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In this study, we investigated the flow dynamics in a fixed bed of hydrogel beads using Particle Tracking Velocimetry to compute the velocity field in the middle of the bed for moderate Reynolds numbers. We discovered that despite the overall stationarity of the flow and relatively low Reynolds number, it exhibits complex multiscale spatial dynamics reminiscent of those observed in classical turbulence. We found evidence of the presence of an inertial range and a direct energy cascade, and were able to obtain a value for a "porous" Kolmogorov constant of $C_2 = 3.1\pm 0.3$. This analogy with turbulence opens up new possibilities for understanding mixing and global transport properties in porous media., Comment: 9 pages, 11 figures, manuscript + supp mat

Turbulence is prevalent in nature and industry, from large-scale wave dynamics to small-scale combustion nozzle sprays. In addition to the multi-scale nonlinear complexity and both randomness and coherent structures in its dynamics, practical turbulence is often non-homogeneous and anisotropic, leading to great modeling challenges. In this letter, an efficient model is proposed to predict turbulent jet statistics with high accuracy. The model leverages detailed knowledge of readily available velocity signals from idealized homogeneous turbulence and transforms them into Lagrangian trajectories of a turbulent jet. The resulting spatio-temporal statistics are compared against experimental jet data showing remarkable agreement at all scales. In particular the intermittency phenomenon is accurately mapped by the model to this inhomogeneous situation, as observed by higher-order moments and velocity increment probability density functions. Crucial to the advancement of turbulence modeling, the transformation is simple to implement, with possible extensions to other inhomogeneous flows such as wind turbine wakes and canopy flows, to name a few.

The evolution of the normal aerodynamic coefficient of 19 configurations of square plates with various porosity patterns, ranging from solid plate to homogeneous porous plate, is experimentally characterized. The variation of the porosity pattern is obtained by partially covering the holes of a commercial fly-swatter using adhesive tape. Evolution of the normal aerodynamic coefficient is assessed from the measurement of the angular position of the porous plate, placed as a freely rotating pendulum swept by a flow in a wind tunnel. These angular measurements are also supported by PIV measurements of the structure of the wake. We show that the porosity pattern determines whether or not an abrupt stall occurs. In particular, the details of the porosity pattern on the edges of the plate are decisive for the existence of abrupt stall.

The settling behavior of individual spheres in a quiescent fluid was studied experimentally. The dynamics of the spheres was analyzed in the parameter space of particle-to-fluid density ratio ($\Gamma$) and Galileo number ($\mathrm{Ga}$), with $\Gamma \in (1.1, 7.9)$ and $\mathrm{Ga} \in (100, 340)$. The experimental results showed for the first time that the mean trajectory angle with the vertical exhibits a complex behavior as $\mathrm{Ga}$ and $\Gamma$ are varied. Numerically predicted regimes such as Vertical Periodic and Planar Rotating were validated at high $\Gamma$ values. In particular, for the denser spheres, a clear transition from planar to non-planar trajectories was observed, accompanied by the emergence of semi-helical trajectories corresponding to the Planar Rotating Regime. The spectra of trajectory oscillations were also quantified as a function of $\mathrm{Ga}$, confirming the existence of oblique oscillating regimes at both low and high frequencies. The amplitudes of the perpendicular velocities in these regimes were also quantified and compared with numerical simulations in the literature. The terminal velocity and drag of the spheres were found to depend on the particle-to-fluid density ratio, and correlations between the drag coefficient and particle Reynolds number ($Re_p$) as a function of Ga were established, allowing for the estimation of drag and settling velocity using $\mathrm{Ga}$, a control parameter, rather than the response parameter $Re_p$.

We present experimental observations of the spatial distribution of large inertial particles suspended in a turbulent swirling flow at high Reynolds number. The plastic particles, which are tracked using several high speed cameras, are heavier than the working fluid so that their dynamics results from a competition between gravitational effects and turbulent agitation. We observe two different regimes of suspension. At low rotation rate, particles are strongly confined close to the bottom and are not able to reach the upper region of the tank whatever their size or density. At high rotation rate, particles are loosely confined: small particles become nearly homogeneously distributed while very large objects are preferentially found near the top as if gravity was reversed. We discuss these observations in light of a minimal model of random walk accounting for particle inertia and show that large particles have a stronger probability to remain in the upper part of the flow because they are too large to reach descending flow regions. As a consequence particles exhibit random horizontal motions near the top until they reach the central region where the mean flow vanishes, or until a turbulent fluctuation gets them down.

