The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.

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The Structure of Turbulent Shear Flow

We review wall-bounded turbulent flows, particularly high–Reynolds number, zero–pressure gradient boundary layers, and fully developed pipe and channel flows. It is apparent that the approach to an asymptotically high–Reynolds number state is slow, but at a sufficiently high Reynolds number the log law remains a fundamental part of the mean flow description. With regard to the coherent motions, very-large-scale motions or superstructures exist at all Reynolds numbers, but they become increasingly important with Reynolds number in terms of their energy content and their interaction with the smaller scales near the wall. There is accumulating evidence that certain features are flow specific, such as the constants in the log law and the behavior of the very large scales and their interaction with the large scales (consisting of vortex packets). Moreover, the refined attached-eddy hypothesis continues to provide an important theoretical framework for the structure of wall-bounded turbulent flows.

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High–Reynolds Number Wall Turbulence

Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Karman “constant,” the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution.

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Wall-bounded turbulent flows at high Reynolds numbers: Recent advances and key issues

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Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers

A model-based description of the scaling and radial location of turbulent fluctuations in turbulent pipe flow is presented and used to illuminate the scaling behaviour of the very large scale motions. The model is derived by treating the nonlinearity in the perturbation equation (involving the Reynolds stress) as an unknown forcing, yielding a linear relationship between the velocity field response and this nonlinearity. We do not assume small perturbations. We examine propagating helical velocity response modes that are harmonic in the wall-parallel directions and in time, permitting comparison of our results to experimental data. The steady component of the velocity field that varies only in the wall-normal direction is identified as the turbulent mean profile. A singular value decomposition of the resolvent identifies the forcing shape that will lead to the largest velocity response at a given wavenumber–frequency combination. The hypothesis that these forcing shapes lead to response modes that will be dominant in turbulent pipe flow is tested by using physical arguments to constrain the range of wavenumbers and frequencies to those actually observed in experiments. An investigation of the most amplified velocity response at a given wavenumber–frequency combination reveals critical-layer-like behaviour reminiscent of the neutrally stable solutions of the Orr–Sommerfeld equation in linearly unstable flow. Two distinct regions in the flow where the influence of viscosity becomes important can be identified, namely wall layers that scale with R+1/2 and critical layers where the propagation velocity is equal to the local mean velocity, one of which scales with R+2/3 in pipe flow. This framework appears to be consistent with several scaling results in wall turbulence and reveals a mechanism by which the effects of viscosity can extend well beyond the immediate vicinity of the wall. The model reproduces inner scaling of the small scales near the wall and an approach to outer scaling in the flow interior. We use our analysis to make a first prediction that the appropriate scaling velocity for the very large scale motions is the centreline velocity, and show that this is in agreement with experimental results. Lastly, we interpret the wall modes as the motion required to meet the wall boundary condition, identifying the interaction between the critical and wall modes as a potential origin for an interaction between the large and small scales that has been observed in recent literature as an amplitude modulation of the near-wall turbulence by the very large scales.

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A critical-layer framework for turbulent pipe flow

Experimental measurements of the three-dimensional (3D) velocity field in a moderate Reynolds number zero pressure-gradient boundary layer are presented. The measurements are analysed to produce 3D correlations and conditional averaging techniques are used to further elucidate the underlying structure. The results show clear evidence of vortex-packet-type structures and shed new light on the detailed 3D structure of such packets in a real zero pressure-gradient boundary layer.

Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 1. Vortex packets

Taylor's hypothesis of frozen flow has frequently been used to convert temporal experimental measurements into a spatial domain. This technique has led to the discovery of long meandering structures in the log-region of a turbulent boundary layer. There is some contention over whether Taylor's approximation is valid over large distances. This paper presents an experiment that compares velocity fields constructed using Taylor's approximation with those obtained from particle image velocimetry (PIV), i.e. spatial data, obtained in the logarithmic region of a turbulent boundary layer.

On the limitations of Taylor's hypothesis in constructing long structures in a turbulent boundary layer

Three-dimensional (3D) measurements of a turbulent boundary layer have been made using high-speed particle image velocimetry (PIV) coupled with Taylor's hypothesis, with the objective of characterising the very long streamwise structures that have been observed previously. The measurements show the 3D character of both low- and high-speed structures over very long volumes. The statistics of these structures are considered, as is their relationship to the important turbulence quantities. In particular, the length of the structures and their wall-normal extent have been considered and their relationship to the other components of the velocity fluctuations and the instantaneous stress.

Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 2. Long structures

We describe several novel morphological features in the nasal region of the hammerhead shark Sphyrna tudes. Unlike the open, rounded incurrent nostril of non-hammerhead shark species, the incurrent nostril of S. tudes is a thin keyhole-like aperture. We discovered a groove running anterior and parallel to the incurrent nostril. This groove, dubbed the minor nasal groove to distinguish it from the larger, previously described, (major) nasal groove, is common to all eight hammerhead species. Using life-sized plastic models generated at 200 μm resolution from an X-ray scan, we also investigated flow in the nasal region. Even modest oncoming flow speeds stimulate extensive, but not complete, circulation within the model olfactory chamber, with flow passing through the two main olfactory channels. Flow crossed from one channel to another via a gap in the olfactory array, sometimes guided by the interlamellar channels. Major and minor nasal grooves, as well as directing flow into the olfactory chamber, can, in conjunction with the nasal bridge separating incurrent and excurrent nostrils, limit flow passing into the olfactory chamber, possibly to protect the delicate nasal structures. This is the first simulation of internal flow within the olfactory chamber of a shark.

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Timothy Nickels

Papers

Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 1. Vortex packets

On the limitations of Taylor's hypothesis in constructing long structures in a turbulent boundary layer

Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 2. Long structures

Functional morphology of the nasal region of a hammerhead shark.

Fluid flow in and around the olfactory organ of a hammerhead shark