Nonlinear mechanics of wavy instability of steady longitudinal vortices and its effect on skin friction rise in boundary layer flow

Physics of Fluids

Volumn 18, Issue 2, 2006, Pages

  Girgis, I G ^a   Liu, Joseph T C ^b,c  

^a Princeton University   (United States)

^b Brown University   (United States)

^c UNIVERSITÉ DE NANTES   (France)

Author keywords

Boundary layer turbulence; Flow instability; Friction; Surface waves (fluid); Vortices

Indexed keywords

FLUID MECHANICS; FRICTION; REYNOLDS NUMBER; STEADY FLOW; SURFACE WAVES; TURBULENCE; TURBULENT FLOW; VORTEX FLOW;

BOUNDARY LAYER TURBULENCE; FLOW INSTABILITY;

BOUNDARY LAYER FLOW;

BOUNDARY LAYER FLOW; FLUID MECHANICS; FRICTION; REYNOLDS NUMBER; STEADY FLOW; SURFACE WAVES; TURBULENCE; TURBULENT FLOW; VORTEX FLOW;

EID: 33644593680     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2158430     Document Type: Article

References (41)

1. I. G. Girgis and J. T. C. Liu, "Mixing enhancement via the release of strongly nonlinear longitudinal Görtler vortices and their secondary instabilities into the mixing region," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002001519 468, 29 (2002).
2. A. S. Sabry, X. Yu, and J. T. C. Liu, "Secondary instabilities of three-dimensional inflectional velocity profiles resulting from longitudinal vorticity elements in boundary layers," in IUTAM Symp. Laminar-Turbulent Transition-1989, edited by R. Michel and D. Arnal (Springer, Berlin, 1990), p. 441.
3. X. Yu and J. T. C. Liu, "The secondary instability of Görtler flow," Phys. Fluids A PFADEB0899-821310.1063/1.857913 3, 1845 (1991).
4. X. Yu and J. T. C. Liu, "On the mechanism of sinuous and varicose modes in three-dimensional viscous instability of Görtler rolls," Phys. Fluids PHFLE61070-663110.1063/1.868312 6, 736 (1994).
5. P. Hall and N. J. Horseman, "The inviscid secondary instability of longitudinal vortex structures in boundary layers," J. Fluid Mech. JFLSA70022-1120 232, 357 (1991).
6. F. Li and R. M. Malik, "Fundamental and subharmonic secondary instabilities of Görtler vortices," J. Fluid Mech. JFLSA70022-1120 297, 77 (1995).
7. J. T. Stuart, "Hydrodynamic stability," in Laminar Boundary Layers, edited by L. Rosenhead (Clarendon, Oxford, 1963), p. 492.
8. J. M. Floryan and W. S. Saric, "Stability of Görtler vortices in boundary layers," AIAA J. AIAJAH0001-1452 20, 316 (1982).
9. P. Hall, "The linear development of Görtler vortices in growing boundary layers," J. Fluid Mech.JFLSA70022-1120 130, 41 (1983).
10. P. Hall, "The nonlinear development of Görtler vortices in growing boundary layers," J. Fluid Mech. JFLSA70022-1120 193, 23 (1988).
11. K. Lee and J. T. C. Liu, "On the growth of mushroomlike structures in nonlinear spatially developing Goertler vortex flow," Phys. Fluids A PFADEB0899-821310.1063/1.858506 4, 95 (1992).
12. A. S. Sabry and J. T. C. Liu, "Longitudinal vorticity elements in boundary layers: Nonlinear development from initial Görtler vortices as a prototype problem," J. Fluid Mech. JFLSA70022-1120 231, 615 (1991).
13. J. T. Stuart, "On the nonlinear mechanics of wave disturbances in stable and unstable parallel flows. Part 1. The basic behavior in plane Poiseuille flow," J. Fluid Mech. JFLSA70022-1120 9, 353 (1960).
14. J. D. Swearingen and R. F. Blackwelder, "The growth and breakdown of streamwise vortices in presence of a wall," J. Fluid Mech. JFLSA70022-1120 182, 255 (1987).
15. H. Peerhossaini and F. Bahri, "On the spectral distribution of the modes in non-linear Görtler instability," Exp. Therm. Fluid Sci. ETFSEO0894-177710.1016/S0894-1777(97)10029-2 16, 195 (1998).
16. A. Ajakh, M. Kestoras and H. Peerhossaini, "Experiments on Görtler instability: Its relation to transition to turbulence," J. Fluids Eng. JFEGA40098-2202 237, 613 (1996).
17. A. Ajakh, M. Kestoras, R. Toé and H. Peerhossaini, "Influence of forced perturbations in the stagnation region of Görtler instability," AIAA J. AIAJAH0001-1452 37, 1572 (1999).
18. H. Mitsudharmadi, S. H. Winoto and D. A. Shah, "Development of boundary-layer flow in the presence of forced wavelength Görtler vortices," Phys. Fluids PHFLE61070-663110.1063/1.1789771 16, 3983 (2004).
