Coherent flow states in a square duct

Physics of Fluids

Volumn 20, Issue 9, 2008, Pages

  Håkan, Wedin ^a   Biau, Damien ^a,c   Bottaro, Alessandro ^a   Nagata, Masato ^b  

^a UNIVERSITY OF GENOA   (Italy)

^b KYOTO UNIVERSITY   (Japan)

^c UNIVERSITÉ DE POITIERS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

PHASE SPACE METHODS; REYNOLDS NUMBER;

CHAOTIC SADDLES; FINITE AMPLITUDE; FLOW STATE; INITIAL CONDITIONS; MODERATE REYNOLDS NUMBERS; PROCESS APPROACH; SQUARE DUCTS; TRAVELING WAVE SOLUTION;

DUCTS;

EID: 53549125551     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2978357     Document Type: Article

References (52)

1. O. Reynolds, "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," Philos. Trans. R. Soc. London PTRSAV0370-231610.1098/rstl.1883.0029 174, 935 (1883).
2. M. J. Lee, J. Kim, and P. Moin, "Structure of turbulence at high shear rates," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112090000532 216, 561 (1990).
3. F. Waleffe, "On a self-sustaining process in shear flows," Phys. Fluids PHFLE61070-663110.1063/1.869185 9, 883 (1997).
4. G. Hagen, "Uber die bewegung des wassers in engen zylidrischen rohren," Ann. Phys. Chem. ANPYA20003-380410.1002/andp.18391220304 46, 423 (1839).
5. J. Poiseuille, "Recherches expérimentales sur le mouvement des liquides dans les tubes de trés petits diamétres," Compt. Rend. COREAF0001-4036 11, 961 (1840); J. Poiseuille, Compt. Rend.COREAF0001-403612, 112 (1841); J. Poiseuille, Compt. Rend. COREAF0001-40369, 433 (1846).
6. T. Sexl, "Zur stabilitatsfrage der Poiseuilleschen and Couetteschen stromung," Ann. Phys. ANPYA20003-380410.1002/andp.19273881405 83, 835 (1927).
7. T. Sexl, "Uber dreidimensionale storungen der Poiseuilleschen stromung," Ann. Phys. ANPYA20003-380410.1002/andp.19273892208 84, 807 (1927).
8. P. J. Schmid and D. S. Henningson, "Optimal energy density growth in Hagen-Poiseuille flow," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112094002739 277, 197 (1994).
9. G. M. Corcos and J. R. Sellars, "On the stability of fully developed flow in a pipe," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112059000088 5, 97 (1959).
10. A. Davey and P. G. Drazin, "The stability of Poiseuille flow in a pipe," J. Fluid Mech. JFLSA70022-112010.1017/S0022112069001613 36, 209 (1969).
11. A. Meseguer and L. N. Trefethen, "Linearized pipe flow to Reynolds number 107," J. Comput. Phys. JCTPAH0021-999110.1016/ S0021-9991(03)00029-9 186, 178 (2003).
12. A. G. Darbyshire and T. Mullin, "Transition to turbulence in constant-mass-flux pipe flow," J. Fluid Mech. JFLSA70022-112010.1017/S0022112095001248 289, 83 (1995).
13. B. Hof, A. Juel, and T. Mullin, "Scaling of the turbulence transition threshold in a pipe," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.91.244502 91, 244502 (2003).
14. J. Peixinho and T. Mullin, "Decay of turbulence in pipe flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.96.094501 96, 094501 (2006).
15. J. Peixinho and T. Mullin, "Recent observations in the transition to turbulence in a pipe," in Proceedings of the IUTAM Symposium on Laminar-Turbulent Transition, edited by R. Govindarajan (Springer, Bangalore, 2006), p. 45.
16. I. Gavarini, A. Bottaro, and F. T. M. Nieuwstadt, "The initial stage of transition in cylindrical pipe flow: Role of optimal base-flow distortions," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112004000825 517, 131 (2004).
17. T. Tatsumi and T. Yoshimura, "Stability of the laminar flow in a rectangular duct," J. Fluid Mech. JFLSA70022-112010.1017/ S002211209000204X 212, 437 (1990).
18. V. Theofilis, P. W. Duck, and J. Owen, "Viscous linear stability analysis of rectangular duct and cavity flows," J. Fluid Mech. JFLSA70022-112010.1017/S002211200400850X 505, 249 (2004).
19. M. Uhlmann and M. Nagata, "Linear stability of flow in an internally heated rectangular duct," J. Fluid Mech. JFLSA70022-112010.1017/S0022112005008487 551, 387 (2006).
20. B. Galletti and A. Bottaro, "Large-scale secondary structures in duct flow," J. Fluid Mech. JFLSA70022-112010.1017/S0022112004009966 512, 85 (2004).
21. A. Bottaro, H. Soueid, and B. Galletti, "Formation of secondary vortices in turbulent square-duct flow," AIAA J. AIAJAH0001-145210.2514/1.17327 44, 803 (2006).
22. J. Jimenez, "Coherent structures and dynamical systems," in Proceedings of the 1987 Summer Program of Center for Turbulence Research (Stanford University, Stanford, CA, 1987), Paper No. SEE N88-23086 16-34, pp. 323-324.
23. H. Wedin, "Nonlinear solutions to pipe flow," Ph.D. thesis, University of Bristol, 2004.
24. H. Wedin and R. R. Kerswell, "Exact coherent structures in pipe flow: Travelling wave solutions," J. Fluid Mech. JFLSA70022-112010.1017/S0022112004009346 508, 333 (2004).
25. R. R. Kerswell, "Recent progress in understanding the transition to turbulence in a pipe," Nonlinearity NONLE50951-771510.1088/ 0951-7715/18/6/R01 18, R17 (2005).
