Eddy structure in turbulent boundary layers

Abstract

In this paper a new analysis is proposed for the driving mechanisms and the statistics for turbulent boundary layers at very high Reynolds numbers. It differs from theories for moderate to low Reynolds numbers and is based on the results of (linear) rapid distortion theory, and both laboratory and field experimental data. The large-scale eddy structure near the wall in boundary layers is distorted in several ways: by the strong mean shear, by the blocking of the normal velocity component and by the moving internal shear layers produced by large eddies as they impinge and scrape along the wall. Elongated streamwise vortices are formed with length scales that are several times the boundary layer height. An approximate stability argument suggests that if the Reynolds number for the turbulence, Re τ≫10 4 , these internal layers are fully turbulent and that the large eddies can burst upward where the vortical eddies interact. The forms of the main statistical quantities, such as variances, spectra, length scales, are derived in terms of outer layer quantities using surface similarity and inhomogeneous linear theory. These `top-down' eddy-impingement, inner-layer/eddy-interaction/ejection mechanisms at very high Reynolds number are sensitive to changes in surface conditions and to variations in pressure gradients. They may therefore require different techniques for their control from those used at lower Reynolds number when boundary layers are driven by `bottom-up' instability/surface-interaction mechanisms. Furthermore, accurate numerical modelling of boundary layers at high Reynolds number requires resolving surface processes at very fine resolution. By inference, it is likely that there is some residual `top-down' influence, even at low Re τ .