The extended Görtler-Hämmerlin model for linear instability of three-dimensional incompressible swept attachment-line boundary layer flow

Journal of Fluid Mechanics

Volumn 487, Issue , 2003, Pages 271-313

  Theofilis, Vassilios ^a   Fedorov, Alexander ^b   Obrist, Dominik ^c   Dallmann, Uwe Ch ^a  

^a GERMAN AEROSPACE CENTER DLR   (Germany)

^b MOSCOW INSTITUTE OF PHYSICS AND TECHNOLOGY   (Russian Federation)

^c Cray Computer GmbH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; NUMERICAL METHODS; POLYNOMIALS;

LINEAR STABILITY ANALYSIS;

SYSTEM STABILITY;

ALGORITHM; BOUNDARY LAYER; INCOMPRESSIBLE FLOW; INSTABILITY; MATHEMATICAL ANALYSIS; MODELING; THREE-DIMENSIONAL FLOW;

EID: 0042732003     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112003004762     Document Type: Article

References (43)

1. ARNAL, D., COUSTOLS, R. & JUILLEN, J. 1984 Etude expérimentale et théorique de la transition sur une aile en fléche infinie. La Recherche Aérospatiale 4, 275-290.
2. BALAKUMAR, P. 1998 Finite amplitude stability of attachment-line boundary layers. AIAA Paper 98-0338.
3. BERTOLOTTI, F. P. 2000 On the connection between cross-flow vortices and attachment-line instabilities. In Proc. IUTAM Laminar-Turbulent Symposium V, Sedona, AZ, USA (ed. W. Saric & H. Fasel), pp. 625-630.
4. BOYD, J. 1989 Chebyshev and Fourier Spectral Methods. Springer.
5. BRIDGES, T. & MORRIS, P. 1984 Differential eigenvalue problems in which the parameter appears nonlinearly. J. Comput. Phys. 55, 437.
6. CANUTO, C., HUSSAINI, M. Y., QUARTERONI, A. & ZANG, T. A. 1987 Spectral Methods in Fluid Dynamics. Springer.
7. DALLMANN, U. 1980 Zur Stabilität dreidimensionaler Scherströmungen. Kriterien für reibungsfreie Störungsanregung. Tech. Rep. FB 80-05. DLR.
8. DRAZIN, P. & REID, W. 1981 Hydrodynamic Stability. Cambridge University Press.
9. EHRENSTEIN, U. 1996 On the linear stability of channel flows over riblets. Phys. Fluids 8, 3194-3196.
10. GASTER, M. 1967 On the flow along swept leading edges. Aero. Q. 18, 165-184.
11. GÖRTLER, H. 1955 Dreidimensionale Instabilität der ebenen Staupunktströmung gegenüber wirbelartigen Störungen. In 50 Jahre Grenzschichtforschung (ed. H. Görtler & W. Tollmien), pp. 304-314. Vieweg und Sohn.
12. HALL, P. & MALIK, M. 1986 On the instability of a three-dimensional attachment-line boundary layer: weakly nonlinear theory and a numerical approach. J. Fluid Mech. 163, 257-282.
13. HALL, P., MALIK, M. & POLL, D. 1984 On the stability of an infinite swept attachment-line boundary layer. Proc. R. Soc. Lond. A 395, 229-245.
14. HALL, P. & SEDDOUGUI, S. 1990 Wave interactions in a three-dimensional attachment-line boundary layer. J. Fluid Mech. 217, 367-390.
15. HÄMMERLIN, G. 1955 Zur Instabilitätstheorie der ebenen Staupunktströmung. In 50 Jahre Grenzschichtforschung (ed. H. Görtler & W. Tollmien), pp. 315 327. Vieweg und Sohn.
16. HEEG, R. & GEURTS, B. 1998 Spatial instabilities of incompressible attachment-line flow using sparse matrix Jacobi-Davidson techniques. Appl. Sci. Res. 59, 315 329.
17. HIEMENZ, K. 1911 Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder. Dingl. Polytechn. J. 326, 321 324, thesis, Göttingen.
18. JIMÉNEZ, J., MARTEL, C., AGÜI, J. & ZUFIRIA, J. 1990 Direct numerical simulation of transition in the incompressible leading edge boundary layer. Tech. Rep. MF-903. ETSIA.
19. JOSLIN, R. 1995 Direct simulation of evolution and control of three-dimensional instabilities in attachment-line boundary layers. J. Fluid Mech. 291, 369 392.
20. JOSLIN, R. D. 1996a Simulation of nonlinear instabilities in an attachment-line boundary layer. Fluid Dyn. Res. 18, 81 97.