An experimental Lagrangian study based on particle tracking velocimetry has been completed in an incompressible turbulent round water jet freely spreading into water. The jet is seeded with tracers only through the nozzle: inhomogeneous seeding called nozzle seeding. The Lagrangian flow tagged by these tracers therefore does not contain any contribution from particles entrained into the jet from the quiescent surrounding fluid. The mean velocity field of the nozzle seeded flow, $\langle \boldsymbol{U_\varphi} \rangle$, is found to be essentially indistinguishable from the global mean velocity field of the jet, $\langle \boldsymbol{U} \rangle$, for the axial velocity while significant deviations are found for the radial velocity. This results in an effective compressibility of the nozzle seeded flow for which $\boldsymbol{\nabla \cdot} \langle \boldsymbol{U_\varphi} \rangle \neq 0$ even though the global background flow is fully incompressible. By using mass conservation and self-similarity, we quantitatively explain the modified radial velocity profile and analytically express the missing contribution associated to entrained fluid particles. By considering a classical advection-diffusion description, we explicitly connect turbulent diffusion of mass (through the turbulent diffusivity $K_T$) and momentum (through the turbulent viscosity $\nu_T$) to entrainment. This results in new practical relations to experimentally determine the non-uniform spatial profiles of $K_T$ and $\nu_T$ (and hence of the turbulent Prandtl number $\sigma_T = \nu_T/K_T$) from simple measurements of the mean tracer concentration and axial velocity profiles. Overall, the proposed approach based on nozzle seeded flow gives new experimental and theoretical elements for a better comprehension of turbulent diffusion and entrainment in turbulent jets., Comment: Submitted to Journal of Fluid Mechanics

Topological properties of physical systems play a crucial role in our understanding of nature, yet their experimental determination remains elusive. We show that the mean helicity, a dynamical invariant in ideal flows, quantitatively affects trajectories of fluid elements: the linking number of Lagrangian trajectories depends on the mean helicity. Thus, a global topological invariant and a topological number of fluid trajectories become related, and we provide an empirical expression linking them. The relation shows the existence of long-term memory in the trajectories: the links can be made of the trajectory up to a given time, with particles positions in the past. This property also allows experimental measurements of mean helicity.

A Lagrangian experimental study of an axisymmetric turbulent water jet is performed to investigate the highly anisotropic and inhomogeneous flow field. The measurements were conducted within a Lagrangian exploration module, an icosahedron apparatus, to facilitate optical access of three cameras. The stereoscopic particle tracking velocimetry results in three component tracks of position, velocity and acceleration of the tracer particles within the vertically-oriented jet with a Taylor-based Reynolds number $\mathcal R_\lambda \simeq 230$. Analysis is performed at seven locations from 15 diameters up to 45 diameters downstream. Eulerian analysis is first carried out to obtain critical parameters of the jet and relevant scales, namely the Kolmogorov and large turnover (integral) scales as well as the energy dissipation rate. Lagrangian statistical analysis is then performed on velocity components stationarised following methods inspired by Batchelor (\textit{J. Fluid Mech.}, vol. 3, 1957, pp. 67-80) which aim to extend stationary Lagrangian theory of turbulent diffusion by Taylor to the case of self-similar flows. The evolution of typical Lagrangian scaling parameters as a function of the developing jet is explored and results show validation of the proposed stationarisation. The universal scaling constant $C_0$ (for the Lagrangian second-order structure function), as well as Eulerian and Lagrangian integral time scales are discussed in this context. $C_0$ is found to converge to a constant value (of the order of $C_0 = 3$) within 30 diameters downstream of the nozzle. Finally, the existence of finite particle size effects are investigated through consideration of acceleration dependent quantities.

