Amplification of coherent streaks in the turbulent Couette flow: An inputoutput analysis at low Reynolds number

Journal of Fluid Mechanics

Volumn 643, Issue , 2010, Pages 333-348

  Hwang, Yongyun ^a   Cossu, Carlo ^a  

^a ECOLE POLYTECHNIQUE   (France)

Author keywords

Large scale structures; Optimal perturbations; Streaks; Turbulent flows

Indexed keywords

BUFFER LAYERS; REYNOLDS EQUATION; REYNOLDS NUMBER; STOCHASTIC SYSTEMS; TURBULENT FLOW;

COHERENT PERTURBATION; EXPERIMENTAL REALIZATIONS; INPUT OUTPUT ANALYSIS; LARGE SCALE STRUCTURES; OPTIMAL PERTURBATION; SENSITIVITY TO BOUNDARY CONDITIONS; STREAKS; TURBULENT COUETTE FLOWS;

STRUCTURAL OPTIMIZATION;

BOUNDARY CONDITION; FLOW STRUCTURE; INPUT-OUTPUT ANALYSIS; REYNOLDS NUMBER; STOCHASTICITY; TURBULENT FLOW; VISCOSITY; VORTICITY;

EID: 76349123372     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112009992151     Document Type: Article

References (54)

1. del Á lam o, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15, L41
2. del Á lam o, J. C. & Jiménez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205-213.
3. Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. 2001 On the breakdown of boundary layers streaks. J. Fluid Mech. 428, 29-60.
4. Bamieh, B. & Dahleh, M. 2001 Energy amplification in channel flows with stochastic excitation. Phys. Fluids 13, 3258-3269.
5. Butler, K. M. & Farrell, B. F. 1992 Three-dimensional optimal perturbations in viscous shear flow. Phys. Fluids A 4, 1637-1650.
6. Butler, K. M. & Farrell, B. F. 1993 Optimal perturbations and streak spacing in wall-bounded turbulent shear flow. Phys. Fluids 5, 774-777.
7. Cossu, C. & Brandt, L. 2002 Stabilization of Tollmien-Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer. Phys. Fluids 14, L57-L60.
8. Cossu, C., Pujals, G. & Depardon, S. 2009 Optimal transient growth and very large scale structures in turbulent boundary layers. J. Fluid Mech. 619, 79-94.
9. Ellingsen, T. & Palm, E. 1975 Stability of linear flow. Phys. Fluids 18, 487-488.
10. Farrell, B. F. & Ioannou, P. J. 1993a Optimal excitation of three-dimensional perturbations in viscous constant shear flow. Phys. Fluids 5, 1390-1400.
11. Farrell, B. F. & Ioannou, P. J. 1993b Stochastic forcing of the linearized Navier-Stokes equation. Phys. Fluids A 5, 2600-2609.
12. Farrell, B. F. & Ioannou, P. J. 1996 Generalized stability theory. J. Atmos. Sci. 53, 2025-2053.
13. Farrell, B. F. & Ioannou, P. J. 1998 Perturbation structure and spectra in turbulent channel flow. Theor. Comput. Fluid Dyn. 11, 237-250.
14. Fontane, J., Brancher, P. & Fabre, D. 2008 Stochastic forcing of the Lamb-Oseen vortex. J. Fluid Mech. 613, 233-254.
15. Fransson, J., Talamelli, A., Brandt, L. & Cossu, C. 2006 Delaying transition to turbulence by a passive mechanism. Phys. Rev. Lett. 96, 064501.
16. Gibson, J. F., Halcrow, J. & Cvitanovic, P. 2008 Visualizing the geometry of state space in plane Couette flow. J. Fluid Mech. 611, 107-130.
17. Gustavsson, L. H. 1991 Energy growth of three-dimensional disturbances in plane Poiseuille flow. J. Fluid Mech. 224, 241-260.
18. Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317-348.
19. Ho, C. M. & Huerre, P. 1984 Perturbed shear layers. Annu. Rev. Fluid Mech. 16, 365-424.
20. Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1-28.
21. Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. A 365, 647-664.
22. Jang, P. S., Benney, D. J. & Gran, D. L. 1986 On the origin of streamwise vortices in a turbulent boundary layer. J. Fluid Mech. 169, 109-123.
23. Jiménez, J. 2007 Recent developments on wall-bounded turbulence. Rev. R. Acad. Cien. Ser. A Mat. 101, 187-203.
24. Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213-240.
