The structure of a three-dimensional turbulent boundary layer

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.

Near-Wall Measurements of a Three-Dimensional Turbulent Boundary Layer.

“…They found that the near-wall flow should be collateral to leading order, and that W profiles should display a logarithmic region at high Reynolds number. Degani, Smith and Walker (1993) extended that study to fully three-dimensional boundary layers, again seeking a functional form for the W profile.…”

Near-wall measurements in a three-dimensional turbulent boundary layer

“…The most useful models for three-dimensional turbulent boundary layers would be universal streamwise and crossflow mean velocity profiles analogous to the law of the wall. Early attempts to determine a universal crossflow profile have been essentially abandoned, though theoretical limits have been addressed recently by Degani, Smith & Walker (1993). Ölçmen & Simpson (1992) presented a brief review of threedimensional turbulent boundary layer experiments, and applied several variations of the law of the wall.…”

Wind Tunnel ‘Concept of Proof’ Investigations in the Development of Novel Fluid Mechanical Methodologies and Devices

“…In this section, extension of the usage of multi-hole pressure measurement technique mentioned earlier to the development and validation of a novel shear stress measurement technique will be described in greater detail. Measurement techniques for shear stress in three dimensional turbulent boundary layer flows have relied mainly on a combination of physical experimentation and subsequent empirical relationships or theoretical approaches supplemented by experimental correlation [4], [5]. The five-hole pressure measurement technique was first used in 1915.…”