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

The dynamics of turbulence generated and controlled by polymer additives is investigated from the perspective of the coupling between polymer dynamics and flow structures. Direct numerical simulations of channel flow with Reynolds numbers ranging from 1,000 to 10,000 (based on the bulk and the channel height) are used to study the formation and dynamics of elastic instabilities and their effects on the flow. The resulting mechanism of interactions between polymer dynamics and the flow helps resolve a long-standing controversy in the understanding of polymer drag reduction and explains the phenomenon of early turbulence, or onset of turbulence at lower Reynolds numbers than for Newtonian flows, previously observed in polymeric flows.

Analysis of transitional polymeric flows and elastic instabilities

Instabilities in Underexpanded Impinging Jets

Unsteady aerodynamics in the low Reynolds number domain is of great interest in applications to Micro Air Vehicles (MAVs), especially with respect to flow over, and in the wake of, pitching aerofoils The massively separated flow over the upper surface of the pitching aerofoil allows for the production of large transient peaks of lift at this scale This paper extends our previous work 1 to multi-dimensional (3D), multi-component (3C) measurements of this phenomenon by using Tomographic Particle Image Velocimetry (Tomo-PIV) For this purpose the three-component, three-dimensional (3C-3D) velocity fields in the wake of a flat plate undergoing a pitch -hold-return motion is investigated The experiments are conducted in a water tunnel at a Reynolds number of 7,500 and a dimensionless pitching rate of Kc = 093 The instantaneous and phase averaged evolution of the trailing edge vortices is investigated, highlighting the three -dimensional organisation of the coherent vortex structure and its spanwise variation

Multi-component, Multi-dimensional PIV Measurements of a Flat-Plate Pitching Motion

In the present contribution, the aptitude of Stereoscopic Particle Image Velocimetry (SPIV) and of Direct Numerical Simulations (DNS) to investigate coherent structures of near wall turbulence is evaluated. For this purpose, the general properties and constraints of the two techniques are first reviewed. Then, data obtained from stereo-PIV experiments in a boundary layer and DNS in a channel flow are considered. Some statistics of the velocity fields are computed, and the results obtained from the two approaches compared.

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Comparison of high spatial resolution stereo-PIV measurements in a turbulent boundary layer with available DNS dataset

A novel method to determine the average convection velocity of coherent structures in the shear layer of supersonic jets is presented in this paper. The method is based on the Proper Orthogonal Decomposition (POD) of a flow field and the standard advection equation. Substitution of a function satisfying the advection equation with its POD representation followed by the utilization of the fundamental properties of POD modes and coefficients yields an expression for the convection velocity in terms of the derivatives and the inner products of modes. The method is suitable for experimental data (like PIV) as it does not require the data set to be time resolved. For validation and practical applicability of the method, a sensitivity analysis has been performed using a synthetic data set followed by the application of the technique on the simulation data of a realistic research problem.

Julio Soria

Papers

Analysis of transitional polymeric flows and elastic instabilities

Instabilities in Underexpanded Impinging Jets

Multi-component, Multi-dimensional PIV Measurements of a Flat-Plate Pitching Motion

Comparison of high spatial resolution stereo-PIV measurements in a turbulent boundary layer with available DNS dataset

A novel method for determination of convective velocity of coherent structures in high speed flows