25. Jovanović, M. R. & Bamieh, B. 2005 Componentwise energy amplification in channel flow. J. Fluid Mech. 543, 145-183
26. Kim, K. C. & Adrian, R. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417-422.
27. Kitoh, O., Nakabayashi, K. & Nishimura, F. 2005 Experimental study on mean velocity and turbulence characteristics of plane Couette flow: low-Reynolds-number effects and large longitudinal vortical structures. J. Fluid Mech. 539, 199.
28. Kitoh, O. & Umeki, M. 2008 Experimental study on large-scale streak structure in the core region of turbulent plane Couette flow. Phys. Fluids 20, 025107.
29. Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741-773.
30. Komminaho, J., Lundbladh, A. & Johansson, A. V. 1996 Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, 259-285.
31. Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243-251.
32. Landahl, M. T. 1990 On sublayer streaks. J. Fluid Mech. 212, 593-614.
33. Lee, M. J. & Kim, J. 1991 The structure of turbulence in a simulated plane Couette flow. In Eighth Symp. on Turbulent Shear Flow, pp. 5.3.1-5.3.6. Technical University of Munich, Munich, Germany.
34. Moffatt, H. K. 1967 The interaction of turbulence with strong wind shear. In Proceedings of URSI-IUGG Colloquium on Atomspheric Turbulence and Radio Wave Propagation (ed. A. M. Yaglom & V. I. Tatarsky), pp. 139-154. Nauka.
35. Moin, P. & Kim, J. 1982 Numerical investigation of turbulent channel flow. J. Fluid Mech. 118, 341-377.
36. Pujals, G., Garćia-Villalba, M., Cossu, C. & Depardon, S. 2009 A note on optimal transient growth in turbulent channel flows. Phys. Fluids 21, 015109.
37. Reddy, S. C. & Henningson, D. S. 1993 Energy growth in viscous channel flows. J. Fluid Mech. 252, 209-238.
38. Reddy, S. C., Schmid, P. J., Baggett, J. S. & Henningson, D. S. 1998 On the stability of streamwise streaks and transition thresholds in plane channel flows. J. Fluid Mech. 365, 269-303.
39. Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (02), 263-288.
40. Schmid, P. J. 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129-162.
41. Schmid, P. J. & Henningson, D. S. 1994 Optimal energy density growth in Hagen-Poiseuille flow. J. Fluid Mech. 277, 197-225.
42. Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.
43. Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57-108.
44. Smith, J. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27-54.
45. Tillmark, N. 1995 Experiments on transition and turbulence in plane Couette flow. PhD thesis, Department of Mechanics, Royal Institute of Technology (KTH), Stockholm.
46. Tillmark, N. & Alfredsson, H. 1994 Structures in turbulent plane Couette flow obtained from correlation measurements. In Advances in Turbulences V (ed. R. Benzi), pp. 502-507. Kluwer.
47. Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37-74.
48. Tomkins, C. D. & Adrian, R. J. 2005 Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer. J. Fluid Mech. 545, 141-162.
49. Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A. 1993 A new direction in hydrodynamic stability: beyond eigenvalues. Science 261, 578-584.
50. Tsukahara, T., Iwamoto, K. & Kawamura, H. 2007 POD analysis of large-scale structures through DNS of turbulence Couette flow. In Advances in Turbulence XI (ed. J. M. L. M. Palma & A. Silva Lopes) pp. 245-247. Springer.
51. Tsukahara, T., Kawamura, H. & Shingai, K. 2006 DNS of turbulent Couette flow with emphasis on the large-scale structure in the core region. J. Turbul. 7, 19.
52. Waleffe, F. 1995 Hydrodynamic stability and turbulence: beyond transients to a self-sustaining process. Stud. Appl. Math. 95, 319-343.
53. Weideman, J. A. C. & Reddy, S. C. 2000 A MATLAB differentiation matrix suite. ACM Trans. Math. Softw. 26, 465-519.
54. Zhou, K., Doyle, J. C. & Glover, K. 1996 Robust and Optimal Control. Prentice Hall.