Coherent structures in the turbulent channel flow of an elastoviscoplastic fluid

There has been a significant recent interest in using autonomous vehicles to study phenomena in the ocean including temperature and salinity profiles, contaminant transport, and biological processes such as plankton assemblages and algae blooms. It is challenging to deploy mobile robots with bounded actuation and limited communication in a highly nonlinear, time varying, and stochastic flow field such as the ocean. Despite natural stochasticity and arbitrary time dependence, geophysical flows do admit persistent transport controlling features known as Lagrangian coherent structures. These structures, which behave similarly to stable and unstable manifolds in time invariant dynamical systems, serve to characterize transport phenomena and have been shown to have many useful properties for ocean sampling and efficient navigation. In this work, a strategy for tracking manifolds of 2D conservative vector fields is described and the application of this strategy to track coherent structures in general time dependent flows is presented. Computer simulations of the tracking strategy on a variety of analytical and measured flow fields are presented, and it is shown that, in many cases, the strategy is capable of successfully tracking coherent structures in simulation. In addition, the development of an experimental testbed consisting of a fleet of small autonomous surface vessels and three flow tanks is described. Preliminary experimental results related to tracking coherent structures using this flow testbed are presented. The overall results of this effort have indicated that the tracking strategy, although designed for time invariant flows, can be used to track coherent structures in certain time dependent flows quite reliably.

This study investigates the flow behavior in front of a circular cylinder placed near a plane wall using large eddy simulation. It identifies two distinct coherent vortical flow structures occurring during the transition from laminar to turbulent flow upstream of the cylinder. These coherent flows can be triggered by either reducing the gap between the cylinder and the wall or increasing the Reynolds number (ReD, based on the cylinder diameter). The first coherent flow emerges at relatively low ReD and features periodic vortical tubes aligned parallel to the longitudinal axis of the cylinder. These vortical tubes move downstream with the flow, transforming into Λ-shaped structures before jumping over the cylinder. The second type, observed at higher ReD and farther upstream, initially appears as elongated, streaky, streamwise vortices, which evolve into larger hairpin-type vortices as they approach the cylinder. These hairpin vortices also form periodically but at a lower frequency than the vortical tubes and are arranged in a staggered formation. Both types of coherent flows are found to affect the amplitude and frequency of forces acting on the cylinder, which is important in many engineering applications. A similar transition process from laminar to turbulent flow has been observed in the canonical boundary layer; however, the two types of coherent flow structures emerge, develop, and break down within a short distance in front of the cylinder, setting them apart from previous studies.

ABSTRACTLarge‐scale flow structures (LSFS) in the streamwise direction are important features of gravel‐bed river flows, because they may contribute to sediment transport and gas exchange. In the present study, these structures are detected using Huang's empirical mode decomposition and reconstructed with phase‐averaging techniques based on a Hilbert transform of the velocity signal. The analysis is based on the fluctuating component of 15 quasi‐instantaneous velocity profiles measured with a three‐dimensional (3D) acoustic Doppler velocity profiler (ADVP) in an armoured gravel‐bed river with a low relative submergence of 2.9 (ratio between flow depth and bed grain diameter). LSFS were identified in most of the measured profiles and consistently showed similar features. We were able to characterize the geometry of these large‐scale coherent structures: the front has a vertical linear shift in the time domain and a vertical profile corresponding to a first quarter moon with the apex situated at z/h ≈ 0.4. In the vertical, the front scales with flow depth h, and in the streamwise direction, LSFS scale with three to seven times the mean flow depth. On the bed, the effect of LSFS is a periodic non‐linear variation of the friction velocity on average between 0.90 and 1.10 times the mean value. A model for the friction velocity cycle resulting from LSFS oscillation is presented. Copyright © 2014 John Wiley & Sons, Ltd.

Large Eddy Simulations (LES) are performed to investigate the coherent structures in flows past a single and an array of tandem plates. Lagrangian coherent structures (LCS) are used to investigate the nonlinear vortex dynamics of flow past a single plate. The Finite-Time Lyapunov Exponent (FTLE) is calculated using the velocity data obtained from Large Eddy Simulations (LES). All simulations are conducted at Reynolds number of 50,000. LCS for a single plate is presented in this study to elucidate and comprehend highly turbulent flow interactions in these flows. The LCS is compared against most commonly used Eulerian structures which are contours of the vorticity and the Q-criterion. The FTLE fields reveal much clearer turbulent structures compared to the Eulerian structures. FTLE better describes the evolution of larger scale eddies. The Q-criterion of flows past an array of plates is also presented.