21. JOSLIN, R. D. 1996b Simulation of three-dimensional symmetric and antisymmetric instabilities in attachment-line boundary layers. AIAA J. 34, 2432 2434.
22. JOSLIN, R. D. 1997 Direct numerical simulation of evolution and control of linear and nonlinear disturbances in three-dimensional attachment-line boundary layers. Tech. Rep. TP 3623. NASA.
23. LIN, R.-S. & MALIK, M. R. 1996a On the stability of attachment-line boundary layers. Part 1. the incompressible swept hiemenz flow. J. Fluid Mech. 311, 239 255.
24. LIN, R.-S. & MALIK, M. R. 1996b On the stability of attachment-line boundary layers. Part 2. the effect of leading-edge curvature. J. Fluid Mech. 333, 125 137.
25. LUNDBLADH, A., SCHMID, P., BERLIN, S. & HENNINGSON, D. 1994 Simulation of bypass transition in spatially evolving flow. In AGARD CP-551 (ed. B. Cantwell), pp. 18-1 18-13.
26. NAYFEH, A. H. 1980 Stability of three-dimensional boundary layers. AIAA. J. 18, 406 416.
27. OBRIST, D. 2000 On the stability of the swept leading-edge boundary layer. PhD thesis, University of Washington.
28. PFENNINGER, W. & BACON, J. 1969 Amplified laminar boundary layer oscillation and transition at the front attachment line of a 45° swept flat-nosed wing with and without suction. In Viscous Drag Reduction (ed. C. S. Wells), pp. 85 105, Plenum Press.
29. POLL, D. 1979 Transition in the infinite swept attachment line boundary layer. Aero. Q. 30, 607-629.
30. POLL, D., DANKS, M. & YARDLEY, M. 1996 The effects of suction and blowing on stability and transition at a swept attachment line. In Transitional Boundary Layers in Aeronautics (ed. R. Henkes & J. van Ingen). Elsevier.
31. ROSENHEAD, L. 1963 Laminar Boundary Layers. Oxford University Press.
32. SAAD, Y. 1980 Variations of arnoldi's method for computing eigenelements of large unsymmetric matrices. Lin. Algebra Appl. 34, 269 295.
33. SPALART, P. 1988 Direct numerical study of leading-edge contamination. In AGARD CP-438, pp. 5-1-5-13.
34. SPALART, P. 1989 Direct numerical study of crossflow instability. In IUTAM Laminar-Turbulent Symposium III (ed. D. Arnal & R. Michel), pp. 621 630.
35. THEOFILIS, V. 1995 Spatial stability of incompressible attachment line flow. Theor. Comput. Fluid Dyn. 7, 159 171.
36. THEOFILIS, V. 1997 On the verification and extension of the Görtler-Hämmerlin assumption in three-dimensional incompressible swept attachment-line boundary layer flow. Tech. Rep. IB 223-97 A 44. DLR.
37. THEOFILIS, V. 1998a Linear instability in two spatial dimensions. In Proc. European Computational Fluid Dynamics Conf. ECCOMAS '98 (ed. K. D. Papailiou, D. Tsahalis, J. Périaux, C. Hirsch & M. Pandolfi), Athens, Greece, pp. 547 552. John Wiley & Sons.
38. THEOFILIS, V. 1998b On linear and nonlinear instability of the incompressible swept attachment-line boundary layer. J. Fluid Mech. 355, 193-227.
39. THEOFILIS, V. 2003 Advances in global linear instability analysis of nonparallel and three-dimensional flows. Prog. Aero. Sci. 39, 249-315.
40. THEOFILIS, V., HEIN, S. & DALLMANN, U. 2000 On the origins of unsteadiness and three-dimensionality in a laminar separation bubble. Phil. Trans. R. Soc. Lond. A. 358, 3229-324.
41. THEOFILIS, V. & OBRIST, D. 2003 The extention of the Görtler-Hämmerlin model for linear instability in the three-dimensional incompressible swept attachment-line boundary layer. Part 2. Nonlinear mode interactions. In preparation.
42. VAN DYKE, M. 1975 Perturbation Methods in Fluid Mechanics. Parabolic.
43. ZHIGULEV, V. & TUMIN, A. 1987 Occurence of Turbulence. Nauka, Novosibirsk (in Russian). Translated as NASA TT-20340.