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

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Heat Transfer Investigation on Under-expanded Supersonic Impinging Jets by Large Eddy Simulation

The quest for the physical mechanisms underlying turbulent high-speed jet flows is underpinned by the extraction of spatio-temporal coherent structures from their flow fields. Experimental measurements to enable data decomposition need to comprise time-resolved velocity fields with a high-spatial resolution—qualities which current particle image velocimetry hardware are incapable of providing. This paper demonstrates a novel approach that addresses this challenge through the implementation of an experimental high-spatial resolution dual-particle image velocimetry methodology coupled with dynamic mode decomposition. This new approach is exemplified by its application in studying the dynamics of the near-field region of a turbulent high-speed jet, enabling the spatio-temporal structure to be investigated by the identification of the spatial structure of the dominant dynamic modes and their temporal dynamics. The spatial amplification of these modes is compared with that predicted by classical linear stability theory, showing close agreement, which demonstrates the powerful capability of this technique to identify the dominant frequencies and their associated spatial structures in high-speed turbulent flows.

https://www.mdpi.com/2311-5521/8/2/73/pdf?version=1676706263

Investigating the Linear Dynamics of the Near-Field of a Turbulent High-Speed Jet Using Dual-Particle Image Velocimetry (PIV) and Dynamic Mode Decomposition (DMD)

The formation of structures in the shear layer of an unforced, incompressible, free, spatially evolving, round, homogeneous jet is investigated using flow visualisation and multigrid cross-correlation digital particle image velocimetry (MCCDPIV). It has been known for some time that the structures formed in such a jet can either be axisymmetric or helical, however the critical Reynolds number at which these structures occur and at the transition from one form to the other has not been conclusively resolved.

Structures in a round homogeneous jet at low Reynolds number

This project will employ laser-based diagnostics to study electromagnetically driven turbulence. The two-dimensional turbulent flow is created electromagnetically in a saline solution. The presence of the two-dimensional inverse energy cascade, as the initial turbulent region self-organises through the process of spectral condensation will be investigated. The spectral redistribution of the turbulent energy that accompanies the formation of large coherent structures and an overall increase in the energy of the system will be measured using high spatial resolution multigrid cross-correlation digital particle image velocimetry (MCCDPIV).

Electromagnetically Driven Turbulence - Experimental Study

This paper report on the design of an experiment to establish an experimental self-similar adverse pressure gradient (APG) turbulent boundary layer (TBL) flow at the verge of separation in order to characterise its statistical structure and the contribution of the Reynolds stresses to the wall shear stress via quadrant analysis decomposition in conjunction with the Renard&Deck (RD) decomposition of the mean skin friction. In this study high-spatial-resolution (HSR) two-component - two-dimensional (2C-2D) particle image velocimetry (PIV) is employed to measure the self-similar APG-TBL flow. The measurements of the self-similar APG-TBL at the verge of separation, which is referred to as 'strong APG-TBL' is compared with similar HSR 2C-2D PIV measurements of a TBL under zero and mild APG to characterise the effect of the APG on the TBL. In the strong APG-TBL, the outer scaled profiles of the first- and second-order statistics, as well as the defect velocity exhibit self-similarity over the measured streamwise domain of 3.3{\delta}. The quadrant decomposition of the velocity fluctuations shows that the formation of the outer peak in the Reynolds shear stress profile under APG is due to the energisation of sweep motions of high-momentum fluid in the outer region of the boundary layer. The RD decomposition of the mean skin friction shows that the skin friction has larger contributions from ejections than sweeps. This is due to the emergence of the outer peaks with a correspondingly diminishing of the inner peaks in the turbulence production profiles. The skewness and flatness profiles show that the zero skewness and minimum flatness locations of the streamwise and wall-normal velocity fluctuations collapse with the location of the maximum Reynolds streamwise stress in the TBLs irrespective of the pressure gradient imposed on the TBL.

Characterisation of a self-similar turbulent boundary layer near separation measured using high-spatial-resolution two-component - two-dimensional particle image velocimetry

Julio Soria

Papers

Heat Transfer Investigation on Under-expanded Supersonic Impinging Jets by Large Eddy Simulation

Investigating the Linear Dynamics of the Near-Field of a Turbulent High-Speed Jet Using Dual-Particle Image Velocimetry (PIV) and Dynamic Mode Decomposition (DMD)

Structures in a round homogeneous jet at low Reynolds number

Electromagnetically Driven Turbulence - Experimental Study

Characterisation of a self-similar turbulent boundary layer near separation measured using high-spatial-resolution two-component - two-dimensional particle image velocimetry