Near-wall coherent structures in the turbulent channel flow of a dilute polymer solution

Premixed turbulent flame blowoff velocity correlation based on coherent structures in turbulent flows

The identification of coherent structures using proper orthogonal decomposition and dynamic mode decomposition

To meet the increasingly stringent noise regulation, aircraft manufacturers are searching for solutions to jet noise. This, which constitutes a significant amount of the total noise emitted by civil aircrafts, is generated by the mixing processes between the exhaust flow leaving the engine and the atmosphere. A detailed understanding of such mixing process is of paramount importance to identify mechanisms responsible for noise production, i.e. the aeroacoustic source, and, ultimately, to develop noise control strategies. This thesis proposes an unprecedented experimental-based approach to visualize and measure the aeroacoustic sources in jet flows. Time-resolved tomographic particle image velocimetry (TR-TOMO PIV) is employed to obtain time-dependent three-dimensional (3D) measurements of the turbulent flow patterns, while the instantaneous aeroacoustic source is explored using Powell’s aeroacoustic analogy. TR-TOMO PIV experiments are conducted in a tailored jet facility. Measurements are performed both on jets issued through circular and 6-chevron nozzles, with the latter configuration that is nowadays used in jet engines to reduce acoustic emissions. The attention is placed upon the 3D organization and dynamics of flow transition, where coherent flow structures play a role in the generation of noise. The full 3D approach enables unambiguous descriptions of the vortex topology, while the temporal resolution allows addressing the growth and development of the coherent flow structures along with their mutual interaction. In the circular jet, the characteristic pulsatile motion of vortex ring shedding and pairing is accompanied by the growth of azimuthal instabilities and the formation of streamwise vortices leading to the breakdown of the vortex rings. In the chevron jet, instead, the axisymmetric ring-like coherence is replaced by streamwise flow structures whose decay is accompanied by the formation of C-shaped structures. The relation between coherent structures and the instantaneous acoustic source is investigated recalling Powell’s aeroacoustic analogy, with the acoustic source that is identified by the second time derivative of the Lamb vector. The spatio-temporal evolution of the source is mapped and is compared to that of the vortices, to detect flow events involved in the acoustic generation. In the circular jet, most pronounced source activity is observed during the vortex-ring breakdown, whereas, in the chevron configuration, is associated with the process of streamwise vortex decay and C structure formation. Performing unbiased acoustic predictions of the jet noise with TR-TOMO PIV measurements is a challenging task due to the constraints on the extent of the instantaneous measurement domain and on the required spatial and temporal resolutions. To meet this challenge, the thesis finally proposes a strategy to perform far-field acoustic predictions by direct evaluation of Powell’s analogy using TR-TOMO PIV data.

The main thrust of our research has been to apply the coherent structures approach to understand, analyze and model turbulent flows. We consider vorticity as the defining property of coherent structures. Turbulent flows are characterized by vortical structures undergoing deformation and interaction due to self- and mutual inductions. One of the primary objectives of our research is to obtain a detailed understanding of these interactions. The concepts of vortex dynamics, when applied to coherent structures, have helped us to understand many of the peculiarities of the noncircular jets, especially elliptic jets. The structures in these jets have nonplanar advections, thus having the simplicity allowing their evolution yet retaining the 3-D features generic of all coherent structures in turbulent shear flows. 16 refs., 6 figs.

The underlying flow dynamics in a turbulent flow in a periodic square duct is investigated by using the snapshot Proper Orthogonal Decomposition (POD) technique. In this study, the friction Reynolds number based on the duct width is fixed at 300. The coherent structures are identified through the spatial and temporal analysis of POD modes. Analysis of two sets of POD data is performed. In obtaining the first set, POD is performed on the combined fluctuating velocity vector, while for the second set, only the fluctuating velocity along the y- or z-direction is used. It was found that the first two most energetic spatial POD modes are the streamwise-independent or non-propagating roll modes. The third and fourth most energetic modes are observed to be streamwise-dependent, propagating modes. The spatio-temporal analysis of POD modes confirms the presence of traveling waves in the square duct, and its average speed is also calculated. The POD of the second dataset showed only propagating modes, and no non-propagating modes were found. These propagating modes are also rotationally symmetric. It has been shown that there is an energy exchange between non-propagating modes and propagating modes. The flow dynamics of the first four reconstructed POD modes portray the self-sustaining turbulence mechanism in a square duct. The structures obtained from the first POD dataset reconstruction of 10% energy show well organized hairpin vortices. Furthermore, it is found that the energy content of 35% gives detailed information on the coherent structures aligned along the wavy streamwise direction.

