Nonlinear stability of nonstationary cross-flow vortices in compressible boundary layers

Studies in Applied Mathematics

Volumn 96, Issue 1, 1996, Pages 53-84

  Gajjar, J S B ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

VORTEX FLOW;

BASIC FLOW; COMPRESSIBLE BOUNDARY LAYERS; CRITICAL LAYER; CROSSFLOW VORTICES; FLOW PROFILE; LONG WAVELENGTH; NON-LINEAR STABILITIES; NONLINEAR EVOLUTIONS; NONSTATIONARY; THREE-DIMENSIONAL BOUNDARY LAYERS;

BOUNDARY LAYERS;

EID: 0038967595     PISSN: 00222526     EISSN: None     Source Type: Journal    
DOI: 10.1002/sapm199696153     Document Type: Article

References (53)

1. J. S. B. GAJJAR, Nonlinear evolution of a first mode oblique wave in a compressible boundary layer. Part I. Heated/cooled walls, I.M.A.J. Appl. Math. 53:221 (1994).
2. A. P. BASSOM, and J. S. B. GAJJAR, Non-stationary cross-flow vortices in a three-dimensional boundary layer, Proc. Roy. Soc. A 417:179 (1988).
3. M. NISHIOKA, M. ASAI, and S. IIDA, in Laminar Turbulent Transition, IUTAM Meeting, Stuttgart, 1979.
4. P. S. KLEBANOFF, K. D. TIDSTROM, and L. M. SARGENT, The three-dimensional nature of boundary-layer instability, J. Fluid Mech. 12:1 (1962).
5. Y. S. KACHANOV and V. Y. LEVCHENKO, The resonant interaction of disturbances at laminar-turbulent transition in a boundary layer, J. Fluid Mech. 138:209 (1984).
6. T. C. CORKE and R. A. MANGANO, Resonant growth of three-dimensional modes in transitioning Blasius layers. J. Fluid Mech. 209:93 (1989).
7. M. E. GOLDSTEIN and S. W. CHOI, Nonlinear evolution of interacting oblique waves on two-dimensional shear layers, J. Fluid Mech. 207:97 (1989); Corrigendum, J. Fluid Mech. 216:659 (1990).
8. M. E. GOLDSTEIN and S. W. CHOI, Nonlinear evolution of interacting oblique waves on two-dimensional shear layers, J. Fluid Mech. 207:97 (1989); Corrigendum, J. Fluid Mech. 216:659 (1990).
9. P. HALL and F. T. SMITH, On strongly nonlinear vortex/wave interactions in boundary layer transition, J. Fluid Mech. 245:641 (1991).
10. M. E. GOLDSTEIN and S. S. LEE, Fully coupled resonant-triad interaction in an adverse pressure-gradient boundary layer, J. Fluid Mech. 245:523 (1992).
11. X. WU, S. S. LEE, and S. J. COWLEY, On the weakly nonlinear three-dimensional instability of shear flows to pairs of oblique waves: The Stokes layer as a paradigm, J. Fluid Mech. 253:681 (1993).
12. X. WU, P. A. STEWART, and S. J. COWLEY, On the weakly nonlinear development of Tollmien Schlichting wave-trains in boundary layers, J. Fluid Mech., to appear (1996).
13. F. T. SMITH and P. A. STEWART, The resonant-triad nonlinear interaction in boundary layer transition, J. Fluid Mech. 179:227 (1987).
14. P. STEWART and F. T. SMITH, Development of three-dimensional nonlinear blow-up from a nearly planar initial disturbance, in boundary layer transition, J. Fluid Mech. 244:79 (1992).
15. F. T. SMITH and R. T. BOWLES, Transition theory and experimental comparisons on (I) amplification into streets and (II) a strongly nonlinear break-up criterion, Proc. Roy..Soc. London A 439:163 (1992).
16. L. S. HULTGREN, Nonlinear spatial equilibration of an externally excited instability wave in a free shear layer, J. Fluid Mech. 236:635 (1992).
17. M. E. GOLDSTEIN, Nonlinear interactions between oblique instability waves on nearly parallel shear flows, Phys. Fluids 6(2):724 (1994).
18. N. GREGORY, J. T. STUART, and W. S. WALKER, On the instability of three-dimensional boundary layers with application to the flow due to a rotating disk, Phil. Trans. Roy. Soc. A 248:155 (1955).
19. L. LEES and C. C. LIN, NASA Tech. Note No. 1115, 1946.
20. L. M. MACK, AGARD Tech. Report No. 709, 1984.
21. L. M. MACK, in Stability of Time-Dependent and Spatially Varying Flows, (D. L. Dwoyer and M. Y. Hussaini, Eds.), Springer, 1986.
22. H. L. REED and W. S. SARIC, Stability of three-dimensional boundary layers, Ann. Rev. Fluid Mech. 21:235 (1989).
23. D. ARNAL, Three-dimensional boundary layers: Laminar-turbulent transition, AGARD Report No. 741, 1986.
24. S. P. WILKINSON and M. R. MALIK, Stability experiments in rotating disk flow, A.I.A.A. Paper No. 83-1760, 1983.
25. H. BIPPES and P. NITCHKE-KOWSKY, Experimental study of instability modes in a three-dimensional boundary layer, A.I.A.A. Paper No. 87-1336, 1987.
26. B. MULLER and H. BIPPES, Experimental study of instability modes in a three-dimensional boundary layer, in Proc. AGARD Symp. on Fluid Dynamics of Three-Dimensional Turbulent Shear Flows and Transition, Cesme, Turkey, 1988.
27. Y. KOHAMA, W. S. SARIC, and J. A. HOOS, A high-frequency secondary instability of cross-flow vortices that leads to transition, in Proc. Roy. Aero. Soc. Conf. on Boundary Layer Transition and Control, p. 4.1, Cambridge, UK, 1991.
28. D. I. A. POLL, Some observations of the transition process on the windward face of a long yawed cylinder, J. Fluid Mech. 150:329 (1985).
29. M. MALIK, The neutral curve for stationary disturbances in rotating disk flow, J. Fluid Mech. 164:275 (1986).
30. P. BALAKUMAR and M. R. MALIK, Travelling disturbances in rotating disk flow, Theor. Comput. Fluid Dyn. 2:125 (1990).
31. P. HALL, An asymptotic investigation of the stationary modes of instability of the boundary layer on a rotating disk, Proc. Roy. Soc London A 406:93 (1986).
32. F. MEYER and L. KLEISER, Numerical investigation of transition in 3D boundary layers, in Proc. AGARD Symp. on Fluid Dynamics of Three-Dimensional Turbulent Shear Flows and Transition, Cesme, Turkey, 1988.
33. M. MALIK and F. LI, Three-dimensional boundary layer stability and transition, S.A.E. Tech. Paper No. 921991, 1992.
34. M. MALIK, F. LI, and C. L. CHANG, Crossflow disturbances in three-dimensional boundary layers: Nonlinear development, wave nteraction and secondary instability, J. Fluid Mech. 268:1 (1994).
35. K. STEWARTSON, Marginally stable inviscid flows with critical layers, I.M.A.J. Appl. Math. 27:133 (1981).
36. S. A. MASLOWE, Critical layers in shear flows, Ann. Rev. Fluid Mech. 18:405 (1986).
37. S. J. COWLEY and X. WU, Asymptotic approaches to transition modelling, AGARD Report No. 793, chap. 3, pp. 1-38, 1994.
38. M. E. GOLDSTEIN, P. A. DURBIN, and S. J. LEIB, Roll-up of vorticity in an adverse pressure gradient boundary layer, J. Fluid Mech 183:325 (1987).
39. M. E. GOLDSTEIN and S. J. LEIB, Nonlinear roll-up of externally excited free shear layers, J. Fluid Mech. 191:481 (1988).
40. M. E. GOLDSTEIN and L. S. HULTGREN, Nonlinear spatial evolution of an externally excited instability wave in a free shear layer, J. Fluid Mech. 197:295 (1988).
41. M. E. GOLDSTEIN and D. W. WUNDROW, Spatial evolution of nonlinear acoustic mode instabilities on hypersonic boundary layers, J. Fluid Mech. 219:585 (1990).
42. F. J. HICKERNELL, Time-dependent critical layers in shear flows on the beta-plane, J. Fluid Mech. 142:431 (1984).
43. J. S. B. GAJJAR, Nonlinear development of a stationary-cross flow vortex, J. Fluid Mech., submitted (1995)
44. J. S. B. GAJJAR and M. AREBI, Nonlinear spatial/temporal development of non-stationary cross-flow vortices, in preparation.
45. X. WU, Nonlinear temporal-spatial modulation of near-planar Rayleigh waves in shear flows: Formation of streamwise vortices, J. Fluid Mech. 256:684 (1993).
46. S. J. LEIB, Nonlinear evolution of subsonic and supersonic disturbances on a compressible mixing layer, J. Fluid Mech. 224:551 (1991).
47. F. T. SMITH and R. J. BODONYI, Nonlinear critical layers and their development in streaming flow stability, J. Fluid Mech. 118:165 (1982).
48. R. HABERMAN, Critical layers in parallel flows, Stud. Appl. Math. 51:139 (1972).
49. J. S. B. GAJJAR and J. W. COLE, Upper branch stability of compressible boundary layer flows, Theor. Comput. Fluid Dyn. 1:105 (1989).
50. J. S. B. GAJJAR and F. T. SMITH, On the global instability of free disturbances with a time-dependent nonlinear viscous critical layer, J. Fluid Mech. 157:53 (1985).
51. J. S. B. GAJJAR and P. SIBANDA, The hydrodynamic stability of channel flow with compliant boundaries, Theor. Comput. Fluid Dyn., to appear (1996).
52. F. T. SMITH, S. N. BROWN, and P. BROWN, Initiation of three-dimensional nonlinear transition paths from an inflexional profile, Eur. J. Fluid Mech. 12:447 (1993).
53. D. M. WUNDROW, Ph.D. Thesis, State University of New York at Buffalo, 1989.