Skip to main content
SpringerLink
Log in

On Local Perturbations of a Three-Dimensional Boundary Layer

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

A high-Reynolds steady-state viscous incompressible fluid flow is investigated in the neighborhood of a small three-dimensional irregularity located on the smooth surface of a body and oriented almost along the skin-friction lines. The regime in which quasi-two-dimensional flow with a given pressure gradient is realized on the irregularity scale is studied in detail. The numerical solution of the corresponding boundary value problem for the boundary layer equations is obtained. It is shown that, as distinct from the plane case, this solution is unique.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. F. T. Smith, “Pipeflows distorted by nonsymmetric indentation or branching,” Mathematika, 23, No. 45, 62 (1976).

    Google Scholar 

  2. F. T. Smith, R. I. Sykes, and P. W. M. Brighton, “A two-dimensional boundary layer encountering a three dimensional hump,” J. Fluid Mech., 83, 163 (1977).

    Google Scholar 

  3. V.V. Bogolepov, “Investigation of small three-dimensional perturbations of a laminar boundary layer,” Zh. Prikl. Mekh. Tekh. Fiz., No. 5, 69 (1987).

  4. F. T. Smith, “Steady and unsteady 3-D interactive boundary layers,” Comput. and Fluids, 20, 243 (1991).

    Google Scholar 

  5. Vik. V. Sychev, “Three-dimensional flows near irregularities on the surface of an axisymmetric body,” Uch. Zap. TsAGI, 24, No. 1, 12 (1993).

    Google Scholar 

  6. S. N. Timoshin and F. T. Smith, “Singularities encountered in three-dimensional boundary layers under an adverse or favorable pressure gradient,” Phil. Trans. Roy. Soc. London. Ser. A, 352, No. 1698, 45 (1995).

    Google Scholar 

  7. I. I. Lipatov and I.V. Vinogradov, “Three-dimensional flows near surface distortions for the compensation regime,” Phil. Trans. Roy. Soc. London. Ser. A, 358, No. 1777, 3143 (2000).

    Google Scholar 

  8. L. F. Cradtree, D. Küchemann, and L. Sowerby, “Three-dimensional boundary layers,” in: L. Rosenhead (Ed.), Laminar Boundary Layers, Clarendon Press, Oxford (1963), P. 409.

    Google Scholar 

  9. Vik. V. Sychev, “Local perturbation of a boundary layer with small skin friction,” Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 6, 87 (1998).

  10. Vik. V. Sychev, “On interaction and separation for internal flows with small skin friction,” Izv. Ros. Akad. Nauk, Mekh. Zhidk. Gaza, No. 5, 98 (1996).

  11. A. I. Ruban, “A singular solution of the boundary layer equations which can be continuously continued through the point of zero skin friction,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 42 (1981).

  12. S. Goldstein, “On laminar boundary-layer flow near a position of separation,” Quart. J. Mech. Appl. Math., 1, 43 (1948).

    Google Scholar 

  13. K. Stewartson, “Is the singularity at separation removable?,” J. Fluid Mech., 44, 347 (1970).

    Google Scholar 

  14. O. R. Tutty, “Nonlinear development of flow in channels with non-parallelwalls,” J. Fluid Mech., 326, 265 (1996).

    Google Scholar 

  15. Vik. V. Sychev, “Local separation zones in flows with small surface friction,” Uch. Zap. TsAGI, 33, No. 1-2, 1 (2002).

    Google Scholar 

  16. G. L. Korolev, “Flow separation and nonuniqueness of the solution of the boundary layer equations,” Zh. Vychisl. Matematiki i Mat. Fiziki, 31, No. 11, 1706 (1991).

    Google Scholar 

  17. V.V. Sychev, A. I. Ruban, Vik. V. Sychev et al., Asymptotic Theory of Separation Flows [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  18. V. B. Zametaev, “Formation of singularities in the three-dimensional boundary layer,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 58 (1989).

  19. A. I. Ruban, “Asymptotic theory of short separation zones on the leading edge of a slender foil,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 42 (1982).

  20. K. Stewartson, F. T. Smith, and K. Kaups, “Marginal separation,” Stud. Appl. Math., 67, 45 (1982).

    Google Scholar 

  21. S.N. Brown and K. Stewartson, “On an integral equation of marginal separation,” SIAM J. Appl. Math., 43, 1119 (1983).

    Google Scholar 

  22. O. S. Ryzhov and F. T. Smith, “Short-length instabilities, breakdown, and initial value problems in dynamic stall,” Mathematika, 31, No. 62, 163 (1984).

    Google Scholar 

  23. V. B. Zametaev, “Marginal separation in three-dimensional flows,” Theoret. Comput. Fluid Dyn., 8, No. 3, 183 (1996).

    Google Scholar 

  24. A. Kluwick, “Interacting laminar and turbulent boundary layers,” in: A. Kluwick (Ed.), Recent Advances in Boundary Layer Theory, Springer, Wien (1998), P. 231.

    Google Scholar 

  25. S. N. Brown, “Singularities associated with separating boundary layers,” Phil. Trans. Roy. Soc. London. Ser. A, 257, No. 1084, 409 (1965).

    Google Scholar 

Download references

Authors
  1. G. L. Korolev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vik. V. Sychev
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korolev, G.L., Sychev, V.V. On Local Perturbations of a Three-Dimensional Boundary Layer. Fluid Dynamics 38, 273–283 (2003). https://doi.org/10.1023/A:1024277220242

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1024277220242

Search

Navigation