19. R. Toé, A. Ajakh and H. Peerhossaini, "Heat transfer enhancement by Görtler instability," Int. J. Heat Fluid Flow IJHFD20142-727X10.1016/S0142-727X(01)00149-7 23, 194 (2002).
20. L. Momayez, P. Dupont and H. Peerhossaini, "Some unexpected effects of wavelength and perturbation strength on heat transfer enhancement by Görtler instability," Int. J. Heat Mass Transfer IJHMAK0017-931010.1016/j.ijheatmasstransfer.2004.04.006 47, 3783 (2004).
21. L. Momayez, P. Dupont and H. Peerhossaini, "Effect of vortex organization on heat transfer by Görtler instability," Int. J. Therm. Sci. IJTSFZ1290-072910.1016/j.ijthermalsci.2004.02.015 43, 753 (2004).
22. J. M. Floryan, "On Görtler instability of boundary layers." Prog. Aerosp. Sci. PAESD60376-042110.1016/ 0376-0421(91)90006-P 28, 235 (1991).
23. W. S. Saric, "Görtler vortices," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fluid.26.1.379 26, 379 (1994).
24. C. C. Lin, The Theory of Hydrodynamic Stability. (Cambridge University Press, Cambridge, UK, 1955).
25. R. E. Kelly, "On the stability of an inviscid shear layer which is periodic in space and time," J. Fluid Mech. JFLSA70022-1120 27, 657 (1967).
26. J. T. C. Liu, "Interactions between large-scale coherent structures and fine-grained turbulence in free shear flows," in Transition and Turbulence, edited by R. E. Meyer (Academic, New York, 1981), p. 167.
27. D. E. Nikitopoulis and J. T. C. Liu, "Nonlinear three-mode interactions in a developing mixing layer," Phys. Fluids PHFLE61070-663110.1063/1.1351857 13, 966 (2001).
28. W. Liu and A. Domaradzski, "Direct numerical simulation of transition to turbulence in Görtler flow," J. Fluid Mech. JFLSA70022-1120 240, 267 (1993).
29. L. F. Souza, M. T. Mendonça, M. A. F. Medeiros and M. J. Kloker, "Görtler vortex secondary stability: Varicose mode," in Proceedings of the 21st International Congress on Theoretical and Applied Mechanics, edited by W. Gutkowski and T. A. Kowalewski (IPPT PAN, Warsaw, Poland, 2004), p. 126.
30. D. R. S. Ko, T. Kubota, and L. Lees, "Finite disturbance effect in the stability of laminar incompressible wake behind a flat plate," J. Fluid Mech. JFLSA70022-1120 40, 315 (1970).
31. T. Herbert, "Parabolized stability equations," Annu. Rev. Fluid Mech. ARVFA30066-418910.1146/annurev.fluid.29.1.245 29, 245 (1997).
32. D. Meksyn and J. T. Stuart, "Stability of viscous motion between parallel planes for finite disturbances," Proc. R. Soc. London, Ser. A PRLAAZ1364-5021 208, 517 (1951).
33. M. Gaster, "A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability," J. Fluid Mech. JFLSA70022-1120 14, 222 (1962).
34. L. C. Kaufman, "The LZ algorithm to solve generalized eigenvalue problem for complex matrices," ACM Trans. Math. Softw. ACMSCU0098-350010.1145/355644.355652 1, 271 (1975).
35. A. Chorin, "A numerical method for solving incompressible flow problems," J. Comput. Phys. JCTPAH0021-999110.1016/ 0021-9991(67)90037-X 2, 12 (1967).
36. J. T. Stuart, "On the effects of the Reynolds stresses on hydrodynamic stability," Z. Angew. Math. Mech. ZAMMAX0044-2267 36, S32 (1956).
37. J. T. C. Liu and A. S. Sabry, "Concentration and heat transfer in nonlinear Görtler vortex flow and the analogy with longitudinal momentum transfer," Proc. R. Soc. London, Ser. A PRLAAZ1364-5021 432, 1 (1991).
38. M. Asai, M. Minagawa and M. Nishioka, "The instability and breakdown of a near-wall low-speed streak," J. Fluid Mech. JFLSA70022-112010.1017/S0022112001007431 455, 289 (2002).
39. M. Matsubara and P. H. Alfredson, "Disturbance growth in boundary layers subjected to free stream turbulence," J. Fluid Mech. JFLSA70022-112010.1017/S0022112000002810 430, 149 (2001).
40. W. Schoppa and F. Hussain, "Coherent structure generation in near-wall turbulence," J. Fluid Mech. JFLSA70022-112010.1017/ S0022112002008066 453, 57 (2002).
41. L. Brandt and D. S. Henningsen, "Transition of streamwise streaks in zero-pressure gradient boundary layers," J. Fluid Mech. JFLSA70022-112010.1017/S0022112002002331 472, 229 (2002).