Journal of Applied Mechanics and Technical Physics

, Volume 12, Issue 5, pp 706–713 | Cite as

Asymptotic theory of the turbulent boundary layer as a problem of singular perturbations

  • D. N. Vasil'ev
Article
  • 23 Downloads

Abstract

We consider an asymptotic theory of the turbulent boundary layer [1,2]. In this paper we make an attempt to further develop the mathematical aspects of this theory. We demonstrate the features of this theory by applying it to a problem which is close to the so-called equilibrium turbulent boundary layer with a pressure gradient and blowing.

Keywords

Mathematical Modeling Boundary Layer Mechanical Engineer Pressure Gradient Industrial Mathematic 

Notation

x, y

coordinates, parallel and perpendicular to the wall

u

velocity component in the x direction

p, ϱ',v

pressure, density, and kinematic viscosity coefficient

l'

scale of turbulence

τ

tangential stress

speed at the outer edge of the boundary layer

δ

thickness of the boundary layer

δ*

displacement thickness

δ**

momentum loss thickness

Cf

coefficient of friction

R

Reynolds number

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Literature cited

  1. 1.
    S. S. Kutateladze and A. I. Leont'ev, Turbulent Boundary Layer of a Compressible Gas [in Russian], Izv. Sibirsk. Otd., Akad. Nauk SSSR, Novosibirsk (1962).Google Scholar
  2. 2.
    S. S. Kutateladze, A. I. Leont'ev, N. A. Rubtsov etal., Heat-Mass Transfer and Friction in the Turbulent Boundary Layer [in Russian], Izv. Sibirsk. Otd., Akad. Nauk SSSR, Novosibirsk (1964).Google Scholar
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    J. Rotta, “Turbulent boundary layers in incompressible flow,” in: Progress in Aeronautical Sciences, Vol. 2, Pergamon, London (1962).Google Scholar
  4. 4.
    F. H. Clauser, “The turbulent boundary layer,” in: Advances in Applied Mechanics, Vol. 4, Academic, New York (1956).Google Scholar
  5. 5.
    M. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic, New York (1964).Google Scholar
  6. 6.
    H. H. Ferbholz, “Experimentelle Untersuchung einer inkompressiblen turbulenten grenzschicht mit wandreibung nahe null an enem längsangeströmten kreiszylinder,” Z. Flugwiss., Irg. 16, H. 11 (1968).Google Scholar
  7. 7.
    B. Stratford, “An experimental flow with zero skin friction throughout its region of pressure rise,” J. Fluid Mech.,5, Part 1 (1959).Google Scholar

Copyright information

© Consultants Bureau, a division of Plenum Publishing Corporation 1974

Authors and Affiliations

  • D. N. Vasil'ev
    • 1
  1. 1.Gor'kii

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