In this experimental study, we report on the mixing properties of interfacial colloidal floaters (glass bubbles) by chemical and hydrodynamical currents generated by self-propelled camphor disks swimming at the air-water interface. Despite reaching a statistically stationary state for the glass bubbles distribution, those floaters always remain only partially mixed. This intermediate state results from a competition between (i) the mixing induced by the disordered motion of many camphor swimmers and (ii) the unmixing promoted by the chemical cloud attached to each individual self-propelled disk. Mixing/unmixing is characterized globally using the standard deviation of concentration and spectra, but also more locally by averaging the concentration field around a swimmer. Besides the demixing process, the system develops a "turbulent-like" concentration spectra, with a large-scale region, an inertial regime and a Batchelor region. We show that unmixing is due to the Marangoni flow around the camphor swimmers, and is associated to compressible effects., Comment: 17 pages, 11 figures, to be published in Physical Review Fluids

In this paper we present a novel hydrodynamic experiment using liquid $^4$He. The flow is forced inertially by a canonical oscillating grid using either its normal (He~I) or superfluid (He~II) phase, generating a statistically stationary turbulence. We characterise the turbulent properties of the flow using 2D Lagrangian Particle tracking on hollow glass micro-spheres. As expected for tracer particles, the Vorono\"{i} tessellation on particle positions does not show a significant departure from a random Poisson process neither in He~I nor He~II phase. Particles' positions are tracked with high temporal resolution, allowing to resolve velocity fluctuations at integral and inertial scales while properly assessing the noise contribution. Additionally, we differentiate the particles' positions (by convolution with Gaussian kernels) in order to access small scale quantities like acceleration. Using these measured quantities and the formalism of classical Homogeneous Isotropic Turbulence (HIT) to perform an energy budget across scales we extract the energy injection rate at the large scale, the energy flux cascading through inertial scales, down to small scales at which it is dissipated. We found that in such inertially driven turbulence, regardless of the normal or superfluid state of the fluid, estimates of energy at the different scales are compatible with each other and consistent with oscillating grid turbulence results reported for normal fluids in the literature. The largest discrepancy shows up at small scales where the signal to noise ratio is harder to control and where the 2D measurement is contaminated by the 3D nature of the flow. This motivates to focus future experimental projects towards small scales, low noise and 3D measurements., Comment: 20 pages, 15 figures, submitted to Peer journal

The transitions between two states of a bistable system are investigated experimentally and analyzed in the framework of rare-event statistics. Considering a disk pendulum swept by a flow in a wind tunnel, bistability between two aerodynamic branches is observed, with spontaneous transitions from one branch to the other. The waiting times before spontaneous transition are distributed following a double-exponential as a function of the control parameter, spanning four orders of magnitude in time, for both transitions. Inspired by a model originally applied to the transition to turbulence, we show that, for the disk pendulum, both transitions are controlled by rare events of the aerodynamic forces acting on the disk which we propose to link in particular to the vortex shedding-induced fluctuations. Beyond the aerodynamic aspects, this work has interesting fundamental outcomes regarding the broad field of rare events in out-of-equilibrium systems.

We present a sweep-stick mechanism for heavy particles transported by a turbulent flow under the action of gravity. Direct numerical simulations show that these particles preferentially explore regions of the flow with close to zero Lagrangian acceleration. However, the actual Lagrangian acceleration of the fluid elements where particles accumulate is not zero, and has a dependence on the Stokes number, the gravity acceleration, and the settling velocity of the particles., Comment: 8 pages, 9 figures

An innovative method based on the traversal of rays, originating from detected particles, through a three-dimensional grid of voxels is presented. The methodology has as main advantage that the outcome of the method is independent of the order of the input; the order of the cameras and the order of the rays presented as input to the algorithm does not influence the outcome. The algorithm finds matches in decreasing value of match quality, ensuring that globally best matches are matched before worse matches. The time complexity of the algorithm is found to scale efficiently with the number of cameras and particles. A variety of show-cases are given to exemplify the algorithm for different geometries and different number of cameras. The method is designed for the tracking of tracer or inertial particles in fluid mechanics, for which the particle size generally ranges from O({\mu}m)--O(cm). The method, however, does not impose a size limit on the particles.

