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The structure of a three-dimensional turbulent boundary layer

Smith, FT; Degani, AT; Walker, JDA; (1993) The structure of a three-dimensional turbulent boundary layer. Journal of Fluid Mechanics , 250 43 - 68. 10.1017/S0022112093001375. Green open access

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Abstract

The three-dimensional turbulent boundary layer is shown to have a self-consistent two-layer asymptotic structure in the limit of large Reynolds number. In a streamline coordinate system, the streamwise velocity distribution is similar to that in two-dimensional flows, having a defect-function form in the outer layer which is adjusted to zero at the wall through an inner wall layer. An asymptotic expansion accurate to two orders is required for the cross-stream velocity which is shown to exhibit a logarithmic form in the overlap region. The inner wall-layer flow is collateral to leading order but the influence of the pressure gradient, at large but finite Reynolds numbers, is not negligible and can cause substantial skewing of the velocity profile near the wall. Conditions under which the boundary layer achieves self-similarity and the governing set of ordinary differential equations for the outer layer are derived. The calculated solution of these equations is matched asymptotically to an inner wall-layer solution and the composite profiles so formed describe the flow throughout the entire boundary layer. The effects of Reynolds number and cross-stream pressure gradient on the cross-stream velocity profile are discussed and it is shown that the location of the maximum cross-stream velocity is within the overlap region.

Type: Article
Title: The structure of a three-dimensional turbulent boundary layer
Open access status: An open access version is available from UCL Discovery
DOI: 10.1017/S0022112093001375
Publisher version: http://dx.doi.org/10.1017/S0022112093001375
Language: English
Additional information: © 1993 Cambridge University Press
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/82798
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