The role of coherent structures in the production and dissipation of turbulence in a boundary layer is characterized, summarizing the results of recent investigations. Coherent motion is defined as a three-dimensional region of flow where at least one fundamental variable exhibits significant correlation with itself or with another variable over a space or time range significantly larger than the smallest local scales of the flow. Sections are then devoted to flow-visualization experiments, statistical analyses, numerical simulation techniques, the history of coherent-structure studies, vortices and vortical structures, conceptual models, and predictive models. Diagrams and graphs are provided.

Coherent Motions in the Turbulent Boundary Layer

The structure of energy-containing turbulence in the outer region of a zero-pressure-
 gradient boundary layer has been studied using particle image velocimetry (PIV) to measure the instantaneous velocity fields in a streamwise-wall-normal plane. Experiments performed at three Reynolds numbers in the range 930 0) that occur on a locus inclined at 30–60° to the wall.In the outer layer, hairpin vortices occur in streamwise-aligned packets that propagate with small velocity dispersion. Packets that begin in or slightly above the buffer layer are very similar to the packets created by the autogeneration mechanism (Zhou, Adrian & Balachandar 1996). Individual packets grow upwards in the streamwise direction at a mean angle of approximately 12°, and the hairpins in packets are typically spaced several hundred viscous lengthscales apart in the streamwise direction. Within the interior of the envelope the spatial coherence between the velocity fields induced by the individual vortices leads to strongly retarded streamwise momentum, explaining the zones of uniform momentum observed by Meinhart & Adrian (1995). The packets are an important type of organized structure in the wall layer in which relatively small structural units in the form of three-dimensional vortical structures are arranged coherently, i.e. with correlated spatial relationships, to form much longer structures. The formation of packets explains the occurrence of multiple VITA events in turbulent ‘bursts’, and the creation of Townsend's (1958) large-scale inactive motions. These packets share many features of the hairpin models proposed by Smith (1984) and co-workers for the near-wall layer, and by Bandyopadhyay (1980), but they are shown to occur in a hierarchy of scales across most of the boundary layer.In the logarithmic layer, the coherent vortex packets that originate close to the wall frequently occur within larger, faster moving zones of uniform momentum, which may extend up to the middle of the boundary layer. These larger zones are the induced interior flow of older packets of coherent hairpin vortices that originate upstream and over-run the younger, more recently generated packets. The occurence of small hairpin packets in the environment of larger hairpin packets is a prominent feature of the logarithmic layer. With increasing Reynolds number, the number of hairpins in a packet increases.

Vortex organization in the outer region of the turbulent boundary layer

▪ AbstractWe review the experimental evidence on turbulent flows over rough walls. Two parameters are important: the roughness Reynolds number ks+, which measures the effect of the roughness on the buffer layer, and the ratio of the boundary layer thickness to the roughness height, which determines whether a logarithmic layer survives. The behavior of transitionally rough surfaces with low ks+ depends a lot on their geometry. Riblets and other drag-reducing cases belong to this regime. In flows with δ/k ≲ 50, the effect of the roughness extends across the boundary layer, and is also variable. There is little left of the original wall-flow dynamics in these flows, which can perhaps be better described as flows over obstacles. We also review the evidence for the phenomenon of d-roughness. The theoretical arguments are sound, but the experimental evidence is inconclusive. Finally, we discuss some ideas on how rough walls can be modeled without the detailed computation of the flow around the roughness element...

Turbulent flows over rough walls

Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.

