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

Measurements of velocity and vorticity in grid turbulence using PIV

Lagrangian mean evolution of a developing zero pressure gradient turbulent boundary layer (Reθ = 730 to 1954) is investigated using data from a direct numerical simulation performed by Wu & Moin (2010). Conditional mean trajectories (CMTs) for the evolution of the invariants of the velocity gradient tensor (VGT) are calculated based on the mean rate of change of the invariants, conditioned on their location in the (RA,QA) invariants plane. Following Chong et al. (1990) the location in this plane distinguish the focal or non-focal nature of flow at that point, such that CMTs represent the mean topological evolution of points in the flow. In the present case CMTs for strong gradients in all regions of the boundary layer pass around a focus at the origin and asymptote towards the right-hand side of a saddle point located near the of the line dividing unstable focal and unstable nodal structures. Closer to the origin weaker gradients follow an almost periodic clockwise spiralling evolution from stablefocus stretching to unstable-focus contraction, unstable-node saddle/saddle and stable-node saddle/saddle topology. Increasing time-scales are observed for both the strong and weak gradient trajectories further above the wall. Mean timescales associated with the spiralling evolution in terms of inner scales are 67.9 ν/uτ in the viscous layer, 151 ν/uτ in the buffer layer and 658 ν/uτ in the log and wake region or 1.25 estimated eddy turnover times. INTRODUCTION Reliable modelling or control of wall-bounded turbulent flows requires an understanding of the mechanisms behind the evolution and distribution of turbulence near the wall. Studies involving the temporal evolution of turbulent flows is complicated by the motion of each fluid particle and the dependence of many fluid properties on the relative motion of the observer. Figure 1. Three-dimensional local topologies in the (RA,QA)-plane for incompressible flow. Taken from Soria et al. (1994). This is particularly true for wall-bounded flows which involve significant changes in convection velocity. Such analysis can be simplified by examining quantities such as the velocity gradient tensor (VGT) which is Galilean invariant and independent of a non-accelerating observer, and can be directly related to quantities such as enstrophy density and dissipation. Following the topological approach introduced by

Mean topological evolution in a turbulent boundary layer

Investigation of unsteady flow behind a circular cylinder using a digital PIV method

In wall-bounded turbulent flows, a large portion of total turbulence production happens in the near wall region. Although the viscous and buffer layers are relatively easy for numerical simulations due to local low Reynolds numbers of the important structures, they are very difficult to study experimentally because of their physically small geometry. The aim of this paper is to measure the wall shear stress in a fully developed turbulent channel flow at moderately high Reynolds numbers using a novel stress meter which is capable of measuring surface forces over an extended region of the model. In addition, near wall region in a wall-bounded flow by means of digital holographic microscopic particle image velocimetry will be investigated. DHMPIV provides a solution to overcome the poor axial accuracy and the low spatial resolution. The paper addresses the experimental techniques, articulate calibration procedure, data acquisition, and analysis procedure.

Measurements of Near Wall Velocity and Wall Stress in a Wall-Bounded Turbulent Flow Using Digital Holographic Microscopic PIV and Shear Stress Sensitive Film

The present investigation shows that a triad of three vortices, two co-rotating vortices (TCV) and a secondary vortex lies beneath them and counter-rotating with them, is behind the quasi-periodic self-sustained bursting and reformation of the laminar separation bubble (LSB) and its associated low-frequency flow oscillation (LFO). The upstream vortex of the TCV (UV) is driven by the gradient of the oscillating-velocity across the laminar portion of the separated shear layer and is faithfully aligned with it. The secondary vortex acts as a roller support that facilitates the rotation and orientation of the TCV. A global oscillation in the flow-field around the aerofoil is observed in all of the investigated angles of attack, including at zero angle of attack. The flow switches between an attached-phase against an adverse pressure gradient (APG) and a separated-phase despite a favourable pressure gradient (FPG) in a periodic manner with some disturbed cycles. When the direction of the oscillating-flow is clockwise, it adds momentum to the boundary layer and helps it to remain attached against the APG and vice versa. The transition location along the separated shear layer moves upstream when the oscillating-flow rotates in the clockwise direction causing early-transition and vice versa. The best description of the mechanism is that of a whirligig. When the oscillating-flow rotates in the clockwise direction, the UV whirls in the clockwise direction and store energy until it is saturated, then the process is reversed. The present investigation paves the way for formulating a time-accurate physics-based model of the LFO and stall prediction, and opens the door for control of its undesirable effects.

Julio Soria

Papers

Measurements of velocity and vorticity in grid turbulence using PIV

Mean topological evolution in a turbulent boundary layer

Investigation of unsteady flow behind a circular cylinder using a digital PIV method

Measurements of Near Wall Velocity and Wall Stress in a Wall-Bounded Turbulent Flow Using Digital Holographic Microscopic PIV and Shear Stress Sensitive Film

Bursting and reformation cycle of the laminar separation bubble over a NACA-0012 aerofoil: The underlying mechanism