The so-called Landau-Levich-Deryaguin problem treats the coating flow dynamics of a thin viscous liquid film entrained by a moving solid surface. In this context, we use a simple experimental set-up consisting of a partially-immersed rotating disc in a liquid tank to study the role of inertia, and also curvature, on liquid entrainment. Using water and UCON$^{\mbox{{TM}}}$ mixtures, we point out a rich phenomenology in the presence of strong inertia : ejection of multiple liquid sheets on the emerging side of the disc, sheet fragmentation, ligament formation and atomization of the liquid flux entrained over the disc's rim. We focus our study on a single liquid sheet and the related average liquid flow rate entrained over a thin disc for various depth-to-radius ratio $h/R < 1$. We show that the liquid sheet is created via a ballistic mechanism as liquid is lifted out of the pool by the rotating disc. We then show that the flow rate in the entrained liquid film is controlled by both viscous and surface tension forces as in the classical Landau-Levich-Deryaguin problem despite the three dimensional, non-uniform and unsteady nature of the flow, and also despite the large values of the film thickness based flow Reynolds number. When the characteristic Froude and Weber numbers become significant, strong inertial effects influence the entrained liquid flux over the disc at large radius-to-immersion-depth ratio, namely via entrainment by the disc's lateral walls and via a contribution to the flow rate extracted from the 3D liquid sheet itself, respectively., Comment: Keywords : film coating problem; inertial Landau-Levich film; liquid entrainment & Supplementary videos available here : https://box-ng.univ-lyon1.fr/s/ygJqk7mpasDD57M

Active matter, composed of self-propelled entities, forms a wide class of out-of-equilibrium systems that display striking collective behaviors among which the so-called active turbulence where spatially and time disordered flow patterns spontaneously arise in a variety of {active systems}. De facto, the active turbulence naming suggests a connection with a second seminal class of out-of-equilibrium systems, fluid turbulence, and yet of very different nature with energy injected at global system scale rather than at the elementary scale of single constituents. Indeed the existence of a possible strong-tie between active and canonical turbulence remains an open question and a field of profuse research. Using an assembly of self-propelled interfacial particles, we show experimentally that this active system shares remarkable quantitative similarities with canonical fluid turbulence, as described by the celebrated 1941 phenomenology of Kolmogorov. Making active matter entering into the universality class of fluid turbulence not only benefits to its future development but may also provide new insights for the longstanding description of turbulent flows, arguably one of the biggest remaining mysteries in classical physics.

We develop a stochastic model for Lagrangian velocity as it is observed in experimental and numerical fully developed turbulent flows. We define it as the unique statistically stationary solution of a causal dynamics, given by a stochastic differential equation. In comparison to previously proposed stochastic models, the obtained process is infinitely differentiable at a given finite Reynolds number, and its second-order statistical properties converge to those of an Ornstein-Uhlenbeck process in the infinite Reynolds number limit. In this limit, it exhibits furthermore intermittent scaling properties, as they can be quantified using higher-order statistics. To achieve this, we begin with generalizing the two-layered embedded stochastic process of Sawford (1991) by considering an infinite number of layers. We then study, both theoretically and numerically, the convergence towards a smooth (i.e. infinitely differentiable) Gaussian process. To include intermittent corrections, we follow similar considerations as for the multifractal random walk of Bacry et al. (2001). We derive in an exact manner the statistical properties of this process, and compare them to those estimated from Lagrangian trajectories extracted from numerically simulated turbulent flows. Key predictions of the multifractal formalism regarding acceleration correlation function and high-order structure functions are also derived. Through these predictions, we understand phenomenologically peculiar behaviours of the fluctuations in the dissipative range, that are not reproduced by our stochastic process. The proposed theoretical method regarding the modelling of infinitely differentiability opens the route to the full stochastic modelling of velocity, including the peculiar action of viscosity on the very fine scales., Comment: 49 pages, 5 figures

We present a statistical analysis of the behavior of the kinetic energy spectrum in the dissipative range of scales of fully developed three-dimensional turbulence. We analyze spectra recorded in experiments of grid turbulence generated in the Modane wind tunnel, and spectra obtained from high-resolution direct numerical simulations of the forced Navier-Stokes equation. We focus on wave-number scales in the near-dissipative range. We find that in this domain, the spectra behave as a stretched exponential with an exponent $\alpha = 0.68 \pm 0.19$. This result corroborates previous DNS studies which found that the spectrum in the near-dissipative range is best modeled by a stretched exponential with $\alpha<1$. Moreover, we here give an estimate for the actual value of $\alpha$, which turns out to be in precise agreement with the theoretical prediction $\alpha=2/3$ from the non-perturbative renormalisation group., Comment: 12 pages, 11 figures

