The nonlinear evolution of high-frequency resonant-triad waves in an oscillatory Stokes layer at high Reynolds number

Journal of Fluid Mechanics

Volumn 245, Issue , 1992, Pages 553-597

  Wu, Xuesong ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

OSCILLATION(FLUID; RESONANT-TRIAD; STOKES LAYERS; TRANSITION FLOW; WAVE INTERACTION;

EID: 0026799141     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112092000582     Document Type: Article

References (56)

1. AKHAVAN, R., KAMM, R. D. &SHAPIRO, A. H. 1991a An investigation of transition to turbulence in bounded oscillatory Stokes Flow. Part 1. Experiments. J. Fluid Mech. 225, 395.
2. AKHAVAN, R., KAMM, R. D., 1991 b An investigation of transition to turbulence in bounded oscillatory Stokes Flow. Part 2. Numerical simulations. J. Fluid Mech. 225, 423.
3. BENNEY, D.J. 1961 A nonlinear theory for oscillations in a parallel flow. J. Fluid Mech. 10, 209.
4. BENNEY, D.J. 1984 The evolution of disturbances in shear flows at high Reynolds number. Stud. Appl. Maths 70, 1.
5. BENNEY, D.J. &BERGERON, R. F. 1969 A new class of nonlinear waves in parallel shear flows. Stud. Appl. Maths 48, 181.
6. BLEISTEIN, N. &HANDELMAN, R. A. 1990 Asymptotic Expansions of Integrals. Dover.
7. BODONYI, R. J. &SMITH, F. T. 1981 The upper branch stability of the Blasius boundary layer, including non-parallel effects. Proc. R. Soc. Lond. A375, 65.
8. CIRUMLOV S.M. &SHUKHMAN, I. G. 1987 The nonlinear development of disturbances in a zonal shear flow. Geophys. Astrophys. Fluid Dyn. 101.
9. COLINS, J. I. 1963 Inception of turbulence at the bed under periodic gravity waves. J. Geophys. Res. 18, 6007.
10. COWLEY, S. J. 1987 High frequency Rayleigh instability of Stokes layers. In Stability of Time Dependent and Spatially Varying Flows (ed. D. L. Dwoyer & M. Y. Hussaini, p. 261.
11. CRAIK, A. D. D. 1971 Non-linear resonant instability in boundary layers. J. Fluid Mech. 50, 393.
12. CRAIK, A. D. D. 1975 Second order resonance and subcritical instability. Proc. R. soc. Lond. A 343, 351.
13. CRAIK, A. D. D. 1985 Wave Interactions and Fluids Flows. Cambridge University Press.
14. GOLDSTEIN, M. E. &CHOI, S.-W. 1989 Nonlinear evolution of interacting oblique waves on two-dimensional shear layers. J. Fluid Mech. 207, 97.
15. GOLDSTEIN, M. E., DURBIN, P. A. &LEIB, S. J. 1987 Roll-up of vorticity in adverse-pressure-gradient boundary layers. J. Fluid Mech. 183, 325.
16. GOLDSTEIN, M. E. &HULTGREN, L. S. 1989 Nonlinear spatial evolution of an externally excited instability wave in a free shear layer. J. Fluid Mech. 197, 295.
17. GOLDSTEIN,.M. E. & LEE, S. S. 1992 Fully coupled resonant-triad interaction in an adverse-pressure-gradient boundary layer. J. Fluid Mech. 245, 523.
18. GOLDSTEIN, M. E. &LEIB, S. J. 1988 Nonlinear roll-up of externally excited free shear layers. J. Fluid Mech. 191, 481.
19. GOLDSTEIN, M. E. &LEIB, S. J. 1989 Nonlinear evolution of oblique waves on compressible shear layers. J. Fluid Mech. 207, 73.
20. HALL, P. 1978 The linear instability of flat Stokes layers. Proc. R. Soc. Lond. A 359, 151.
21. HALL, P. 1984 On the stability of the unsteady boundary layer on a cylinder oscillating transversely in a viscous fluid. J. Fluid Mech. 146, 347.
22. 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.
23. HALL, P. &SMITH, F. T. 1989 Nonlinear Tollmien-Schlichting/vortex interaction in boundary layers. Eur. J. Mech. B 9, 179.
24. HALL, P. &SMITH, F. T. 1990 In Proc. ICASE Workshop on Instability and Transition, Vol. II (ed. M. Y. Hussaini & R. G. Voigt), p. 5. Springer.
25. HALL, P. &SMITH, F. T. 1991 On strongly nonlinear vortex/wave interactions in boundary-layer transition. J. Fluid Mech. 227, 641
26. HICKERNELL, F. J. 1984 Time-dependent critical layers in shear flows on the beta-plane. J. Fluid Mech. 142, 431.
27. HINO, M., KASHIWAYANAGI, M., NAKAYAMA, A. &HARA, T. 1983 Experiments on the turbulence statistics and structure of a reciprocating oscillatory flow. J. Fluid Mech. 131, 363.
28. HINO, M., SAWAMOTO, M. &TAKASU, S. 1976 Experiments on transition to turbulence in an oscillatory pipe flow. J. Fluid Mech. 75, 193.
29. Von KERCZEK, C.&DAVIS, S. H. 1974 Linear stability theory of oscillatory Stokes layers. J. Fluid Mech. 62, 753.
30. Von KERCZEK, C.&DAVIS, S. H. 1976 The instability of a stratified periodic boundary layer. J. Fluid Mech. 75, 287.
31. LEIB, S. J. 1991 Nonlinear evolution of subsonic and supersonic disturbances on a compressible free shear layer. J. Fluid Mech. 224, 551.
32. MANKBADI, R. R. 1992 A critical-layer analysis of the near-resonant triad in Blasius boundary-layer instability. J. Fluid Mech. (submitted).
33. MASLOWE, S. A. 1986 Critical layers in shear flows. Ann. Rev. Fluid Mech. 18, 406.
34. MERKLI, P. &THOMANN H. 1975 Transition to turbulence in oscillating pipe flow. J. Fluid Mech. 68, 567.
35. MONKEWITZ, M. A. 1983 Lineare stabilitats – untersuchungen an den oszillierenden Grenzschichten von Stokes. Ph.D. thesis No. 7297, Federal Institute of Technology, Zurich, Switzerland.
36. MONKEWITZ, P. A. &BUNSTER, A. 1987 The stability of the Stokes layer: visual observations and some theoretical considerations. In Stability of Time dependent and spatially Varying Flows (ed D. L. Dwoyer & M. Y. Hussaini, p. 244.
37. OBREMSKI, H. J. &MORKOVIN, M. V. 1969 Application of a quasi-steady stability model to periodic boundary layer. AIAA J. 7, 1298.
38. PAPAGEORGIOU, D. 1987 Stability of the unsteady viscous flow in a curved pipe. J. Fluid Mech. 182, 209.
39. RAETZ, G. S. 1959 A new theory of the cause of transition in fluid flows. Northrop Corp. NOR-59-383 BLC-121.
40. SEMINARA, G. &HALL, P. 1976 Centrifugal instability of a Stokes layer: linear theory. Proc. R. Soc. Lond. A 350, 299.
41. SHUKHMAN, I. G. 1991 Nonlinear evolution of spiral density waves generated by the instability of the shear layer in rotating compressible fluids. J. Fluid Mech. 233, 587.
42. SMITH, F. T. &STEWART, P. A. 1987 The resonant-triad nonlinear interaction in boundary-layer transition. J. Fluid Mech. 179, 227.
43. SMITH, F. T. & WALTON, A. G. 1990 Nonlinear interaction of near-planar TS waves and longitudinal vortices in boundary-layer transition. Mathematika 36, 262.
44. SQUIRE, H. B. 1933 On the stability for three-dimensional disturbances of viscous fluid flows between parallel walls. Proc. R. Soc. Lond. A142, 621.
45. STEWARTSON, K. 1981 Marginally stable inviscid flows with critical layers. IMA J. Appl. Maths 27, 133.
46. STUART, J. T. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. Part 1. J. Fluid Mech. 9, 353.
47. STUART, J. T. 1962a Nonlinear effects in hydrodynamic stability. In Proc. 10th Inti. Congr. Appl. Mech. Stresa, Italy 1960 (ed F. Rolla & W. T. Koiter), p. 63.
48. STUART, J. T. 1962b On three-dimensional nonlinear effects in the stability of parallel flows. Adv. Aero. Sci. 3, 121.
49. THOMAS, M. D. 1992 On the resonant-triad interaction in flows over rigid and flexible boundaries. J. Fluid Mech. 234, 417.
50. TROMANS, P. 1978 Stability and transition of periodic pipe flows. Ph.D. thesis, University of Cambridge.
51. USHER, J. R. &CRAIK, A. D. D. 1975 Nonlinear wave interactions in shear flows. Part 2. Third-order theory. J. Fluid Mech. 70, 437.
52. WARN, T. &WARN, H. 1978 The evolution of a nonlinear critical layer. Stud. Appl. Maths. 59, 37.
53. WATSON, J. 1960 On the non-linear mechanics of wave disturbances in stable and unstable parallel flows. Part 2. J. Fluid Mech. 9, 371.
54. WU, X. 1991 Nonlinear instability of Stokes layers. Ph.D. thesis, University of London.
55. WU, X. &COWLEY, S. J. 1992 The nonlinear evolution of high-frequency disturbances in an oscillatory Stokes layer at high Reynolds number. To be submitted.
56. WU, X., LEE, S. S. &COWLEY, S. J. 1992 On the nonlinear three-dimensional instability of Stokes layers and other shear layers to pairs of oblique waves. J. Fluid Mech. (submitted).