Linear and nonlinear development of localized disturbances in zero and adverse pressure gradient boundary-layers

Physics of Fluids

Volumn 10, Issue 6, 1998, Pages 1405-1418

  Bech, Knut H ^a,c   Henningson, Dan S ^b   Henkes, Ruud A W M ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b Aeronautical Research Institute of Sweden   (Sweden)

^c SINTEF   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000922048     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869665     Document Type: Article

References (32)

1. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, Cambridge, 1982).
2. Th. Herbert, "Secondary instability of boundary layers," Annu. Rev. Fluid Mech. 20, 487 (1988).
3. P. R Spalart and K. S. Yang, "Numerical simulation of boundary layers: Part 2. Ribbon-induced transition in Blasius flow," NASA TM 88221, 1986.
4. T. Ellingsen and E. Palm, "Stability of linear flow," Phys. Fluids 18, 487 (1975).
5. M. T. Landahl, "Wave breakdown and turbulence," SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 28, 735 (1975).
6. K. M. Butler and B. F. Farrell, "Three-dimensional optimal disturbances in viscous shear flow," Phys. Fluids A 4, 1637 (1992).
7. S. C. Reddy and D. S. Henningson, "Energy growth in viscous channel flows," J. Fluid Mech. 252, 209 (1993).
8. L. N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, "Hydrodynamic stability without eigenvalues," Science 261, 578 (1993).
9. J. M. Hamilton, J. Kim, and F. Waleffe, "Regeneration mechanisms of near-wall turbulence structures," J. Fluid Mech. 287, 317 (1995).
10. S. C. Reddy, P. J. Schmid, J. S. Bagett, and D. S. Henningson, "On stability of streamwise streaks and transition thresholds in plane channel flows," J. Fluid Mech. (submitted).
11. P. J. Schmid and D. S. Henningson, "A new mechanism for rapid transition involving a pair of oblique waves," Phys. Fluids A 4, 1986 (1992).
12. S. Berlin, A. Lundbladh, and D. S. Henningson, "Spatial simulations of oblique transition in a boundary layer," Phys. Fluids A 6, 1949 (1994).
13. P. J. Schmid, S. C. Reddy, and D. S. Henningson, "Transition thresholds in boundary layers and channel flows," Advances in Turbulence VI, edited by S. Gavrilakis, L. Machiels, and P. A. Monkewitz (Kluwer, Dordrecht, 1996), pp. 381-384.
14. M. Gaster and I. Grant, "An experimental investigation of the formation and development of a wave packet in a laminar boundary layer," Proc. R. Soc. London, Ser. A 347, 253 (1975).
15. W. O. Crimindale, Jr. and L. S. G. Kovasznay, "The growth of localized disturbances in a laminar boundary layer," J. Fluid Mech. 14, 59 (1962).
16. M. Gaster, "A theoretical model of a wave packet in the boundary layer on a flat plate," Proc. R. Soc. London, Ser. A 347, 271 (1975).
17. J. Cohen, K. S. Breuer, and J. H. Haritonidis, "On the evolution of a wave packet in a laminar boundary layer, J. Fluid Mech. 225, 575 (1991).
18. K. S. Breuer, J. Cohen, and J. H. Haritonidis, "The late stages of transition induced by a low-amplitude wavepacket in a laminar boundary layer," J. Fluid Mech. (to appear).
19. M. T. Landahl, "A note on an algebraic instability of inviscid parallel shear flows," J. Fluid Mech. 98, 243 (1980).
20. A. Lundbladh, "Simulation of bypass transition to turbulence in wall bounded shear flows," Ph.D. dissertation, The Royal Institute of Technology, Stockholm, 1992.
21. K. S. Breuer and J. H. Haritonidis, "The evolution of a localized disturbance in a laminar boundary layer. Part 1. Weak disturbances," J. Fluid Mech. 220, 569 (1990).
22. D. S. Henningson, A. Lundbladh, and A. V. Johanson, "A mechanism for bypass transition from localized disturbances in wall-bounded shear flows," J. Fluid Mech. 250, 169 (1993).
23. A. Lundbladh, D. S. Henningson, and A. V. Johansson, "An efficient spectral integration method for the solution of the Navier-Stokes equations," FFA TN 1992-28. Technical note, the Aeronautical Research Institute of Sweden, 1992.
24. A. Lundbladh, P. J. Schmid, S. Berlin, and D. S. Henningson, "Simulation of bypass transition in spatially evolving flows," Symposium on Application of Direct and Large Eddy Simulation to Transition and Turbulence, Chania, Crete, Greece, 18-21 April 1994.
25. B. A. Singer, "Characteristics of a young turbulent spots," Phys. Fluids 8, 509 (1995).
26. U. Konzelman and H. Fasel, "Numerical simulation of a three-dimensional wave packet in a growing flat plate boundary layer," in Boundary Layer Transition and Control (The Royal Aeronautical Society, Cambridge, 1991), p. 1.
27. B. van Hest, "Laminar-turbulent transition in boundary layers with adverse pressure gradient," Ph.D. dissertation, Delft University of Technology, 1996.
28. max can thus be anywhere in the interval [0,k].
29. P. S. Klebanoff, K. D. Tidstrom, and L. M. Sargent, "The three-dimensional nature of boundary layer instability," J. Fluid Mech. 12, 1 (1962).
30. N. D. Sandham and L. Kleiser, "The late stages of transition to turbulence in channel flow," J. Fluid Mech. 245, 319 (1992).
31. 18 for 1% amplitude, give a maximum growth rate of 0.008 at a higher frequency.
32. In the experiments, the nondimensional frequency 2πf=cα and the spanwise wavenumber β was given, nondimensionalized using the local displacement thickness. The fundamental frequency was 0.014 in both the experiments (x≃390) and in the present DNS (x≃10). The experimental parameters for the subharmonic were f=0.0085 and β=0.26 at x≃780 and an amplitude of approximately 3%. The corresponding parameters from DNS were f=0.0096 and β=0.23 at x=70 and 8% amplitude.