A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points. All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behavior of turbulence correlations near the wall. A number of statistical correlations which are complementary to the existing experimental data are reported for the first time.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087000892

Turbulence statistics in fully developed channel flow at low reynolds number

Since the review of periodic flow phenomena by Berger & Wille (1972) in this journal, over twenty years ago, there has been a surge of activity regarding bluff body wakes. Many of the questions regarding wake vortex dynamics from the earlier review have now been answered in the literature, and perhaps an essential key to our new understandings (and indeed to new questions) has been the recent focus, over the past eight years, on the three-dimensional aspects of nominally two-dimensional wake flows. New techniques in experiment, using laser-induced fluorescence and PIV (Particle-Image-Velocimetry), are vigorously being applied to wakes, but interestingly, several of the new discoveries have come from careful use of classical methods. There is no question that strides forward in understanding of the wake problem are being made possible by ongoing three- dimensional direct numerical simulations, as well as by the surprisingly successful use of analytical modeling in these flows, and by secondary stability analyses. These new developments, and the discoveries of several new phenomena in wakes, are presented in this review.

Vortex Dynamics in the Cylinder Wake

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

A critical review of the intrinsic nature of vortex-induced vibrations

Employing a high-speed video system and hydrogen bubble-wire flow visualization, the characteristics of the low-speed streaks which occur in the near-wall region of turbulent boundary layers have been examined for a Reynolds-number range of 740 [les ] Reθ < 5830. The results indicate that the statistics of non-dimensional spanwise streak spacing are essentially invariant with Reynolds number, exhibiting consistent values of and remarkably similar probability distributions conforming to lognormal behaviour. Further studies show that streak spacing increases with distance from the wall owing to a merging and intermittency process which occurs for y+ [simg ] 5. An additional observation is that, although low-speed streaks are not fixed in time and space, they demonstrate a tremendous persistence, often maintaining their integrity and reinforcing themselves for time periods up to an order of magnitude longer than the observed bursting times associated with wall region turbulence production. A mechanism for the formation of low-speed streaks is suggested which may explain both the observed merging behaviour and the streak persistence.

The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer

It has been suggested that hairpin vortices may play a key role in developing and sustaining the turbulence process in the near-wall region of turbulent boundary layers. To examine this suggestion, a study was done of the hairpin vortices generated by the interaction of a hemisphere protuberancee within a developing laminar boundary layer. Under the proper conditions, hairpin vortices are shed extremely periodically, which allows detailed examination of their behaviour. Shedding characteristics of the hemispheres were determined using hot-film-anemometry techniques. The flow patterns created by the presence of the hairpin vortices have been documented using flow visualization and hot-film-anemometry techniques, and cross-compared with the patterns observed in the near-wall of a fully turbulent boundary layer. In general, it has been observed that many of the visual patterns observed in the near-wall region of a turbulent boundary layer can also be observed in the wake of the hairpin-shedding hemisphere, which appears supportive of the importance of hairpin vortices in the near-wall turbulence production process. Furthermore, velocity measurements indicate the presence of strong inflexional profiles just downstream of the hairpin-vortex generation region which evolve into fuller profiles with downstream distance, eventually developing a remarkable similarity to a turbulent-boundary-layer velocity profile.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087000272

A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance

Situations where an effectively irrotational freest ream contains regions of concentrated vorticity are common in external aerodynamics, where vortices are known to play an important role in the flight of modern helicopters (Carr 1988) and aircraft (Cunningham 1989, Mabey 1989). Vortices may arise as a consequence of shedding from some upstream surface or near certain three-dimensional boundary geometries that act to promote vortex formation. Examples of the former type of vortex gen­ eration include: 1. vortices that trail from the tips of airfoils (Harvey & Perry 1971) and control surfaces on submarines (Lugt 1983), 2. transverse vortices shed from maneuvering airfoil surfaces and helicopter blades in a process known as dynamic stall (McCroskey 1982, Francis & Keesee 1985, Carr 1988), and 3. shedding from stationary obstacles. Geometry-induced creation can occur in any situation where a flow along a wall approaches a surface-mounted obstacle; examples include: 1. airframe features such as wing/body junctions, 2. conning towers on submarines, and 3 . computer chips mounted on electrical circuit boards. Similar geometries are en-

Vortex Interactions with Walls

The flow induced by a vortex ring approaching a plane wall on a trajectory normal to the wall is investigated for an incompressible fluid which is otherwise stagnant. The detailed characteristics of the interaction of the ring with the flow near the surface have been observed experimentally for a wide variety of laminar rings, using dye in water to visualize the flow in the ring as well as near the plane surface. Numerical solutions are obtained for the trajectory of the ring as well as for the unsteady boundary-layer flow that develops on the wall. The experimental and theoretical results show that an unsteady separation develops in the boundary-layer flow, in the form of a secondary ring attached to the wall. A period of explosive boundary-layer growth then ensues and a strong viscous-inviscid interaction occurs in the form of the ejection of the secondary vortex ring from the boundary layer. The primary ring then interacts with the secondary ring and in some cases was observed to induce the formation of a third, tertiary, ring near the wall. The details of this process are investigated over a wide Reynolds number range. The results clearly show how one vortex ring can produce another, through an unsteady interaction with a viscous flow near the wall.

The impact of a vortex ring on a wall

It has been suggested that hairpin vortices are a major sustaining flow structure involved in the perpetuation of turbulent boundary layers, although their origin within the boundary layer is unclear. One hypothesis is that hairpin structures are formed by the breakdown of the low-speed streak structures which develop adjacent to the surface beneath turbulent boundary layers. To examine this hypothesis, a water-channel study has been done which utilizes injection through surface slots in a flat plate to create artificial low-speed streak-type regions beneath a laminar boundary layer. Under appropriate conditions, these synthesized low-speed streaks develop a three-dimensional, shear-layer instability which breaks down to form a hairpin-vortex street. Employing both flow visualization and anemometry measurements, the characteristics of these hairpin structures and the parameters influencing their generation have been examined. The hairpin streets were determined to develop in a very periodic and repeatable manner within a definite range of flow parameters. Detailed flow patterns obtained using dye and hydrogen bubbles, both individually and collectively, indicate a remarkable similarity with previously observed patterns in the near-wall region of turbulent boundary layers. In addition, the development of the hairpin structures is observed to be quite sensitive to external forcing, as well as exhibiting a tendency for organized development of larger, more complex structures through a pairing-type process. Velocity measurements indicate the initial presence of strong inflexional profiles which evolve rapidly to velocity and turbulence-intensity profiles commensurate with those associated with turbulent boundary layers, but which do not exhibit the marked spreading associated with turbulence.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087000284

C. R. Smith

Papers

The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer

A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance

Vortex Interactions with Walls

The impact of a vortex ring on a wall

A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection