On vortex/wave interactions. Part 1. Non-symmetrical input and cross-flow in boundary layers

Journal of Fluid Mechanics

Volumn 307, Issue , 1996, Pages 101-133

  Brown, S N ^a   Smith, F T ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYERS; VORTEX FLOW; VORTEX/WAVE INTERACTIONS;

BOUNDARY LAYERS; INTEGRODIFFERENTIAL EQUATIONS; REYNOLDS NUMBER; VORTEX FLOW;

INVISCID INFLEXIONAL WAVES; NONSYMMETRY; VORTEX/WAVE INTERACTIONS;

FLOW INTERACTIONS;

EID: 0029657011     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112096000067     Document Type: Article

References (38)

1. AIHARA, Y., TOMITA, Y. & ITO, A. 1984 Generation, development and distortion, of longitudinal vortices in boundary layers along concave and flat plates. In Laminar-Turbulent Transition (ed. V. V. Kozlov), pp. 447-454. Springer.
2. ALLEN, T., BROWN, S. N. & SMITH, F. T. 1996 On vortex/wave interactions. Part 2. Originating from axisymmetric flow with swirl. (Submitted.)
3. BASSOM, A. P. & GAJJAR, J. S. B. 1988 Non-stationary cross-flow vortices in three-dimensional boundary-layer flows. Proc. R. Soc. Lond. A 417, 179-212.
4. BENNEY, D. J. & CHOW, C. 1989 A mean flow first harmonic theory for hydrodynamic instabilities. Stud. Appl. Maths 80, 37.
5. BLENNERHASSETT, P. & SMITH, F. T. 1992 Nonlinear interactions of oblique three-dimensional Tollmien-Schlichting waves and longitudinal waves, in channel flows and boundary layers. Proc. R. Soc. Lond. A 436, 585-602.
6. BROWN, P. G., BROWN, S. N., SMITH, F. T. & TIMOSHIN, S. N. 1993 On the starting process of strongly nonlinear vortex/Rayleigh-wave interactions. Mathematika 40, 7-29 (BBST).
7. DAVIS, D. A. R. & SMITH, F. T. 1994 Influence of cross-flow on nonlinear Tollmien-Schlichting/vortex interaction. Proc. R. Soc. Lond. A 446, 319-340.
8. GAJJAR, J. S. B. 1995 On the nonlinear instability of stationary cross-flow vortices in three-dimensional boundary layers. (In preparation.)
9. GOLDSTEIN, M. E. & CHOI, S.-W. 1989 Nonlinear evolution of interacting oblique waves on two-dimensional shear layers. J. Fluid Mech. 207, 97-120 (and corrigendum, 216, 1990, 659-663).
10. HALL, P. 1986 An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disc. Proc. R. Soc. Lond. A 406, 93-106.
11. HALL, P. & SMITH, F. T. 1988 The nonlinear interaction of Tollmien-Schlichting waves and Taylor-Gortler vortices in curved channel flows. Proc. R. Soc. Lond. A 417, 255-282.
12. HALL, P. & SMITH, F. T. 1989 Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers. Eur. J. Mech. B 8, 179-205.
13. HALL, P. & SMITH, F. T. 1991 On strongly nonlinear vortex/wave interactions in boundary-layer transition. J. Fluid Mech. 227, 641-666.
14. HALL, P. & SMITH, F. T. 1990 Near-planar TS waves and longitudinal vortices in channel flow: nonlinear interaction and focusing. ICASE Rep. 89-47.
15. KHOKHLOV, A. P. 1994 The theory of resonance interaction of Tollmien-Schlichting waves. J. Appl. Mech. Tech. Phys. 34, 508-515.
16. KLEBANOFF, P. S. & TIDSTROM, K. D. 1959 Evolution of amplified waves leading to transition in a boundary layer with zero pressure gradient. NASA Tech. Note D-195.
17. KLEISER, L. & ZANG, T. A. 1991 Numerical simulation of transition in wall-bounded shear flows. Ann. Rev. Fluid Mech. 23, 495-537.