26. H. Faisst and B. Eckhardt, "Travelling waves in pipe flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.91.224502 91, 224502 (2003).
27. B. Hof, C. W. H. van Doorne, J. Westerweel, F. T. M. Nieuwstadt, H. Faisst, B. Eckhardt, H. Wedin, R. R. Kerswell, and F. Waleffe, "Experimental observation of nonlinear traveling waves in turbulent pipe flow," Science SCIEAS0036-807510.1126/science.1100393 305, 1594 (2004).
28. B. Hof, C. W. H. van Doorne, J. Westerweel, and F. T. M. Nieuwstadt, "Turbulence regeneration in pipe flow at moderate Reynolds numbers," Phys. Rev. Lett. PRLTAO0031-900710.1103/ PhysRevLett.95.214502 95, 214502 (2005).
29. I. J. Wygnanski and F. H. Champagne, "On transition in a pipe. Part 1. The origin of puffs and slugs and the flow in a turbulent slug," J. Fluid Mech. JFLSA70022-112010.1017/S0022112073001576 59, 281 (1973).
30. I. J. Wygnanski, M. Sokolov, and D. Friedman, "On transition in a pipe. Part 2. The equilibrium puff," J. Fluid Mech. JFLSA70022-112010.1017/S0022112075001449 69, 283 (1975).
31. F. Waleffe, "Homotopy of exact structures in plane shear flows," Phys. Fluids PHFLE61070-663110.1063/1.1566753 15, 1517 (2003).
32. G. Kawahara and S. Kida, "Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst," J. Fluid Mech. JFLSA70022-112010.1017/S0022112001006243 449, 291 (2001).
33. R. R. Kerswell and O. R. Tutty, "Recurrence of travelling waves in transitional pipe flow," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112007006301 584, 69 (2007).
34. H. Faisst and B. Eckhardt, "Sensitivity dependence on initial conditions in transition to turbulence in pipe flow," J. Fluid Mech. JFLSA70022-112010.1017/S0022112004008134 504, 343 (2004).
35. A. P. Willis and R. R. Kerswell, "Critical behaviour in the relaminarization of localized turbulence in pipe flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.98.014501 98, 014501 (2007).
36. B. Hof, J. Westerweel, T. M. Schneider, and B. Eckhardt, "Finite lifetime of turbulence in shear flows," Nature (London) NATUAS0028-083610.1038/nature05089 443, 59 (2006).
37. B. Eckhardt, T. M. Schneider, B. Hof, and J. Westerweel, "Turbulence transition in pipe flow," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fluid.39.050905.110308 39, 447 (2007).
38. M. Nagata, "Three-dimensional finite amplitude solutions in plane Couette flow: Bifurcation from infinity," J. Fluid Mech. JFLSA70022-112010.1017/S0022112090000829 217, 519 (1990).
39. N. Tillmark and H. Alfredsson, "Experiments on transition in plane Couette flow," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112092001046 235, 89 (1992).
40. S. Bottin, O. Dauchot, F. Daviaud, and P. Manneville, "Experimental evidence of streamwise vortices as finite amplitude solutions in transitional plane Couette flow," Phys. Fluids PHFLE61070-663110.1063/1.869773 10, 2597 (1998).
41. O. Dauchot and F. Daviaud, "Finite amplitude perturbation and spots growth mechanism in plane Couette flow," Phys. Fluids PHFLE61070-663110.1063/1.868631 7, 335 (1995).
42. A. Lundbladh and A. V. Johansson, "Direct simulation of turbulent spots in plane Couette flow," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112091003130 229, 499 (1991).
43. D. Viswanath, "Recurrent motions within plane Couette turbulence," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112007005459 580, 339 (2007).
44. C. Pringle and R. R. Kerswell, "Asymmetric, helical and mirror-symmetric travelling waves in pipe flow," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.99.074502 99, 074502 (2007).
45. J. Wang, J. Gibson, and F. Waleffe, "Lower branch coherent states in shear flows: Transition and control," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.98.204501 98, 204501 (2007).
46. S. Gavrilakis, "Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct," J. Fluid Mech. JFLSA70022-112010.1017/S0022112092002982 244, 101 (1992).
47. M. Uhlmann, A. Pinelli, G. Kawahara, and A. Sekimoto, "Marginally turbulent flow in a square duct," J. Fluid Mech. JFLSA70022-112010.1017/S0022112007007604 588, 153 (2007).
48. A. Huser and S. Biringen, "Direct numerical simulation of turbulent flow in a square duct," J. Fluid Mech. JFLSA70022-112010.1017/ S002211209300299X 257, 65 (1993).
49. F. B. Gessner, "The origin of secondary flow in turbulent flow along a corner," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112073002090 58, 1 (1973).
50. D. Biau, H. Soueid, and A. Bottaro, "Transition to turbulence in duct flow," J. Fluid Mech. JFLSA70022-112010.1017/S0022112007009536 596, 133 (2008).
51. F. Waleffe, "Three-dimensional coherent states in plane shear flows," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.81.4140 81, 4140 (1998).
52. S. J. Kline, W. C. Reynolds, F. A. Schraub, and P. W. Runstadler, "The structure of turbulent boundary layers," J. Fluid Mech. JFLSA70022-112010.1017/S0022112067001740 30, 741 (1967).