Stable manifolds and the transition to turbulence in pipe flow

Journal of Fluid Mechanics

Volumn 627, Issue , 2009, Pages 215-233

  Viswanath, D ^a   Cvitanovic P ^b  

^a UNIVERSITY OF MICHIGAN   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LAMINAR FLOW; NUMERICAL METHODS; PIPE FLOW; VELOCITY;

LAMINAR MOTION; STABLE MANIFOLD; TRANSITION TO TURBULENCE; TRAVELLING WAVES; TURBULENT STATE; VELOCITY FIELD;

SHEAR FLOW;

FLOW VELOCITY; LAMINAR FLOW; LAMINAR-TURBULENT TRANSITION; NUMERICAL METHOD; PIPE FLOW; SHEAR FLOW; TURBULENCE;

EID: 67651018527     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009006041     Document Type: Article

References (43)

1. CVITANOVIĆ, P., DAVIDMACK, R. L. & SIMINOS, E. 2007 State space geometry of a spatio-temporally chaotic Kuramoto-Sivashinsky flow. arXiv: 0709. 2944.
2. DARBYSHIRE, A. G. & MULLIN, T. 1995 Transition to turbulence in constant-mass-flux pipe flow. J. Fluid Mech. 289, 83-114.
3. DUGUET, Y., WILLIS, A. P. & KERSWELL, R. R. 2008 Transition in pipe flow: The saddle structure on the boundary of turbulence. J. Fluid Mech. 613, 255-274. arXiv: 0711. 2175.
4. ECKHARDT, B & SCHNEIDER, T. 2008 How does flow in a pipe become turbulent? Euro. Phys. J. B, 64, 457-462.
5. FAISST, H. & ECKHARDT, B. 2003. Traveling waves in pipe flow. Phys. Rev. Lett. 94, 224502.
6. FAISST, H & ECKHARDT, B. 2004 Sensitive dependence on initial conditions in transition to turbulence in pipe flow. J. Fluid Mech. 504, 343-352.
7. GIBSON, J. F., HALCROW, J. & CVITANOVIĆ, P. 2008 Visualizing the geometry of state space in plane Couette flow. J. Fluid Mech. 611, 107-130. arXiv: 0705.3957.
8. GILMORE,E, R & LETELLIER, C. 2007 The Symmetry of Chaos. Oxford University Press.
9. HALCROW, J., GIBSON, J. F., CVITANOVIC, P. & VISWANATH, D. 2009 Heteroclinic connections in plane Couette flow. J. Fluid Mech. 611, 365-376.
10. HOF, B., VAN DOORNE, C. W. H. et al. 2004 Experimental observation of nonlinear traveling waves in turbulent pipe flows. Science 305, 1594-1598.
11. HOF, B., JUEL, A. & MULLIN, T. 2003 Scaling of the turbulence transition threshold in a pipe. Phys. Rev. Lett. 91, 244502.
12. ITANO, T., & TOH, S. 2001 The dynamics of bursting process in wall turbulence. J. Phys. Soc Jpn 70, 701-714.
13. KAWAHARA, G. 2005 Laminarization of minimal plane Couette flow: going beyond the basin of attraction of turbulence. Phys. Fluids 17, 041702.
14. KERSWELL, R. R. 2005 Recent progress in understanding the transition to turbulence in a pipe. Nonlinearity 18, R17-R44.
15. KERSWELL, R. R. & TUTTY, O. R. 2007 Recurrence of travelling waves in transitional pipe flow. J. Fluid Mech. 584, 69-102.
16. KREISS, G., LUNDBLADH, A. & HENNINGSON, D. S. 1994 Bounds for threshold amplitudes in subcritical shear flows. J. Fluid Mech. 270, 175-198.
17. LANDAHL, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243-251.
18. MELLIBOVSKY, F. & MESEGUER, A. 2006 The role of streamwise perturbations in pipe flow transition. Phys. Fluids 18, 074104.
19. MELLIBOVSKY, F. & MESEGUER, A. 2007 Pipe flow transition threshold following localized impulsive perturbations. Phys. Fluids 19 044102.