18. KOHAMA, Y., SARIC, W. S. & Noos, J. A. 1991 A high frequency secondary instability of crossflow vortices that leads to boundary-layer transition. In Boundary Layer Transition and Control. R. Aero. Soc. Symp. Cambridge University Press.
19. NISHIOKA, M., ASAI, N. & IIDA, S. 1979 An experimental investigation of the secondary instability. In Laminar-Turbulent Transition, IUTAM Symp. Stuttgart. Springer.
20. REED, H. & SARIC, W. S. 1989 Stability of three-dimensional boundary layers. Ann. Rev. Fluid Mech. 21, 235-284.
21. REMPFER, D. & FASEL, H. F. 1994 Evolution of three-dimensional coherent structures in a flat-plate boundary layer. J. Fluid Mech. 260, 351-375.
22. SANDHAM, N. D. & KLEISER, L. 1992 The late stages of transition to turbulence in channel flow. J. Fluid Mech. 245, 319-348.
23. SMITH, F. T. & BOWLES, R. I. 1992 Transition theory and experimental comparisons on (I) amplification into streets and (II) a strongly nonlinear break-up criterion. Proc. R. Soc. Lond. A 439, 163-175.
24. SMITH, F. T., BROWN, S. N. & BROWN, P. G. 1993 Initiation of three-dimensional nonlinear transition paths from an inflexional profile. Eur. J. Mech. B12, 447-473. (SBB.)
25. SPALART, P. R. & YANG, K.-S. 1987 Numerical study of ribbon-induced transition in Blasius flow. J. Fluid Mech. 178, 345-365.
26. STEWART, P. A. & SMITH, F. T. 1987 Three-dimensional instabilities in steady and unsteady nonparallel boundary layers, including effects of Tollmien-Schlichting disturbances and cross-flow. Proc. R. Soc. Lond. A 409, 229-248.
27. STEWART, P. A. & SMITH, F. T. 1992 Three-dimensional nonlinear blow-up from a nearly planar initial disturbance in boundary-layer transition : theory and experimental comparisons. J. Fluid Mech. 244, 79-100.
28. STUART, J. T. 1963 Hydrodynamic Stability. In Laminar Boundary Layers (ed. L. Rosenhead), Chap. IX. Oxford University Press.
29. TANI, I. & SAKAGAMI, J. 1962 In Proc. Intl Council on Aeron. Sci., pp. 391-403, Third Congress, Stockholm. New York: Spartan.
30. TIMOSHIN, S. N. & SMITH, F. T. 1995 Vortex/inflectional-wave interactions with weakly three-dimensional input. (Submitted.)
31. WALTON, A. G., BOWLES, R. I. & SMITH, F. T. 1994 Vortex-wave interaction in separating flows. Eur. J. Mech. B 13, 629-655.
32. WALTON, A. G. & SMITH, F. T. 1992 Properties of strong nonlinear vortex/Tolhnien-Schlichting interactions. J. Fluid Mech. 244, 649-676.
33. WRAY, A. & HUSSAINI, M. Y. 1984 Numerical experiments in boundary-layer stability. Proc. R. Soc. Lond. A 392, 373-389.
34. Wu, X. 1993a Nonlinear temporal-spatial modulation of near-planar Rayleigh waves in shear flows: formation of streamwise vortices. J. Fluid Mech. 256, 685-719.
35. Wu, X. 1993b On critical-layer and diffusion-layer nonlinearity in the three-dimensional stage of boundary-layer transition. Proc. R. Soc. Lond. A 433, 95-106.
36. WU, X. 1995 Viscous effects on fully coupled resonant-triad interactions : an analytical approach. J. Fluid Mech. 292, 377-407.
37. WU, X. & COWLEY, S. J. 1995 On the nonlinear evolution of instability modes in unsteady shear layers: the Stokes layer as a paradigm. Q. J. Mech. Appl. Maths 48, 159-188.
38. WU, X., LEE, S. S. & COWLEY, S. J. 1993 On the weakly nonlinear three-dimensional instability of shear layers to pairs of oblique waves: the Stokes layer as a paradigm. J. Fluid Mech. 253, 681-721.