TURBULENT BOUNDARY LAYERS WITH NEGLIGIBLE WALL STRESS: A SINGULAR-PERTURBATION THEORY

A singular-perturbation theory of turbulent boundary layers with negligible wall stress is developed. The first-order analysis is based on the premise that at an arbitrarily large Reynolds number the flow under consideration should be primarily dominated by inertia effects rather than by viscosity. The constraints of the wall introduce only second-order effects, since in the situation with zero wall stress viscous shear stresses are very small. A single-layer model, utilizing the free-stream velocity scale and the boundary-layer thickness as the length scale, therefore, is used in the first-order analysis. In the second-order analysis the effects of the constraints of the wall are included by assuming a two-layer model. An analysis of the second-order inner layer for the flow under consideration leads to a second-order 'law of the wall'. The second-order correction to the velocity profile in the outer layer leads to a second-order 'velocity-defect law'. Asymptotic matching between the wall law and the velocity-defect law results in a semi-logarithmic distribution of the velocity profile in an overlap region. A comparison between Stratford's experimental data and the results of this analysis indicates a satisfactory agreement.

  • Corporate Authors:

    Pergamon Press, Incorporated

    Maxwell House, Fairview Park
    Elmsford, NY  USA  10523
  • Authors:
    • Chawla, T C
    • Tennekes, H
  • Publication Date: 1973-1

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Filing Info

  • Accession Number: 00050155
  • Record Type: Publication
  • Source Agency: Engineering Index
  • Files: TRIS
  • Created Date: Nov 14 1973 12:00AM