This study focuses on numerically investigating the impact of fluid viscoelasticity on the flow dynamics around a transversely forced oscillating cylinder operating in the laminar vortex shedding regime at a fixed Reynolds number of $Re = 100$ . Specifically, we explore how fluid viscoelasticity affects the boundary between the lock-in and no lock-in regions and the corresponding wake characteristics compared with a simple Newtonian fluid. Our findings reveal that fluid viscoelasticity enables the synchronization of the vortex street with the cylinder motion at lower oscillation frequencies than those required for a Newtonian fluid. Consequently, the lock-in region boundary for a viscoelastic fluid differs from that of a Newtonian fluid and expands in the non-dimensional cylinder oscillation amplitude and frequency parameter space. In the primary synchronization region, the wake of a Newtonian fluid exhibits ‘2S’ (two single vortices) and ‘P+S’ (a pair of vortices and a single vortex) shedding modes. In contrast, a ‘2P’ (two pairs of vortices) vortex mode is observed for a viscoelastic fluid within the same region. To gain a deeper understanding of the differences in the coherent flow structures and their associated frequencies between the two fluids, we employ the data-driven reduced-order modelling technique, known as the dynamic mode decomposition (DMD) technique. Utilizing this technique, we successfully extract and visualize the two competing fundamental frequencies (cylinder oscillation and natural vortex shedding frequencies) and their associated flow structures in the case of the no lock-in state, whereas only the dominant cylinder oscillation frequency and associated flow structure in the case of the lock-in state. Furthermore, we propose that the presence of excess strain resulting from the stretching of polymer molecules in viscoelastic fluids leads to a distinct difference in the wake structure compared with Newtonian fluids. This observation aligns with the findings obtained from the $Q$ -criterion and vorticity transport analysis of the wake.

This study investigates the energy exchange between coherent structures in flows over four low-aspect-ratio (low-) plates using the tomographic particle image velocimetry dataset originally obtained by Zhu et al. (2024. J. Fluid Mech.983, A35). The chord-based Reynolds number is $5400$ , with fixed angle of attack $6 ^\circ$ . In this study, multiscale proper orthogonal decomposition is applied to extract the coherent structures, including those associated with the vortex-shedding frequency $St_1$ and its subharmonic counterpart. Subsequently, the coherent kinetic energy budget is analysed with a focus on inter-scale energy transfer. This study demonstrates that the energy transfer between the scales centred at $St_1$ and $0.5\,St_1$ can exhibit a reverse or forward direction, depending on the transformation pattern of the leading-edge vortices (LEVs). Specifically, different triadic interactions are excited during the LEV transformation, and manifest themselves during the formation of hairpin vortices downstream. Understanding this nonlinear energy transfer is essential for elucidating mechanisms underlying the development of turbulence in three-dimensional flows over low- plates.

Coherent structures in turbulent square duct flow

Flows behind obstacles (such as islands) are shallow if the transverse scale of the flow is much larger than water depth. Field, laboratory and numerical data show that the flow pattern in shallow wakes exhibits a complex eddy‐like motion. Experimental and theoretical analyses provide evidence for the presence of two‐dimensional coherent structures in shallow water flows and show that the development of shallow wakes is different from the wakes in deep water due to the following reasons: first, the development of three‐dimensional instabilities is prevented by limited water depth and second, bottom friction acts as a stabilizing mechanism for suppressing the transverse growth of perturbations. Several authors have used the linear and weakly nonlinear stability theory in order to understand when shallow flows become unstable. Two‐dimensional depth‐averaged Saint‐Venant equations are usually used for the analysis. One of the main assumptions in shallow water theory is the independence of the velocity distribution on the vertical coordinate. In many cases, however, this assumption may not be valid. This paper presents an attempt to evaluate the influence of the assumption on the results of linear stability analysis of shallow wake flows with bottom friction. Momentum correction coefficients β 1 and β 2 are used in order to take into account the non‐uniformity of the velocity distribution in the vertical direction. Linear stability calculations show that the stability boundary is quite sensitive to the variation of the parameters β 1 and β 2. The role of the linear and weakly nonlinear stability analysis on the formation of two‐dimensional coherent structures in shallow water flows is discussed.

We consider the spectral proper orthogonal decomposition (SPOD) for experimental data of a turbulent swirling jet. This newly introduced method combines the advantages of spectral methods, such as Fourier decomposition or dynamic mode decomposition, with the energy-ranked proper orthogonal decomposition (POD). This poster visualizes how the modal energy spectrum transitions from the spectral purity of Fourier space to the sparsity of POD space. The transition is achieved by changing a single parameter – the width of the SPOD filter. Each dot in the 3D space corresponds to an SPOD mode pair, where the size and color indicates its spectral coherence. What we notice is that neither the Fourier nor the POD spectrum achieves a clear separation of the dynamic phenomena. Scanning through the graph from the front plane (Fourier) to the back plane (POD), we observe how three highly coherent SPOD modes emerge from the dispersed Fourier spectrum and later branch out into numerous POD modes. The spatial properties of these three individual SPOD modes are displayed in the back of the graph using line integral convolution colored by vorticity. The first two modes correspond to single-helical global instabilities that are well known for these flows. Their coexistence, however, has not been observed until now. The third mode is of double- helical shape and has not been observed so far. For this considered data set and many others, the SPOD is superior in identification of coherent structures in turbulent flows. Hopefully, it gives access to new fluid dynamic phenomena and enriches the available methods.