Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow

Journal of Fluid Mechanics

Volumn 708, Issue , 2012, Pages 149-196

  Farrell, Brian F ^a   Ioannou, Petros J ^b  

^a HARVARD UNIVERSITY   (United States)

^b UNIVERSITY OF ATHENS   (Greece)

Author keywords

parametric instability; transition to turbulence; turbulent transition

Indexed keywords

ATMOSPHERIC BOUNDARY LAYER; ATMOSPHERIC THERMODYNAMICS; DYNAMICAL SYSTEMS; NONLINEAR DYNAMICAL SYSTEMS; REYNOLDS EQUATION; REYNOLDS NUMBER; STABILITY; STOCHASTIC MODELS; STOCHASTIC SYSTEMS; TURBULENCE MODELS; TURBULENT FLOW;

LABORATORY EXPERIMENTS; MINIMAL REPRESENTATION; PARAMETRIC INSTABILITIES; STOCHASTIC TURBULENCE MODEL; STRUCTURAL STABILITIES; TRANSITION TO TURBULENCE; TURBULENT TRANSITION; WALL-BOUNDED SHEAR FLOW TURBULENCES;

SHEAR FLOW;

COUETTE FLOW; LAMINAR-TURBULENT TRANSITION; NUMERICAL MODEL; REYNOLDS NUMBER; SHEAR FLOW; STOCHASTICITY; STREAMFLOW; SUPERCRITICAL FLOW; TURBULENCE; TURBULENT FLOW;

EID: 84866635596     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2012.300     Document Type: Article

References (97)

