Nonlinear shortwave Tollmien-Schlichting instability in a boundary layer on a film-coated wall

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 454, Issue 1980, 1998, Pages 3223-3256

  Bowles, R I ^a   Caporn, P ^a   Timoshin, S N ^a  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

Asymptotic theory; Nonlinear waves; Secondary instability; Triple deck flow; Two fluid flow; Wave resonance

Indexed keywords

EID: 0000904320     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1998.0299     Document Type: Article

References (38)

1. Akylas, T. R. 1982 A nonlinear theory for the generation of water waves by wind. Stud. Appl. Math. 67, 1-24.
2. Andreussi, P., Asali, J. C. & Hanratty, T. J. 1985 Initiation of roll waves in gas-liquid flows. AIChE J. 31, 119-126.
3. Brotherton-Ratcliffe, R. V. 1986 Boundary-layer effects in liquid layer flows. PhD thesis, University of London, UK.
4. Conlisk, A. T., Burggraf, O. R. & Smith, F. T. 1987 Trans ASME FED 52, 119-121.
5. Cowley, S. J. 1985 High frequency Rayleigh instability of Stokes layers. In Stability of time dependent and spatially varying flows (cd. D. L. Dwoyer & M. Y. Hussaini), pp. 261-275. New York: Springer.
6. Craik, A. D. D. 1982 The drift velocity of water waves. J. Fluid Mech. 116, 187-205.
7. Dangelmayr, G. & Knobloch, E. 1987 The Takens-Bogdanov bifurcation with O(2)-symmetry. Phil. Trans. R. Soc. Land. A 322, 243-279.
8. Dore, B. D. 1970 Mass transport in layered fluid systems. J. Fluid Mech. 40, 113-126.
9. Dore, B. D. 1976 Double boundary layers in standing interfacial waves. J. Fluid Mech. 76, 819-828.
10. Dore, B. D. 1977 On mass transport velocity due to progressive waves. Q. J. Mech. Appl. Math. 30, 157-173.
11. Drazin, P. G. 1970 Kelvin-Helmholtz instability of finite amplitude. J. Fluid Mech. 42, 321-335.
12. Drazin, P. G. & Reid, W. H. 1981 Hydrodynamic stability. Cambridge University Press.
13. Guckenheimer, J. & Knobloch, E. 1983 Nonlinear convection in a rotating layer: amplitude expansions and normal forms. Geophys. Astrophys. Fluid Dyn. 23, 247-272.
14. Hall, P. 1995 A phase-equation approach to boundary-layer instability theory: TollmienSchlichting waves. J. Fluid Mech. 304, 185-212.
15. Hall, P. & Bennett, J. 1986 Taylor-Gortler instabilities of Tollmien-Schlichting waves and other flows governed by the interactive boundary-layer equations. J. Fluid Mech. 171, 441-457.
16. Hall, P. & Smith, F. T. 1984 On the effects of non-parallelism, three-dimensionality, and mode interaction in nonlinear boundary-layer stability. Stud. Appl. Alath. 70, 91-120.
17. Hanratty, T. J. & Engen, J. M. 1957 Interaction between a turbulent air stream and a moving water surface. AIChE J. 3, 299-304.
18. Kachanov, Y. S., Ryzhov, O. S. & Smith, F. T. 1993 Formation of solitons in transitional boundary layers: theory and experiment. J. Fluid Mech. 251, 273-297.
19. Kao, T. W. & Park, C. 1972 Experimental investigations of the stability of channel flows. Part 2. Two-layered co-current flow in a rectangular channel. J. Fluid Mech. 52, 401-423.
20. Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Land. A 245, 535-581.
21. Ludwieg, H. & Hornung, H. 1989 The instability of a liquid film on a wall exposed to an air flow. J. Fluid Mech. 200, 217-233.
22. Moroz, I. M. & Leibovich, S. 1985 Oscillatory and competing instabilities in a nonlinear model for Langmuir circulations. Phys. Fluids 28, 2050-2061.
23. Nelson, J. J., Alving, A. E. & Joseph, D. D. 1995 Boundary layer flow of air over water on a flat plate. J. Fluid Mech. 284, 159-169.
24. Pedlosky, J. 1970 Finite-amplitude baroclinic waves. J. Atmos. Sei. 27, 15-30.
25. Ruban, A. I. 1983 A nonlinear equation for the Tollmien-Schlichting wave amplitude in a boundary layer. Izv. Akad. Nauk SSSR, Mekh. Zhidk. i Gaza 6, 60-67.
26. Smith, F. T. 1979 Nonlinear stability of boundary layers for disturbances of various sizes. Proc. R. Soc. Lond. A 368, 573-589.
27. Smith, F. T. 1986 Two-dimensional disturbance travel, growth and spreading in boundary layers. J. Fluid Mech. 169, 353-377.
28. Smith, F. T. &: Bodonyi, R. J. 1985 On short-scale inviscid instabilities in flow past surface-mounted obstacles and other non-parallel motions. Aero. J. June/July, 205-212.
29. Smith, F, T. & Burggraf, O. R. 1985 On the development of large-sized short-scaled disturbances in boundary layers. Proc. R. Soc. Land. A 399, 25-55.
30. Timoshin, S. N. 1997 Instabilities in a high-Reynolds number boundary layer on a film-coated surface. J. Fluid Mech. 353, 163-195.
31. Tsao, J.-C., Rothmayer, A. P. & Ruban, A. I. 1996 Stability of air flow past thin liquid films on airfoils. AIAA Paper 96-2155.
32. Tsao, J.-C., Rothmayer, A. P. &: Ruban, A. I. 1997 Stability of air flow past thin liquid films on airfoils. Comp. Fluids 353, 163-195.
33. Tutty, O. R. &: Cowley, S. J. 1986 On the stability and the numerical solution of the unsteady interactive boundary-layer equation. J. Fluid Mech. 168, 431-456.
34. Van Dommelen, L. L. & Shen, S. F. 1982 The genesis of separation. In Numerical methods and physical aspects of aerodynamic flows (ed. T. Cebeci), pp. 293-311. New York: Springer.
35. Van Duin, C. A. 1996 An asymptotic theory for generation of nonlinear surface gravity waves by turbulent air flow. J. Fluid Mech. 320, 287-304.
36. von Kerczek, C. &: Davis, S. H. 1974 Linear stability theory of oscillatory Stokes layers. J. Fluid Mech. 62, 753-773.
37. Weissman, M. A. 1979 Nonlinear wave packets in the Kelvin-Helmholtz instability. Phil. Trans. R. Soc. Land. A 290, 639-681.
38. Zhuk, V. I. &: Ryzhov, O. S. 1982 Locally non-viscous perturbations in a boundary layer with self-induced pressure. Dokl. Akad. Nauk SSSR 263, 56-59.