20. NAGATA, M. 1990 Three dimensional finite amplitude solutions in plane Couette flow: Bifurcation from infinity. J. Fluid Mech. 217, 519-527.
21. NARASIMHA, R. 1989 The utility and drawbacks of traditional approaches. In Whither Turbulence? Turbulence at the Cross-Road (ed. J. Lumley), pp. 13-48. Springer.
22. O'SULLIVAN, P. L. & BREUER, K. S. 1994 Transient growth in circular pipe flow. Part 2. Nonlinear development. Phys. Fluids 6, 3652-3664.
23. PEIXINHO, J. & MULLIN, T. 2007 Finite-amplitude thresholds for transition in pipe flow. J. Fluid Mech. 582, 169-178.
24. PRINGLE, C. C. T. & KERSWELL, R. R. 2007 Asymmetric, helical, and mirror-symmetric traveling waves in pipe flow. Phys. Rev. Lett. 99, 074502.
25. 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.
26. ROBINSON, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601-639.
27. SCHMIEGEL, A. & ECKHARDT, B. 1997 Fractal stability border in plane Couette flow. Phys. Rev. Lett. 79, 5250.
28. SCHNEIDER, T. M., ECKHARDT, B. & VOLLMER, J. 2007a Statistical analysis of coherent structures in transitional pipe flow. Phys. Rev. E 75, 066313.
29. SCHNEIDER, T. M., ECKHARDT, B. & YORKE, J. A. 2007b Turbulence transition and edge of chaos in pipe flow. Phys. Rev. Lett. 99, 034502.
30. SCHNEIDER, T. M., GIBSON, J. E, LAGHA, M., DE LILLO, F. & ECKHARDT, B. 2008 Laminar-turbulent boundary in plane Couette flow. Phys. Rev. E 78, 037301. arXiv: 0805. 1015.
31. TOH, S. & ITANO, T. 2003 A periodic-like solution in channel flow. J. Fluid Mech. 481, 67-76.
32. TREFETHEN, L. N. 2000 Spectral Methods in Matlab. SIAM.
33. VISWANATH, D. 2007 Recurrent motions within plane Couette turbulence. J. Fluid Mech. 580, 339-358.
34. VISWANATH, D. 2008a The critical layer in pipe flow at high Re. Phil Trans. R. Soc. A. 367, 561-576.
35. VISWANATH, D. 2008b The dynamics of transition to turbulence in plane Couette flow. In Mathematics and Computation, a Contemporary View: The Abel Symposium 2006 (H. Munthe-Kaas & B. Owren), vol. 3, pp. 109-127. Springer. arXiv: 0701337.
36. WALEFFE, F. 1998 Three-dimensional coherent states in plane shear flows. Phys. Rev. Lett. 81, 4140-4143.
37. WANG, J., GIBSON, J. F. & WALEFFE, F. 2007 Lower branch coherent states in shear flows: Transition and control. Phys. Rev. Lett. 98, 204501.
38. WEDIN, H. & KERSWELL, R. R. 2004 Exact coherent structures in pipe flow: Travelling wave solutions. J. Fluid Mech. 508, 333-371.
39. WILLIS, A. P. & KERSWELL, R. R. 2008 Coherent structures in localised and global pipe turbulence. Phys. Rev. Lett. 100, 124501.
40. WILLIS, A. P. & KERSWELL, R. R. 2009 Turbulent dynamics of pipe flow captured in a reduced model: Puff relaminarisation and localised 'edge' states. J. Fluid Mech. 619, 213-233.
41. WILLIS, A. P., PEIXINHO, J., KERSWELL, R. R. & MULLIN, T. 2008 Experimental and theoretical progress in pipe flow transition. Phil. Trans. R. Soc. A, 366, 2671-2684.
42. WYGNANSKI, I. J. & CHAMPAGNE, F. H. 1973 On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech., 59, 281-335.
43. WYGNANSKI, I., SOKOLOV, M. & FRIEDMAN, D. 1975 On transition in a pipe. Part 2. The equilibrium puff. J. Fluid Mech. 69, 283-304.