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Complete breakdown of an unsteady interactive boundary layer (over a surface distortion or in a liquid layer)

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

R. V. Brotherton-Ratcliffe  and
F. T. Smith
R. V. Brotherton-Ratcliffe
Affiliation:
Flat 3, 164, Queenstown Road, London, SW8 3QH.
F. T. Smith
Affiliation:
Department of Mathematics, University College London, Gower Street, London. WC1E6BT.
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Summary

It is shown first that internal or external boundary-layer flow over obstacles or other surface distortions is susceptible to a novel kind of viscous-inviscid instability, involving growth rates much larger than those of traditional Tollmien-Schlichting and Gortler modes for instance. The same instabilities arise in liquid-layer flow at sub-critical Froude number, and they are associated with an interacting boundary-layer problem where the normalized pressure is equal to the normalized displacement decrement. Second, certain limiting linear and nonlinear disturbances are studied to shed more light on the overall instability process and each form of disturbance leads to a finite-time collapse, although different in each case. Thirdly, and in consequence, the work finds the significant feature that the whole interacting boundary layer can break down nonlinearly within a finite scaled time.

MSC classification

Secondary: 76D10: Boundary-layer theory, separation and reattachment, higher-order effects
Type
Research Article
Information
Mathematika , Volume 34 , Issue 1 , June 1987 , pp. 86 - 100
Copyright
Copyright © University College London 1987

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References

1.Smith, F. T. and Daniels, P. G.. J. Fluid Meek, 110 (1981), 1–37.CrossRefGoogle Scholar
2.Gajjar, J. and Smith, F. T.. Mathematika, 30 (1983), 77–93.CrossRefGoogle Scholar
3.Smith, F. T. and Burggraf, O. R.. Proc Roy. Soc, A399 (1985), 25–55.Google Scholar
4.Bennett, J. & Hall, P., Meek, j. Fluid, (1986).Google Scholar
5.Stewart, P. A. and Smith, F. T.. Proc. Roy. Soc, A409 (1987), 229–248.Google Scholar
6.Reshotko, E.. In Turbulence and Chaotic Phenomena in Fluids, ed. Tatsumi, T. (Elsevier, 1984).Google Scholar
7.Smith, F. T., Brighton, P. W. M., Jackson, P. S. and Hunt, J. C. R.. j. Fluid Mech., 113 (1981), 123–152.Google Scholar
8.Smith, F. T.. Proc. Roy. Soc. A366 (1979), 91 and A368 (1979), 573.Google Scholar
9.Burggraf, O. R., Conlisk, A. T. and Smith, F. T.. To appear in Trans. A.S.M.E. Forum on unsteady separation, June 1987, Cincinati, Ohio, U.S.A.Google Scholar
10.Ryzhov, O. S. and Smith, F. T.. Mathematika, 31 (1984), 163–177.CrossRefGoogle Scholar
11.Whitham, G. B.. Linear and Nonlinear Waves (Wiley, 1974).Google Scholar
12.Smith, F. T.. Utd. Tech. Res. Cent., Hartford, E., CT, U.S.A., Rept. UT85-55 (1985); also, Proc Symp. on the Stability of Spatially-Varying and Time-Dependent Flows, Editors Dwoyer, D. L. and Hussaini, M. Y. (Springer, 1987).Google Scholar
13.Brotherton-Ratclifle, R. V.. Ph.D. Thesis (Univ. of London, 1987).Google Scholar