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

Digital particle image velocimetry (DPIV) is a non-intrusive analysis technique that is very popular for mapping flows quantitatively. To get accurate results, in particular in complex flow fields, a number of challenges have to be faced and solved: The quality of the flow measurements is affected by computational details such as image pre-conditioning, sub-pixel peak estimators, data validation procedures, interpolation algorithms and smoothing methods. The accuracy of several algorithms was determined and the best performing methods were implemented in a user-friendly open-source tool for performing DPIV flow analysis in Matlab.

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PIVlab – Towards User-friendly, Affordable and Accurate Digital Particle Image Velocimetry in MATLAB

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

Small-scale turbulence has been an area of especially active research in the recent past, and several useful research directions have been pursued. Here, we selectively review this work. The emphasis is on scaling phenomenology and kinematics of small-scale structure. After providing a brief introduction to the classical notions of universality due to Kolmogorov and others, we survey the existing work on intermittency, refined similarity hypotheses, anomalous scaling exponents, derivative statistics, intermittency models, and the structure and kinematics of small-scale structure—the latter aspect coming largely from the direct numerical simulation of homogeneous turbulence in a periodic box.

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The phenomenology of small-scale turbulence

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems.
 However, existing DMD theory deals primarily with sequential time series for which the measurement dimension is much larger than the number of measurements taken.
 We present a theoretical framework in which we define DMD as the eigendecomposition of an approximating linear operator.
 This generalizes DMD to a larger class of datasets, including nonsequential time series.
 We demonstrate the utility of this approach by presenting novel sampling strategies that increase computational efficiency and mitigate the effects of noise, respectively.
 We also introduce the concept of linear consistency, which helps explain the potential pitfalls of applying DMD to rank-deficient datasets, illustrating with examples.
 Such computations are not considered in the existing literature but can be understood using our more general framework.
 In addition, we show that our theory strengthens the connections between DMD and Koopman operator theory.
 It also establishes connections between DMD and other techniques, including the eigensystem realization algorithm (ERA), a system identification method, and linear inverse modeling (LIM), a method from climate science.
 We show that under certain conditions, DMD is equivalent to LIM.

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On dynamic mode decomposition: Theory and applications

Light-field particle image velocimetry (LF-PIV) was recently introduced to measure three-dimensional, three-component velocity field with just a single light-field camera. One of the major challenges lies in the small viewing aperture affecting the depth resolution of such a single-camera based LF-PIV approach. In the present study, we show that this limitation may be mitigated by a dual light-field camera framework, one which includes a novel volumetric calibration model derived from Gaussian optics, a particle intensity reconstruction algorithm based on the multiplicative algebraic reconstruction technique and a post-processing technique for the reconstructed particle intensity field. The proposed approach was firstly validated with synthetic light-field particle images as well as experimental light-field images of five tiny glass beads imitating tracer particles. Secondly, parametric studies were conducted to analyze the influence of the viewing angle and seeding particle density on the reconstruction quality and spatial resolution. In particular, synthetic light-field particle images of a direct numerical simulation jet data set were utilized to compare the performance of single- and dual-camera LF-PIV techniques. Finally, experimental volumetric flow field results of a circular vortex-ring were also measured by single- and dual-camera LF-PIV techniques and compared. It is determined here that an additional light-field camera can mitigate the elongation effects of reconstructed particles and improve the measurement resolution in the depth direction.

High resolution volumetric dual-camera light-field PIV

Proper orthogonal decomposition can be used to determine the dominant coherent structures present within a turbulent flow. In many flows, these structures are well represented by only a few high-energy modes. However, additional modes with clear spatial structure, but low-energy contribution can often be present in the proper orthogonal decomposition analysis, even for flows with a high degree of periodicity. One such mode has been observed in both free and impinging jets determined from particle image velocimetry. Both experimental and synthetic data are used to investigate the role of this particular mode, linking its existence to the unsteadiness of shear-layer large-scale coherent structures.

Signatures of shear-layer unsteadiness in proper orthogonal decomposition

This project extends the study of the structure of wall-bounded flows using the topological properties of eddying motions as developed by Chong et al. (1990), Soria et al. (1992, 1994), and as recently extended by Blackburn et al. (1996) and Chacin et al. (1996). In these works, regions of flow which are focal in nature are identified by being enclosed by an isosurface of a positive small value of the discriminant of the velocity gradient tensor. These regions resemble the attached vortex loops suggested first by Theodorsen (1955). Such loops are incorporated in the attached eddy model versions of Perry & Chong (1982), Perry et al. (1986), and Perry & Marusic (1995), which are extensions of a model first formulated by Townsend (1976). The DNS data of wall bounded flows studied here are from the zero pressure gradient flow of Spalart (1988) and the boundary layer with separation and reattachment of Na & Moin (1996). The flow structures are examined from the viewpoint of the attached eddy hypothesis.

Julio Soria

Papers

High resolution volumetric dual-camera light-field PIV

Signatures of shear-layer unsteadiness in proper orthogonal decomposition

A study of the turbulence structures of wall-bounded shear flows using DNS data

Accuracy of out-of-plane vorticity measurements using in-plane velocity vector field data

Analysis of a drag reduced flat plate turbulent boundary layer via uniform momentum zones