Exact coherent structures in pipe flow: Travelling wave solutions

Journal of Fluid Mechanics

Volumn 508, Issue , 2004, Pages 333-371

  Wedin, H ^a   Kerswell, R R ^a  

^a UNIVERSITY OF BRISTOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); REYNOLDS NUMBER; SHEAR FLOW;

COHERENT STRUCTURES; GOVERNING EQUATIONS; TRAVELING WAVES;

PIPE FLOW;

BIFURCATION; MATHEMATICAL ANALYSIS; PIPE FEEDER; PIPE FLOW; PRESSURE; STRUCTURAL ANALYSIS; THREE-DIMENSIONAL FLOW; WAVE;

EID: 2942685048     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112004009346     Document Type: Article

References (63)

1. ANSON, D. K., MULLIN, T. & CLIFFE, K. A. 1989 A numerical and experimental investigation of a new solution in the Taylor vortex problem. J. Fluid Mech. 207, 475-489.
2. BARNES, D. R. & KERSWELL, R. R. 2000 New results in rotating Hagen-Poiseuille flow. J. Fluid Mech. 417, 103-126.
3. BENNEY, D. J. 1984 The evolution of disturbances in shear flows at high Reynolds numbers. Stud. Appl. Maths 70, 1-19.
4. BERGSTRÖM, L. 1993 Optimal growth of small disturbances in pipe Poiseuille flow. Phys. Fluids 5, 2710-2720.
5. BOBERG, L. & BROSA, U. 1988 Onset of turbulence in a pipe. Z. Naturforsch 43, 697-726.
6. BOTTIN, S., DAUCHET, O., DAVIAUD, F. & MANNEVILLE, P. 1998 Experimental evidence of streamwise vortices as finite amplitude solutions in transitional plane Couette flow. Phys. Fluids 10, 2597-2607.
7. CARLSON, D. R., WIDNALL, S. E. & PEETERS, M. F. 1982 A flow-visualization study of transition in plane Poiseuille flow. J. Fluid Mech. 121, 487-505.
8. CHAPMAN, S. J. 2002 Subcritical transition in channel flows. J. Fluid Mech. 451, 35-97.
9. CLEVER, R. M. & BUSSE, F. H. 1992 Three-dimensional convection in a horizontal fluid layer subjected to a constant shear. J. Fluid Mech. 234, 511-527.
10. CLEVER, R. M. & BUSSE, F. H. 1997 Tertiary and quaternary solutions for plane Couette flow. J. Fluid Mech. 344, 137-153.
11. DARBYSHIRE, A. G. & MULLIN, T. 1995 Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83-114.
12. DAUCHOT, O. & DAVIAUD, F. 1995 Finite amplitude perturbation and spots growth mechanism in plane Couette flow. Phys. Fluids 7, 335-343.
13. DAVEY, A. & NGUYEN, H. P. F. 1971 Finite-amplitude stability of pipe flow. J. Fluid Mech. 45, 701-720.
14. DAVIAUD, F., HEGSETH, J. & BERGÉ, P. 1992 Subcritical transition to turbulence in plane Couette flow. Phys. Rev. Lett. 69, 2511-2514.
15. DAVIES, S. J. & WHITE, C. M. 1928 An experimental study of the flow of water in pipes of rectangular section. Proc. R. Soc. Land. A 119, 92-107.
16. DRAAD, A. A., KUIKEN, G. D. C. & NIEUWSTADT, F. T. M. 1998 Laminar-turbulent transition in pipe flow for Newtonian and non-Newtonian fluids. J. Fluid Mech. 377, 267-312.
17. ECKHARDT, B., FAISST, H., SCHMIEGEL, A. & SCHUMACHER, J. 2002 Turbulence transition in shear flows. Advances in Turbulene IX: Proc. Ninth European Turbulence Conference, Barcelona (ed. I. P. Castro, P. E. Hancock & T. G. Thomas) pp. 701-708. ISBN 84-95999-07-2.
18. ELIAHOU, S., TUMIN, A. & WYGNANSKI, I. 1998 Laminar-turbulent transition in Poiseuille pipe flow subjected to periodic perturbation emanating from the wall. J. Fluid Mech. 361, 333-349.
19. FAISST, H. & ECKHARDT, B. 2000 Transition from the Couette-Taylor system to the plane Couette system. Phys. Rev. E 61, 7227-7230.
20. FAISST, H. & ECKHARDT, B. 2003 Travelling waves in pipe flow. Phys. Rev. Lett. 91, art. 224502.
21. GARG, V. K. & ROULEAU, W. T. 1972 Linear stability of pipe Poiseuille flow. J. Fluid Mech. 54, 113-127.
22. HAMILTON, J. M., KIM, J. & WALEFFE, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317-348.
23. HAN, G., TUMIN, A. & WYGNANSKI, I. 2000 Laminar-turbulent transition in Poisenille pipe flow subjected to periodic perturbation emanating from the wall. Part 2. Late stage of transition. J. Fluid Mech. 419, 1-27.
24. HERRON, I. H. 1991 Observations on the role of vorticity on the stability of wall bounded flows. Stud. Appl. Maths 85, 269-286.
25. HOF, B., JUEL, A. & MULLIN, T. 2003 Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, art. 244502.
26. JOSEPH, D. D. & CARML, S. 1969 Stability of Poiseuille flow in pipes, annuli and channels. Q. Appl. Maths 26, 575-599.
27. KEEFE, L., MOIN, P. & KIM, J. 1992 The dimension of attractors underlying periodic turbulent Poiseuille flow. J. Fluid Mech. 242, 1-29.
28. KERSWELL, R. R. & DAVEY, A. 1996 On the linear instability of elliptic pipe flow. J. Fluid Mech. 316, 307-324.
29. LANDMAN, M. J. 1990a On the generation of helical waves in circular pipe flow. Phys. Fluids A 2, 738-747.
30. LANDMAN, M. J. 1990b Time-dependent helical waves in rotating pipe flow. J. Fluid Mech. 221, 289-310.
31. LESSEN, M., SADLER, G. S. & LIU, T.-Y. 1968 Stability of pipe Poiseuille flow. Phys. Fluids 11, 1404-1409.
32. LUNDBLADH, A. & JOHANSSON, A. V. 1991 Direct simulation of turbulent spots in plane Couette flow. J. Fluid Mech. 229, 499-516.
33. 7. J. Comput. Phys. 186, 178-197.
34. NAGATA, M. 1990 Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech. 217, 519-527.
35. NAGATA, M. 1997 Three-dimensional traveling-wave solutions in plane Couette flow. Phys. Rev. E 55, 2023-2025.
36. NAGATA, M. 1998 Tertiary solutions and their stability in rotating plane Couette flow. J. Fluid Mech. 358, 357-378.
37. O'SULLIVAN, P. L. & BREUER, K. S. 1994 Transient growth in a circular pipe flow. II. Nonlinear development. Phys. Fluids 6, 3652-3662.
38. PATERA, A. T. & ORSZAG, S. A. 1981 Finite-amplitude stability of axisymmetric pipe flow. J. Fluid Mech. 112, 467-474.
39. REDDY, S. C., SCHMID, P. J., BAGGETT, J. S. & HENNINGSON, D. S. 1998 On stability of streamwise streaks and transition thresholds in plane channel flows. J. Fluid Mech. 365, 269-303.
40. REYNOLDS, O. 1883 An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous and of the law of resistance in parallel channels. Phil. Trans, R. Soc. Lond. 174, 935-982.
41. RHEINBOLDT, W. C. & BURKARDT, J. V. 1983a A locally parameterized continuation process. ACM Trans. Math. Software 9, 215-235.
42. RHEINBOLDT, W. C. & BURKARDT, J. V. 1983b ALGORITHM 596 A program for a locally parameterized continuation process. ACM Trans. Math, Software 9, 236-241.
43. RUMANOV, V. A. 1973 Stability of plane-parallel Couette flow. Functional Anal. Applics. 7, 137-146.
44. 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.
45. SALWEN, H., COTTEN, F. W. & GROSCH, C. E. 1980 Linear stability of Poiseuille flow in a circular pipe. J. Fluid Mech. 98, 273-284.
46. SCHLICHTING, H. 1968 Boundary-Layer Theory. McGraw-Hill.
47. SCHMID, P. J. & HENNINGSON, D. S. 1994 Optimal energy density growth in Hagen-Poiseuille flow. J. Fluid Mech. 277, 197-225.
48. SCHMIEGEL, A. & ECKHARDT, B. 1997 Fractal stability border in plane Couette flow. Phys. Rev. Lett. 79, 55250-5253.
49. SMITH, F. T & BODONYI, R. J. 1982 Amplitude-dependent neutral modes in the Hagen-Poiseuille flow through a circular pipe. Proc. R. Soc. Lond. A 384, 463-489.
50. TILLMARK, N. & ALFREDSSON, P. H. 1992 Experiments on transition in plane Couette flow. J. Fluid Mech. 235, 89-102.
51. TOPLOSKY, N. & AKYLAS, T. R. 1988 Nonlinear spiral waves in rotating pipe flow. J. Fluid Mech. 190, 39-54.
52. WALEFFE, F. 1995a Hydrodynamic stability and turbulence: Beyond transients to a self-sustaining process. Stud. Appl. Maths 95, 319-343.
53. WALEFFE, F. 1995b Transition in shear flows: Nonlinear normality versus non-normal linearity. Phys. Fluids 7, 3060-3066.
54. WALEFFE, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883-900.
55. WALEFFE, F. 1998 Three-dimensional coherent states in plane shear flows. Phys. Rev. Lett. 81, 4140-4143.
56. WALEFFE, F. 2001 Exact coherent structures in channel flow. J. Fluid Mech. 435, 93-102.
57. WALEFFE, F. 2003 Homotopy of exact coherent structures in plane shear flows. Phys. Fluids 15, 1517-1534.
58. WALEFFE, F. & KIM, J. 1997 How streamwise rolls and streaks self-sustain in a shear flow. Self- Sustaining Mechanisms of Wall Turbulence (ed. R. L. Panton), pp. 385-422. Computational Mechanics, Southampton.
59. WALEFFF, F. & KIM, J. 1998 How streamwise rolls and streaks self-sustain in a shear flow: Part 2. AIAA Paper 98-2997.
60. WALTON, A. G. 2002 The temporal evolution of neutral modes in impulsively started flow through a circular pipe and their connection to the nonlinear stability of Hagen-Poiseuille flow. J. Fluid Mech. 457, 339-376.
61. WYGNANSKI, I. J & CHAMPAGNE, F. H. 1973 On transition in a pipe. Part 1. The origin of puffs and slags and the flow in a turbulent slug. J. Fluid Mech. 59, 281-351.
62. WYGNANSKI, I. J, SOKOLOV, M. & FRIEDMAN, D. 1975 On transition in a pipe. Part 2. The equilibrium puff. J. Fluid Mech. 69, 283-304.
63. ZIKANOV, O. Y. 1996 On the instability of pipe Poiseuille flow. Phys. Fluids 8, 2923-2932.