Hairpin vortex organization in wall turbulencea)

Detailed measurements of flow velocity and its turbulent fluctuation were obtained over fixed, two-dimensional dunes in a laboratory channel. Laser Doppler anemometry was used to measure the downstream and vertical components of velocity at more than 1800 points over one dune wavelength. The density of the sampling grid allowed construction of a unique set of contour maps for all mean flow and turbulence parameters, which are assessed using higher moment measures and quadrant analysis. These flow field maps illustrate that: (1) the time-averaged downstream and vertical velocities agree well with previous studies of quasi-equilibrium flow over fixed and mobile bedforms and show a remarkable symmetry from crest to crest; (2) the maximum root-mean-square (RMS) of the downstream velocity values occur at and just downstream of flow reattachment and within the flow separation cell; (3) the maximum vertical RMS values occur within and above the zone of flow separation along the shear layer and this zone advects and diffuses downstream, extending almost to the next crest; (4) positive downstream skewness values occur within the separation cell, whereas positive vertical skewness values are restricted to the shear layer; (5) the highest Reynolds stresses are located within the zone of flow separation and along the shear layer; (6) high-magnitude, high-frequency quadrant-2 events (‘ejections’) are concentrated along the shear layer (Kelvin-Helmholtz instabilities) and dominate the contribution to the local Reynolds stress; and (7) high-magnitude, high-frequency quadrant-4 events occur bounding the separation zone, near reattachment and close to the dune crest, and are significant contributors to the local Reynolds stress at each location. These data demonstrate that the turbulence structure associated with dunes is controlled intrinsically by the formation, magnitude and downstream extent of the flow separation zone and resultant shear layer. Furthermore, the origin of dune-related macroturbulence lies in the dynamics of the shear layer rather than classical turbulent boundary layer bursting. The fluid dynamic distinction between dunes and ripples is reasoned to be linked to the velocity differential across the shear layer and hence the magnitude of the Kelvin-Helmholtz instabilities, which are both greater for dunes than ripples. These instabilities control the local flow and turbulence structure and dictate the modes of sediment entrainment and their transport rates.

Mean flow and turbulence structure over fixed, two-dimensional dunes: implications for sediment transport and bedform stability

Burst structures in the near wall region of turbulent flows are associated with a large portion of the turbulent momentum transport from the wall. However, quantitative measures of the timescales associated with the burst event are not well defined, largely due to ambiguities associated with the methods used to detect a burst.In the present study, Eulerian burst-detection schemes were developed through extensions of the uv quadrant 2, VITA, and u-level techniques. Each of the basic techniques detects ejections. One or more ejections are contained in each burst and hence the key idea is to identify and to group those ejections from a single burst into a single-burst detection. When the ejection detections were grouped appropriately into burst detections, all of the extended techniques yielded the same average time between bursts as deduced from flow visualization for fully-developed channel flow in the range 8700 [les ] Reh [les ] 17 800. The present results show that inner variables (wall shear stress and kinematic viscosity) are the best candidates for the proper scaling of the average time between bursts. Conditional velocity sampling during burst and ejection detections shows that these burst events are closely correlated with slower-than-average moving fluid, moving both away from the wall and toward the wall.

Timescale and structure of ejections and bursts in turbulent channel flows

When drag-reducing additives are confined entirely to the linear sublayer of a turbulent channel flow of water, both the spanwise spacing and bursting rate of the wall-layer structure are the same as those for a water flow and there is no evidence of drag reduction. Drag reduction is measured downstream of the location where the additives injected into the sublayer begin to mix in significant quantities with the buffer region (10 y + The superscript + denotes a dimensionless quantity scaled with the kinematic viscosity ν and the wall shear velocity v * = (τ w /ρ) ½ . of the channel flow. At streamwise locations where drag reduction does occur and where the injected fluid is not yet uniformly mixed with the channel flow, the dimensionless spanwise streak spacing increases and the average bursting rate decreases. The decrease in bursting rate is larger than the corresponding increase in streak spacing. The wall-layer structure is like the structure in the flow of a homogeneous, uniformly mixed, drag-reducing solution. Thus, the additives have a direct effect on the flow processes in the buffer region and the linear sublayer appears to have a passive role in the interaction of the inner and outer portions of a turbulent wall layer.

T. S. Luchik

Papers

Timescale and structure of ejections and bursts in turbulent channel flows

Wall-layer structure and drag reduction