1. ADRIAN, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.
2. ALFREDSSON, P. H. & MATSUBARA, M. 1996 Streaky structures in transition. In Proc. Transitional Boundary Layers in Aeronautics (ed. R. A. W. M. Henkes & J. L. van Ingen). pp. 373-386. Royal Netherlands Academy of Arts and Sciences. Elsevier.
3. ANDERSSON, P., BERGGREN, M. & HENNINGSON, D. S. 1999 Optimal disturbances and bypass transition in boundary layers. Phys. Fluids 11, 134-150.
4. ANDERSSON, P., BRANDT, L., BOTTARO, A. & HENNINGSON, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29-60.
5. BAKAS, N. A. & IOANNOU, P. J. 2011 Structural stability theory of two-dimensional fluid flow under stochastic forcing. J. Fluid Mech. 682, 332-361.
6. BAKCHINOV, A. A., KATASONOV, M. M. & KOZLOV, V. V. 1997 Experimental study of localized disturbances and their development in a flat plate boundary layer. Preprint No. l-97, ITAM, Russian Academy of Sciences, Novosibirsk, Russia (in Russian).
7. BAMIEH, B. & DAHLEH, M. 2001 Energy amplification in channel flows with stochastic excitation. Phys. Fluids 13, 3258-3269.
8. BATCHELOR, G. K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.
9. BENNEY, D. J. 1960 A nonlinear theory for oscillations in a parallel flow. J. Fluid Mech. 10 (02), 209-236.
10. BENNEY, D. J. 1984 The evolution of disturbances in shear flows at high Reynolds numbers. Stud. Appl. Maths 70 (02), 1-19.
11. BERKOOZ, G., HOLMES, P. & LUMLEY, J. L. 1993 The proper orthogonal decomposition in the analysis of turbulent flows. Annu. Rev. Fluid Mech. 25 (1), 539-575.
12. BERLIN, S. & HENNINGSON, D. S. 1999 A nonlinear mechanism for receptivity of free stream disturbances. Phys. Fluids 11 (02), 3749-3760.
13. BEWLEY, T. R. & LIU, S. 1998 Optimal and robust control and estimation of linear paths to transition. J. Fluid Mech. 365, 23-57.
14. BRANDT, L., HENNINGSON, D. S. & PONZIANI, D. 2002 Weakly nonlinear analysis of boundary layer receptivity to free stream disturbances. Phys. Fluids 14, 1426-1441.
15. BRANDT, L., SCHLATTER, P. & HENNINGSON, D. S. 2004 Transition in boundary layers subject to free stream turbulence. J. Fluid Mech. 517, 167-198.
16. BUTLER, K. M. & FARRELL, B. F 1992 Three-dimensional optimal perturbations in viscous shear flows. Phys. Fluids 4, 1637-1650.
17. CHAPMAN, S. J. 2002 Subcritical transition in channel flows. J. Fluid Mech. 451, 35-97.
18. COSSU, C. & BRANDT, L. 2002 Stabilization of Tollmien-Schlichting waves by finite amplitude optimal streaks in the Blasius boundary layer. Phys. Fluids 14 (8), 57-60.
19. COSSU, C., BRANDT, L., BAGHERI, S. & HENNINGSON, D. S. 2011 Secondary threshold amplitudes for sinuous streak breakdown. Phys. Fluids 23 (7), 074103.
20. DELSOLE, T. 2004 Stochastic models of quasi-geostrophic turbulence. Surv. Geophys. 25, 107-194.
21. DELSOLE, T. & FARRELL, B. F. 1996 The quasi-linear equilibration of a thermally mantained stochastically excited jet in a quasi-geostrophic model. J. Atmos. Sci. 53, 1781-1797.
22. ELLINGSEN, T. & PALM, E. 1975 Stability of linear flow. Phys. Fluids 18, 487-488.
23. FARRELL, B. F. 1988 Optimal excitation of perturbations in viscous shear flow. Phys. Fluids 31, 2093-2102.
24. FARRELL, B. F. & IOANNOU, P. J. 1993a Optimal excitation of three-dimensional perturbations in viscous constant shear flow. Phys. Fluids 5, 1390-1400.
25. FARRELL, B. F. & IOANNOU, P. J. 1993b Perturbation growth in shear flow exhibits universality. Phys. Fluids 5, 2298-2300.
26. FARRELL, B. F. & IOANNOU, P. J. 1993c Stochastic dynamics of baroclinic waves. J. Atmos. Sci. 50, 4044-4057.
27. FARRELL, B. F. & IOANNOU, P. J. 1993d Stochastic forcing of perturbation variance in unbounded shear and deformation flows. J. Atmos. Sci. 50, 200-211.
28. FARRELL, B. F. & IOANNOU, P. J. 1993e Stochastic forcing of the linearized Navier-Stokes equations. Phys. Fluids A 5, 2600-2609.
29. FARRELL, B. F. & IOANNOU, P. J. 1994 Variance maintained by stochastic forcing of non-normal dynamical systems associated with linearly stable shear flows. Phys. Rev. Lett. 72, 1118-1191.
30. FARRELL, B. F. & IOANNOU, P. J. 1995 Stochastic dynamics of the midlatitude atmospheric jet. J. Atmos. Sci. 52, 1642-1656.
31. FARRELL, B. F. & IOANNOU, P. J. 1996a Generalized stability. Part I. Autonomous operators. J. Atmos. Sci. 53, 2025-2040.
