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Probability Density Distribution in Turbulent Wall Boundary-Layer Flows

  • Conference paper
Turbulent Shear Flows 5

Abstract

The present paper provides a summary of a literature survey on statistical properties of wall boundary-layer flows. Existing knowledge on the subject and the authors’ own investigations are described that were initially carried out to yield mean and fluctuating flow properties in turbulent wall boundary layers at high Reynolds numbers. From these investigations, instantaneous velocity information resulted which was processed to yield local velocity information in the form of mean velocity and probability density distributions of the turbulent velocity fluctuations. It is shown that the latter obey a general analytical distribution law. Hence, it is possible to describe probability density distributions in turbulent boundary-layer flows in an analytical form. In the sublayer as well as in the wake region of the boundary layer, a simple form of the general distribution, known as the hyperbolic function, describes the probability density distributions of the velocity fluctuations very well. The latter curve contains four parameters whereas the general distribution requires seven parameters for describing the entire probability density distribution of turbulent velocity fluctuations. The distributions of these parameters across a wall boundary-layer flow are given in the paper.

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Abbreviations

A):

Additive constant of log-law

f̅B):

Mean frequency of occurrence of coherent structure

F):

Flatness factor

Lτ):

Integral time scale

n, k):

Coefficients for hot-wire power-law calibration curve

p(K)):

Probability density distribution

Rθ):

Reynolds number based on momentum thickness

S):

Skewness factor

SS):

Super-skewness factor

SF):

Super-flatness factor

T¯B):

Mean time duration of coherent structure

Δt):

Sampling interval

u):

Instantanious streamwise velocity component

u+):

Non-dimensional velocityu + = u/u τ

uτ):

Friction velocity\({u_{\tau }} = \sqrt {{{\tau _{w}}/\varrho }}\)

U):

Average velocity

U∞):

Free stream velocity

Δu/u τ ):

Coles’s wake parameter

y +):

Non-dimensional distance from the wall y + = yu τ/ v

γ):

Intermittency factor or parameter of general distribution function

δ):

Boundary layer thickness or parameter of general distribution function

ϑ):

Momentum thickness of investigated boundary layer

K):

Von Karman’s constant

v):

Kinematic viscosity

ϱ):

Fluid density

τw):

Wall shear stress

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Author information

Authors and Affiliations

  1. Lehrstuhl für Strömungsmechanik, Universität Erlangen-Nürnberg, Egerlandstr. 13, 8520, Erlangen, Germany

    F. Durst

  2. Boris Kidric Institute of Nuclear Sciences, P.O. Box 522, 11001, Beograd, Yugoslavia

    J. Jovanovic & Lj. Kanevce

Authors
  1. F. Durst
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  2. J. Jovanovic
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  3. Lj. Kanevce
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Editor information

Editors and Affiliations

  1. Lehrstuhl für Strömungsmechanik, Technische Fakultät, Friedrich-Alexander-Universität, Egerlandstraße 13, D-8520, Erlangen, Fed. Rep. of Germany

    Franz Durst

  2. Department of Mechanical Engineering, Institute of Science and Technology, University of Manchester, PO Box 88, Manchester, M60 1QD, England

    Brian E. Launder

  3. Sibley School of Mechanical Aero Engineering, Cornell University, 238 Upson Hall, Ithaca, NY, 14853, USA

    John L. Lumley

  4. Mechanical Engineering Department, The Pennsylvania State University, University Park, PA, 16802, USA

    Frank W. Schmidt

  5. Department of Mechanical Engineering, Imperial College of Science and Technology, Exhibition Road, London, SW7 2BX, England

    James H. Whitelaw

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© 1987 Springer-Verlag Berlin Heidelberg

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Durst, F., Jovanovic, J., Kanevce, L. (1987). Probability Density Distribution in Turbulent Wall Boundary-Layer Flows. In: Durst, F., Launder, B.E., Lumley, J.L., Schmidt, F.W., Whitelaw, J.H. (eds) Turbulent Shear Flows 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-71435-1_18

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  • DOI: https://doi.org/10.1007/978-3-642-71435-1_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-71437-5

  • Online ISBN: 978-3-642-71435-1

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