Skip to main content
SpringerLink
Log in

Amplitude-Dependent Neutral Modes in Compressible Boundary Layer Flows

  • Conference paper
Instability and Transition

Part of the book series: ICASE/ NASA LaRC Series ((ICASE/NASA))

Abstract

The ideas of Benney and Bergeron (1969) and Davies (1969) on nonlinear critical layers are extended, and some new nonlinear neutral modes are computed for compressible boundary layer flow. A special case of the work is when the generalized inflexion point criterion holds. Neutral modes are found for a range of phase-speeds, dependent on the Mach number, and the properties of these are discussed. As in the linear case when the flow is relatively supersonic, multiple neutral modes exist. The behavior of the neutral amplitude in some limiting cases is also considered, and it is found that the results are significantly different from that in incompressible flow when the flow is locally supersonic.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Benney, D. J., Stud. Appl. Math. 48, 1969, 181.

    Google Scholar 

  2. Bodonyi, R. J., Smith, F. T., and Gajjar, J., I.M.A. Jour. Appl. Math. 30, 1983, 1.

    MathSciNet  ADS  MATH  Google Scholar 

  3. Cole, J. W., Thesis, University of Exeter, 1989, in preparation.

    Google Scholar 

  4. Cowley, S. J. and Hall, P., ICASE Report No. 88–72, 1989.

    Google Scholar 

  5. Davies, R. E., Jour. Fluid Mech. 36, 1969, 337.

    Article  ADS  Google Scholar 

  6. Gajjar, J. and Smith, F. T., Jour. Fluid Mech. 157, 1985, 53.

    Article  MathSciNet  ADS  Google Scholar 

  7. Gajjar, J. S. B. and Cole, J. W., Theor. Comp. Fluid Dyn. 1, 1989a, 105.

    MATH  Google Scholar 

  8. Gajjar, J. S. B. and Cole, J. W., in preparation, 1989b.

    Google Scholar 

  9. Goldstein, M. E., Durbin, P. A., and Leib, S. J., Jour. Fluid Mech. 183, 1987, 325.

    Article  ADS  Google Scholar 

  10. Goldstein, M. E. and Hultgren, L., Jour. Fluid Mech. 197,1988, 295.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Goldstein, M. E. and Leib, S. J., to appear in Jour. Fluid Mech. 1989.

    Google Scholar 

  12. Haberman, R., Stud. Appl. Math. 51, 1972, 139.

    Google Scholar 

  13. Jackson, T. L. and Grosch, C. E., ICASE Report No. 88–33, 1988.

    Google Scholar 

  14. Lees, L. and Lin, C. C., NASA Tech. Note No. 1115,1946.

    Google Scholar 

  15. Lees, L. and Reshotko, E., Jour. Fluid Mech. 12, 1962, 555.

    Article  MathSciNet  ADS  Google Scholar 

  16. Mack, L. M., AGARD Report No. 709,1984.

    Google Scholar 

  17. Mack, L. M., Proc. of the Symp. on the Stability of Spatially Varying and Time Dependent Flows (eds. D. L. Dwoyer and M. Y. Hussaini), Springer-Verlag, 1986.

    Google Scholar 

  18. Malik, M. R., AIAA Paper No. 87–1414, 1987.

    Google Scholar 

  19. Reshotko, E., NASA Tech. Note No. D1220, 1960.

    Google Scholar 

  20. Reshotko, E., Ann. Rev. Fluid Mech. 8, 1976, 311.

    Article  ADS  Google Scholar 

  21. Smith, F. T., Jour. Fluid Mech. 198, 1989, 127.

    Article  ADS  Google Scholar 

  22. Smith, F. T. and Bodonyi, R. J., Jour. Fluid Mech. 118, 1982, 165.

    Article  MathSciNet  ADS  Google Scholar 

  23. Smith, F. T., Doorly, D., and Rothmeyer, A., Jour. Fluid Mech. to appear, 1989.

    Google Scholar 

  24. Stewartson, K., IMA Jour. Appl. Math. 27, 1981, 133.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics North Park Road, University of Exeter, Exeter, EX4 4QE, England

    J. S. B. Gajjar

Authors
  1. J. S. B. Gajjar
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Institute for Computer Applications in Science and Engineering (ICASE) ICASE, NASA Langley Research Center, 23665, Hampton, VA, USA

    M. Y. Hussaini  & R. G. Voigt  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag New York Inc.

About this paper

Cite this paper

Gajjar, J.S.B. (1990). Amplitude-Dependent Neutral Modes in Compressible Boundary Layer Flows. In: Hussaini, M.Y., Voigt, R.G. (eds) Instability and Transition. ICASE/ NASA LaRC Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3432-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3432-6_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-97324-1

  • Online ISBN: 978-1-4612-3432-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation