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Singular solution of boundary layer equations which can be extended continuously through the point of zero surface friction

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Abstract

It is shown that the Prandtl equations for an incompressible boundary layer admit a solution which can be extended continuously through the point of zero friction on the surface and is singular at this point. A solution of this type is realized, in particular, at the leading edge of a slender profile at an angle of attack to the oncoming flow.

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Literature cited

  1. L. Prandtl, “:Uber Flüssigkeitsbewegung bei sehr kleiner Reibung,” Verhandlung, des 3-re Internat. Math. Kongr. Heidelberg, 1904, Leipzig (1904).

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

  3. L. D. Landau and E. M. Lifshitz, Mechanics of Continuous Media [in Russian], Gostekhizdat, Moscow (1944).

    Google Scholar 

  4. S. N. Brown and K. Stewartson, “Laminar separation,” Annu. Rev. Fluid Mech.,1, Palo Alto, Calif. (1969).

  5. K. Stewartson, “Is the singularity at separation removable?” J. Fluid Mech.,44, Pt. 2 (1970).

  6. Yu. N. Ermak, “Flow of a viscous incompressible fluid past the rounded leading edge of a slender aerofoil,” Tr. TsAGI, No. 1141 (1969).

  7. M. J. Werle and R. T. Davis, “Incompressible laminar boundary layers on a parabola at angle of attack: a study of the separation point,” Trans. ASME, Ser. E.—J. Appl. Mech.,39, No. 1 (1972).

  8. J. D. Cole, Perturbation Methods in Applied Mathematics, Blaisdell, Waltham, Mass. (1968).

    Google Scholar 

  9. K. Stewartson, “On Goldstein's theory of laminar separation,” Q. J. Mech. Appl. Math-,11, Pt. 4 (1958).

  10. A. F. Nikiforov and V. B. Uvarov, Fundamentals of the Theory of Special Functions [in Russian], Nauka, Moscow (1974).

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Authors and Affiliations

  1. Moscow

    A. I. Ruban

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  1. A. I. Ruban
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Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 42–52, October–December, 1931.

I thank V. V. Sychev and Vik. V. Sychev for discussing the work and helpful comments.

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Ruban, A.I. Singular solution of boundary layer equations which can be extended continuously through the point of zero surface friction. Fluid Dyn 16, 835–843 (1981). https://doi.org/10.1007/BF01089710

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  • DOI: https://doi.org/10.1007/BF01089710

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