Linear instability of a corrugated vortex sheet - A model for streak instability

Journal of Fluid Mechanics

Volumn 483, Issue , 2003, Pages 315-342

  Kawahara, Genta ^a   Jiménez, Javier ^b,c   Uhlmann, Markus ^b   Pinelli, Alfredo ^b  

^a KYOTO UNIVERSITY   (Japan)

^b UNIVERSIDAD POLITÉCNICA DE MADRID   (Spain)

^c STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; LINEAR SYSTEMS; MATHEMATICAL MODELS;

CORRUGATED VORTEX SHEET;

VORTEX FLOW;

MATHEMATICAL MODELING; TURBULENT FLOW; VORTEX SHEET;

EID: 0038648716     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S002211200300421X     Document Type: Article

References (44)

1. ACARLAR, M. S. & SMITH, C. R. 1987 A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43-83.
2. ASAI, M., MINAGAWA, M. & NISHIOKA, M. 2002 The instability and breakdown of a near-wall low-speed streak. J. Fluid Mech. 455, 289-314.
3. BAKEWELL, H. P. & LUMLEY, J. L. 1967 Viscous sublayer and adjacent wall region in turbulent pipe flow. Phys. Fluids 10, 1880-1889.
4. BROOKE, J. W. & HANRATTY, T. J. 1993 Origin of turbulence-producing eddies in a channel flow. Phys. Fluids A 5, 1011-1021.
5. COWLEY, S. J., BAKER, G. R. & TANVEER, S. 1999 On the formation of Moore curvature singularities in a vortex sheet. J. Fluid Mech. 378, 233-267.
6. CRIGHTON, D. G. 1973 Instability of an elliptic jet. J. Fluid Mech. 59, 665-672.
7. HALL, P. & HORSEMAN, N. J. 1991 The linear inviscid secondary instability of longitudinal vortex structures in boundary layers. J. Fluid Mech. 232, 357-375.
8. HAMILTON, J. M., KIM, J. & WALEFFE, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317-348.
9. HOCKING, L. M. 1964 The instability of a non-uniform vortex sheet. J. Fluid Mech. 18, 177-186.
10. ITANO, T. & TOH, S. 2001 The dynamics of bursting process in wall turbulence. J. Phys. Soc. Japan 70, 701-714.
11. JEONG, J., HUSSAIN, F., SCHOPPA, W. & KIM, J. 1997 Coherent structures near the wall in a turbulent channel flow, J. Fluid Mech. 332, 185-214.
12. JIMÉNEZ, J. 1994 On the structure and control of near-wall turbulence. Phys. Fluids 6, 944-953.
13. JIMÉNEZ, J. & MOIN, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213-240.
14. JIMÉNEZ, J. & PINELLI, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335-359.
15. JIMÉNEZ, J. & SIMENS, M. P. 2001 Low-dimensional dynamics in a turbulent wall flow. J. Fluid Mech. 435, 81-91.
16. KAWAHARA, G., JIMÉNEZ, J., UHLMANN, M. & PINELLI, A. 1998 The instability of streaks in near-wall turbulence. CTR Annu. Res. Briefs. Stanford University, pp. 155-170.
17. KAWAHARA, G. & KIDA, S. 2001 Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst. J. Fluid Mech. 449, 291-300.
18. KIM, H. T., 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.
19. KIM, J., MOIN, P. & MOSER, R. 1987 Turbulence statistics in a fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133-166.
20. 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.
21. LASHERAS, J. C. & CHOI, H. 1988 Three-dimensional instability of a plane free shear layer: an experimental study of the formation and evolution of streamwise vortices. J. Fluid Mech. 189, 53-86.
22. MOORE, D. W. 1979 The spontaneous appearance of a singularity in the shape of an evolving vortex sheet, Proc. R. Soc. Lond. A 365, 105-119.
23. NAGATA, M. 1990 Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity. J. Fluid Mech. 217, 519-527.
24. ORLANDI, P. & JIMÉNEZ, J. 1994 On the generation of turbulent wall friction. Phys. Fluids 6, 634-641.
25. PANTON, R. (Ed.) 1997 Self-Sustaining Mechanisms of Wall Turbulence. Computational Mechanics Publications.
26. RAYLEIGH, LORD 1879 On the instability of jets. Proc. Lond. Math. Soc. 10, 4-13.
27. 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.
28. SAFFMAN, P. G. 1992 Vortex Dynamics. Cambridge University Press.
29. SAXENA, V., LEIBOVICH, S. & BERKOOZ, G. 1999 Enhancement of three-dimensional instability of free shear layers. J. Fluid Mech. 379, 23-38.
30. SCHOPPA, W. 2000 Studies of coherent structure generation in near-wall turbulence. PhD disseration. University of Houston.
31. SCHOPPA, W. & HUSSAIN, F. 1997 Genesis and dynamics of coherent structures in near-wall turbulence: A new look. In Self-Sustaining Mechanisms of Wall Turbulence (ed. R. Panton), pp. 385-422. Computational Mechanics Publications.
32. SCHOPPA, W. & HUSSAIN, F. 1998 Formation of near-wall streamwise vortices by streak instability. AIAA Paper 98-3000.
33. SCHOPPA, W. & HUSSAIN, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57-108.
34. SCHOPPA, W., HUSSAIN, F. & METCALFE, R. W. 1995 A new mechanism of small-scale transition in a plane mixing layer: core dynamics of spanwise vortices. J. Fluid Mech. 298, 23-80.
35. SREENIVASAN, K. R. 1988 A unified view of the origin and morphology of the turbulent boundary layer structure. In Proc. IUTAM Symp. on Turbulence Management and Relaminarisation (ed. H. W. Liepmann and R. Narasimha), pp. 37-61. Springer.
36. STRETCH, D. 1990. Automated pattern eduction from turbulent flow diagnostics. CTR Annu. Res. Briefs, Stanford University, pp. 145-157.
37. SWEARINGEN, J. D. & BLACKWELDER, R. F. 1987 The growth and breakdown of streamwise vortices in the presence of a wall. J. Fluid Mech. 182, 255-290.
38. TOH, S. & ITANO, T. 1999 Low-dimensional dynamics embedded in a plane Poiseuille flow turbulence. Traveling-wave solution is a saddle point? Preprint. arXiv.org e-Print Archive, http://xxx.lanl.gov/abs/physics/9905012.
39. TOH, S. & ITANO, T. 2001 On the regeneration mechanism of turbulence in the channel flow - role of the traveling-wave solution. In Proc. IUTAM Symp. on Geometry and Statistics of Turbulence (ed. T. Kambe, T. Nakano & T. Miyauchi), pp. 305-310. Kluwer.
40. WALEFFE, F. 1995 Hydrodynamic stability and turbulence: Beyond transients to a self-sustaining process. Stud. Appl. Maths 95, 319-343.
41. WALEFFE, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883-900.
42. WALEFFE, F. 1998 Three-dimensional coherent states in plane shear flows. Phys. Rev. Lett. 81, 4140-4143.
43. WALEFFE, F. 2001 Exact coherent structure in channel flow. J. Fluid Mech. 435, 93-102.
44. WALEFFE, F. & KIM, J. 1997 How streamwise rolls and streaks self-sustain in a shear flow. In Self-Sustaining Mechanisms of Wall Turbulence (ed. R. Panton), pp. 309-332. Computational Mechanics Publications.