THE STRUCTURE OF A 3-DIMENSIONAL TURBULENT BOUNDARY-LAYER

The three-dimensional turbulent boundary layer is shown to have a self -consistent two-layer asymptotic structure in the limit of large Reyno lds number. In a streamline coordinate system, the streamwise velocity distribution is similar to that in two-dimensional flows, having a de fect-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 t o exhibit a logarithmic form in the overlap region. The inner wall-lay er flow is collateral to leading order but the influence of the pressu re gradient, at large but finite Reynolds numbers, is not negligible a nd can cause substantial skewing of the velocity profile near the wall . Conditions under which the boundary layer achieves self-similarity a nd the governing set of ordinary differential equations for the outer layer are derived. The calculated solution of these equations is match ed asymptotically to an inner wall-layer solution and the composite pr ofiles so formed describe the flow throughout the entire boundary laye r. The effects of Reynolds number and cross-stream pressure gradient o n the cross-stream velocity profile are discussed and it is shown that the location of the maximum cross-stream velocity is within the overl ap region.