Flow visualization studies of the zero-pressure-gradient turbulent boundary layer over the Reynolds-number range 500 < Reθ < 17500 have shown large Reynolds-number effects on boundary-layer structure.At high Reynolds numbers (Reθ > 2000, say) the layer appears to consist very largely of elongated hairpin vortices or vortex pairs, originating in the wall region and extending through a large part of the boundary-layer thickness or beyond it; they are for the most part inclined to the wall at a characteristic angle in the region of 40–50°. Large-scale features, which exhibit a slow overturning motion, appear to consist mainly of random arrays of such hairpin vortices, although there is some evidence of more systematic structures.At low Reynolds numbers (Reθ < 800, say) the hairpin vortices are very much less elongated and are better described as horseshoe vortices or vortex loops; large-scale features now consist simply of isolated vortex loops (at the very lowest Reynolds numbers), or of several such loops interacting strongly, and show a relatively brisk rate of rotation.

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The interaction between strain-rate and rotation in shear flow turbulence from inertial range to dissipative length scales Phys. Fluids 23, 061704 (2011); 10.1063/1.3599080Small scale structure of homogeneous turbulent shear flow

This paper describes an experimental study of turbulent boundary layers over two-dimensional spanwise groove and three-dimensional sandgrain roughnesses in the ‘transition regime’ between hydraulically smooth and fully rough conditions. Mean-flow measurements show that a state of kinematic near-self-preservation is also reached by sandgrain roughness and not just by d-type grooved roughness alone as commonly believed; sandgrain roughness simply requires an order-of-magnitude-longer length to reach such a state. The two roughness Reynolds numbers demarcating the boundaries of the transition regime of k-type roughnesses are found to decrease with increasing roughness-element spanwise aspect ratio (span/height). A more important role of the upper-Reynolds-number limit of the transition regime in the drag behaviour is indicated. The two Reynolds-number limits of the transition regime correlate with the two critical Reynolds numbers that describe the stability of the vortex-shedding process existing behind a similar but isolated roughness element lying submerged in an otherwise laminar boundary layer. The results provide a guideline for reducing k-type rough-wall drag by lowering the spanwise aspect ratio of the roughness elements. The vortex-shedding process in rough-wall turbulent boundary layers is described by the stability parameter $U\tau (\overline{T}/\nu)^{\frac{1}{2}}$ whose value is the same for all roughnesses examined herein; here Uτ is the friction velocity, $\overline{T}$ is the mean time period of vortex shedding and v is the kinematic viscosity of the fluid.