph D D 1975 Stability of Fluid Motions vols 1 and 2 (Berlin: Springer)
48. Kadanoff L P and Tang C 1984 Proc. Natl Acad. Sci. USA 81 1276
49. Kaneda K 1990 Phys. Lett. A 149 105-12
50. Kantz H and Grassberger P 1985 Physica D 17 75-86
51. Kerswell R R 2005 Nonlinearity 18 R17-44
52. Kerswell R R and Tutty O R 2007 J. Fluid Mech. 584 69-102
53. Kim L and Moehlis J 2006 Phys. Lett. A 358 431-7
54. Koschmieder E L 1993 Bénard Cells and Taylor Vortices (Cambridge: Cambridge University Press)
55. Kreiss G, Lundbladh A and Henningson D 1994 J. Fluid Mech. 270 175-98
56. Lagha M and Manneville P 2007 Eur. Phys. J. B 58 433-47
57. Lai Y C and Winslow R L 1995 Phys. Rev. Lett. 74 5208-11
58. Manneville P and Locher F 2000 C. R. Acad. Sci., Ser. IIB Mech. Phys. Astron. 328 159-64o
59. Mellibovsky F and Meseguer A 2006 Phys. Fluids 18 074104
60. Mellibovsky F and Meseguer A 2007 Phys. Fluids 19 044102
61. Meseguer A and Trefethen L 2003 J. Comput. Phys. 186 178-97
62. Moehlis J, Faisst H and Eckhardt B 2004 New J. Phys. 6 56 (17pp)
63. Moehlis J, Faisst H and Eckhardt B 2005 SIAM J. Appl. Dyn. Syst. 4 352-76
64. Mullin T and Kerswell R R (ed) 2005 IUTAM Symp. on Laminar-Turbulent Transition and Finite Amplitude Solutions (Dordrecht: Springer)
65. Mullin T and Peixinho J 2005 IUTAM Symp. Transition in Shear Flows ed R Govindarajan (Berlin: Springer)
66. Mullin T and Peixinho J 2006 J. Low Temp. Phys. 145 75-88
67. Nagata M 1990 J. Fluid Mech. 217 519-27
68. Peixinho J and Mullin T 2006 Phys. Rev. Lett. 96 094501 (4pp)
69. Peixinho J and Mullin T 2007 J. Fluid Mech. 582 169-78
70. Pfenniger W 1961 Boundary Layer and Flow Control ed G Lachman (Oxford: Pergamon) pp 970-80
71. Philip J, Svizher A and Cohen J 2007 Phys. Rev. Lett. 98 154502
72. Prandtl L and Tietjens O 1931 Hydro- und Aeromechanik (Berlin: Julius Springer)
73. Prigent A, Gregoire G, Chate H, Dauchot O and van Saarloos W 2002 Phys. Rev. Lett. 89 014501
74. Pringle C and Kerswell R R 2007 Phys. Rev. Lett. 99 074502
75. Reddy S C, Schmid P J and Henningson D S 1993 SIAM J. Appl. Math. 53 15-47
76. Rempel E L and Chian A C L 2003 Phys. Lett. A 319 104-9
77. Reynolds O 1883a Phil. Trans. R. Soc. (Lond.) 174 935-82 + 3 plates
78. Reynolds O 1883b Proc. R. Soc. (Lond.) 35 84-99
79. Rotta J 1956 Ing.-Arch. 24 258-81
80. Salwen H, Cotton F W and Grosch C E 1980 J. Fluid Mech. 98 273-84
81. Schmid P J and Henningson D S 1999 Stability and Transition of Shear Flows (New York: Springer)
82. Schmiegel A and Eckhardt B 1997 Phys. Rev. Lett. 79 5250-3
83. Schneider T M 2007 State space properties of transitional pipe flow PhD Thesis Philipps Universität Marburgm
84. Schneider T M and Eckhardt B 2006 Chaos 16 020604
85. Schneider T M, Eckhardt B and Vollmer J 2007 Phys. Rev. E 75 066313
86. Schneider T M, Eckhardt B and Yorke J A 2007 Phys. Rev. Lett. 99 034502
87. Schoepe W 2004 Phys. Rev. Lett. 92 095301
88. Skufca J D, Yorke J A and Eckhardt B 2006 Phys. Rev. Lett. 96 174101 (4pp)
89. Smith T R, Moehlis J and Holmes P 2005 J. Fluid Mech. 538 71-110
90. Tél T 1991 Directions in Chaos vol 3 ed H Bai-Lin et al (Singapore: World Scientific) p 149
91. Toh S and Itano T 2003 J. Fluid Mech. 481 67-76
92. Trefethen L N, Trefethen A E, Reddy S C and Driscoll T A 1993 Science 261 578-84
93. Viswanath D 2007a A Contemporary View: Abel Symposium 2006 (lesund) (Abel Symposia vol 3) (Berlin: Springer) (Math. Comput.) (Preprint 0701337)
94. Viswanath D 2007b J. Fluid Mech. 580 339-58
95. Vollmer J, Schneider T and Eckhardt B 2007 in preparation
96. Waleffe F 1995 Phys. Rev. Lett. 7 3060-6
97. Waleffe F 1997 Phys. Fluids 9 883-900
98. Waleffe F 1998 Phys. Rev. Lett. 81 4140-3
99. Waleffe F 2001 J. Fluid Mech. 435 93-102
100. Waleffe F 2003 Phys. Fluids 15 1517-34
101. Wang J, Gibson J and Waleffe F 2007 Phys. Rev. Lett. 98 204501
102. Wedin H and Kerswell R R 2004 J. Fluid Mech. 508 333-71
103. Willis A P and Kerswell R R 2007 Phys. Rev. Lett. 98 014501
104. Wygnanski I J and Champagne F H 1973 J. Fluid Mech. 59 281-335
105. Wygnanski I, Sokolov M and Friedman D 1975 J. Fluid Mech. 69 283-304