32. FARRELL, B. F. & IOANNOU, P. J. 1996b Generalized stability. Part II. Non-autonomous operators. J. Atmos. Sci. 53, 2041-2053.
33. FARRELL, B. F. & IOANNOU, P. J. 1998a Perturbation structure and spectra in turbulent channel flow. Theor. Comput. Fluid Dyn. 11, 215-227.
34. FARRELL, B. F. & IOANNOU, P. J. 1998b Turbulence supresssion by active control. Phys. Fluids 8, 1257-1268.
35. FARRELL, B. F. & IOANNOU, P. J. 1999 Perturbation growth and structure in time dependent flows. J. Atmos. Sci. 56, 3622-3639.
36. FARRELL, B. F. & IOANNOU, P. J. 2003 Structural stability of turbulent jets. J. Atmos. Sci. 60, 2101-2118.
37. FARRELL, B. F. & IOANNOU, P. J. 2007 Structure and spacing of jets in barotropic turbulence. J. Atmos. Sci. 64, 3652-3665.
38. FARRELL, B. F. & IOANNOU, P. J. 2008a Formation of jets by baroclinic turbulence. J. Atmos. Sci. 65, 3353-3375.
39. FARRELL, B. F. & IOANNOU, P. J. 2008b The stochastic parametric mechanism for generation of surface water waves by wind. J. Phys. Oceanogr. 38, 862-879.
40. FARRELL, B. F. & IOANNOU, P. J. 2009 A stochastic structural stability theory model of the drift wave-zonal flow system. Phys. Plasmas 16, 112903.
41. GAYME, D. F., MCKEON, B. J., PAPACHRISTODOULOU, A., BAMIEH, B. & DOYLE, J. C. 2010 A streamwise constant model of turbulence in plane Couette flow. J. Fluid Mech. 665, 99-119.
42. GIBSON, J., HALCROW, J. & CVITANOVÍC, P. 2008 Visualizing the geometry of state space in plane Couette flow. J. Fluid Mech. 611, 107-130.
43. HALCROW, J., GIBSON, J. F., CVITANOVIC, P. & VISWANATH, D. 2009 Heteroclinic connections in plane Couette flow. J. Fluid Mech. 621, 365-376.
44. HALL, P. & SHERWIN, S. 2010 Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures. J. Fluid Mech. 661, 178-205.
45. HAMILTON, K., KIM, J. & WALEFFE, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317-348.
46. HERNON, D., WALSH, E. J. & MCELIGOT, D. M. 2007 Experimental investigation into the routes to bypass transition and the shear-sheltering phenomenon. J. Fluid Mech. 591, 461-479.
47. HOEPFFNER, J. & BRANDT, L. 2008 Stochastic approach to the receptivity problem applied to bypass transition in boundary layers. Phys. Fluids 20, 024108.
48. HOGBERG, M., BEWLEY, T. R. & HENNINGSON, D. S. 2003 Relaminarization of Re D 1000 turbulence using linear state-feedback control. Phys. Fluids 15, 3572-3575.
49. HUTCHINS, N. & MARUSIC, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1-28.
50. HWANG, Y. & COSSU, C. 2010a Amplification of coherent structures in the turbulent Couette flow: an input-output analysis at low Reynolds number. J. Fluid Mech. 643, 333-348.
51. HWANG, Y. & COSSU, C. 2010b Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow. J. Fluid Mech. 664, 51-73.
52. JACOBS, R. G. & DURBIN, P. A. 2001 Simulations of bypass transition. J. Fluid Mech. 428, 185-212.
53. JANG, P. S., BENNEY, D. J. & GRAN, R. L. 1986 On the origin of streamwise vortices in a turbulent boundary layer. J. Fluid Mech. 169, 109-123.
54. JIḾENEZ, J. & MOIN, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213-240.
55. JIḾE NEZ, J. & PINELLI, A. 1999 The autonomous cycle of near wall turbulence. J. Fluid Mech. 389, 335-359.
56. JOVANOVIC, M. & BAMIEH, B. 2005 Componentwise energy amplification in channel flows. J. Fluid Mech. 534, 145-183.
57. KAWAHARA, G. & KIDA, S. 2001 Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst. J. Fluid Mech. 449, 291-300.
58. KIM, J. & BEWLEY, T. R. 2007 A linear systems approach to flow control. Annu. Rev. Fluid Mech. 39, 383-417.
59. KIM, J., KLINE, S. J. & REYNOLDS, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layers. J. Fluid Mech. 50, 133-160.
60. KIM, J. & LIM, J. 2000 A linear process in wall bounded turbulent shear flows. Phys. Fluids 12, 1885-1888.
61. KLEBANOFF, P. S., TIDSTROM, K. D. & SARGENT, L. M. 1962 The three-dimensional nature of boundary-layer instability. J. Fluid Mech. 12, 1-34.
62. KOMMINAHO, J., LUNDBLADH, A. & JOHANSSON, A. 1996 Very large structures in plane turbulent Couette flow. J. Fluid Mech. 320, 259-285.
63. KREISS, G., LUNDBLADH, A. & HENNINGSON, D. S. 1994 Bounds for threshold amplitudes in subcritical shear flows. J. Fluid Mech. 270 (1), 175-198.
64. KURIAN, T. & FRANSSON, J. H. M. 2009 Grid-generated turbulence revisited. Fluid Dyn. Res. 41, 1-32.
65. LANDAHL, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98, 243.
66. LAVAL, J.-P., DUBRULLE, B. & MCWILLIAMS, J. C. 2003 Langevin models of turbulence: renormalization group, distant interaction algorithms or rapid distortion theory? Phys. Fluids 15, 1327-1339.
67. LUCHINI, P. 2000 Reynolds-number-independent instability of the boundary layer over a flat surface: optimal perturbations. J. Fluid Mech. 404, 289-309.
68. LUMLEY, J. L. 1967 The structure of inhomogeneous turbulence. In Atmospheric Turbulence and Radio Wave Propagation (ed. A. M. Yaglom & V. I. Tatarskii). pp. 166-178. Nauka.
69. MARSTON, J. B. 2010 Statistics of the general circulation from cumulant expansions. Chaos 20, 041107.
70. MARSTON, J. B., CONOVER, E. & SCHNEIDER, T. 2008 Statistics of an unstable barotropic jet from a cumulant expansion. J. Atmos. Sci. 65, 1955-1966.
71. MATSUBARA, M. & ALFREDSSON, P. H. 2001 Disturbance growth in boundary layers subjected to free stream turbulence. J. Fluid Mech. 430, 149-168.
72. MONOKROUSOS, A., BOTTARO, A., BRANDT, L., DI VITA, A. & HENNINGSON, D. S. 2011 Non-equilibrium thermodynamics and the optimal path to turbulence in shear flows. Phys. Rev. Lett. 106, 134502.
73. NAGATA, M. 1990 Three-dimensional travelling-wave solutions in plane Couette flow. J. Fluid Mech. 217, 519-527.
74. NAGATA, M. 1997 Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. Phys. Rev. E 55, 2023-2025.
75. PEDLOSKY, J. & THOMSON, J. 2003 Baroclinic instability of time-dependent currents. J. Fluid Mech. 490, 189-215.
76. POULIN, F. J., FLIERL, G. R. & PEDLOSKY, J. 2003 Parametric instability in oscillatory shear flows. J. Fluid Mech. 481, 329-353.
77. POULIN, F. J., FLIERL, G. R. & PEDLOSKY, J. 2010 The baroclinic adjustment of time-dependent shear flows. J. Phys. Oceanogr. 40, 1851-1865.
78. REDDY, S. C. & HENNINGSON, D. S. 1993 Energy growth in viscous shear flows. J. Fluid Mech. 252, 209-238.
79. 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.
80. SCHLATTER, P., BRANDT, L., DE LANGE, H. C. & HENNINGSON, D. S. 2008 On streak breakdown in bypass transition. Phys. Fluids 20 (10), 101505.
81. SCHMID, P. J. & HENNINGSON, D. S. 1992 A new mechanism for rapid transition involving a pair of oblique waves. Phys. Fluids A: Fluid Dyn. 4, 1986-1989.
82. SCHMID, P. J. & HENNINGSON, D. S. 2001 Stability and Transition in Shear Flows. Springer.
83. SCHOPPA, W. & HUSSAIN, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57-108.
84. SIROVICH, L., BALL, K. S. & KEEFE, L. R. 1990 Plane waves and structures in turbulent channel flow. Phys. Fluids A 2, 2217-2226.
85. SMITH, C. 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.
86. SRINIVASAN, K. & YOUNG, W. R. 2012 Zonostrophic instability. J. Atmos. Sci. 69 (5), 1633-1656.
87. TOBIAS, S. M., DAGON, K. & MARSTON, J. B. 2011 Astrophysical fluid dynamics via direct numerical simulation. Astrophys. J. 727, 127.
88. TREFETHEN, L. N., TREFETHEN, A. E., REDDY, S. C. & DRISCOLL, T. A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578-584.
89. WALEFFE, F. 1995 Hydrodynamic stability and turbulence: beyond transients to a self-sustaining proccess. Stud. Appl. Maths 95, 319-343.
90. WALEFFE, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids A 9, 883-900.
91. WALEFFE, F. 1998 Three-dimensional coherent states in plane shear flows. Phys. Rev. Lett. 81, 4140-4143.
92. WALEFFE, F. 2001 Exact coherent structures in channel flow. J. Fluid Mech. 435, 93-102.
93. WALEFFE, F. 2003 Homotopy of exact coherent structures in plane shear flows. Phys. Fluids 15, 1517-1534.
94. WESTIN, K. J. A., BAKCHINOV, A. A., KOZLOV, V. V. & ALFREDSSON, P. H. 1998 Experiments on localized disturbances in a flat plate boundary layer. Part 1. The receptivity and evolution of a localized free stream disturbance receptivity and evolution of a localized free stream disturbance. Eur. J. Mech. (B/Fluids) 17, 823-846.
95. WESTIN, K. J. A., BOIKO, A. V., KLINGMANN, B. G. B., KOZLOV, V. V. & ALFREDSSON, P. H. 1994 Experiments in a boundary layer subjected to free stream turbulence. Part 1. Boundary layer structure and receptivity. J. Fluid Mech. 281, 193-218.
96. WU, X. & MOIN, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressuregradient flat-plate boundary layer. J. Fluid Mech. 630, 5-41.
97. ZHANG, Y. & HELD, I. M. 1999 A linear stochastic model of a GCM's midlatitude storm tracks. J. Atmos. Sci. 56, 3416-3435.