We investigate the sedimentation of initially packed paramagnetic particles in presence of a homogeneous external magnetic field, in a Hele-Shaw cell filled with water. Although the magnetic susceptibility of the particles is small and the particle-particle induced magnetic interactions are significantly smaller compared to the gravitational acceleration, we do observe a measurable reduction of the decompaction rate as the amplitude of the applied magnetic field is increased. While induced magnetic dipole-dipole interactions between particles can be either attracting or repulsive depending on the particles relative alignment, our observations reveal an effective overall enhancement of the cohesion of the initial pack of particles due to the induced interactions, very likely promoting internal chain forces in the initial pack of particles. The influence of the magnetic field on the particles once they disperse after being decompacted is on the other hand found to remain marginal.

Due to large scale flow inhomogeneities and the effects of temperature, turbulence small-scale structure in thermal convection is still an active field of investigation, especially considering sophisticated Lagrangian statistics. Here we experimentally study Lagrangian pair dispersion (one of the canonical problems of Lagrangian turbulence) in a Rayleigh-B\'enard convection cell. A sufficiently high temperature difference is imposed on a horizontal layer of fluid to observe a turbulent flow. We perform Lagrangian tracking of sub-millimetric particles on a large measurement volume including part of the Large Scale Circulation (LSC) revealing some large inhomogeneities. Our study brings to light several new insights regarding our understanding of turbulent thermal convection: (i) by decomposing particle Lagrangian dynamics into the LSC contribution and the turbulent fluctuations, we highlight the relative impact of both contributions on pair dispersion; (ii) using the same decomposition, we estimate the Eulerian second-order velocity structure functions from pair statistics and show that after removing the LSC contribution, the remaining statistics recover usual homogeneous and isotropic behaviours which are governed by a local energy dissipation rate to be distinguished from the global dissipation rate classically used to characterise turbulence in thermal convection; and (iii) we revisit the super-diffusive Richardson-Obukhov regime of particle dispersion and propose a refined estimate of the Richardson constant., Comment: 9 figures

We study analytically the joint dispersion of Gaussian patches of salt and colloids in linear flows, and how salt gradients accelerate or delay colloid spreading by diffusiophoretic effects. Because these flows have constant gradients in space, the problem can be solved almost entirely for any set of parameters, leading to predictions of how the mixing time and the Batchelor scale are modified by diffusiophoresis. We observe that the evolution of global concentrations, defined as the inverse of the patches areas, are very similar to those obtained experimentally in chaotic advection. They are quantitatively explained by examining the area dilatation factor, in which diffusive and diffusiophoretic effects are shown to be additive and appear as the divergence of a diffusive contribution or of a drift velocity. An analysis based on compressibility is developed in the salt-attracting case, for which colloids are first compressed before dispersion, to predict the maximal colloid concentration as a function of the parameters. This maximum is found not to depend on the flow stretching rate nor on its topology (strain or shear flow), but only on the characteristics of salt and colloids (diffusion coefficients and diffusiophoretic constant) and the initial size of the patches., Comment: JFM, 16 pages, 7 figures

Lagrangian tracking of particle pairs is of fundamental interest in a large number of environmental applications dealing with contaminant dispersion and passive scalar mixing. The aim of the present study is to extend the observations available in the literature on relative dispersion of fluid particle pairs to wall-bounded turbulent flows, by means of particle pair tracking in direct numerical simulations (DNS) of a turbulent channel flow. The mean-square change of separation between particle pairs follows a clear ballistic regime at short times for all wall distances. The Eulerian structure functions governing this short-time separation are characterised in the channel, and allow to define a characteristic time scale for the ballistic regime, as well as a suitable normalisation of the mean-square separation leading to an overall collapse for different wall distances. Through fluid particle pair tracking backwards and forwards in time, the temporal asymmetry of relative dispersion is illustrated. At short times, this asymmetry is linked to the irreversibility of turbulence, as in previous studies on homogeneous isotropic flows. The influence of the initial separation (distance and orientation) as well as the influence of mean shear are addressed. By decomposing the mean-square separation into the dispersion by the fluctuating velocity field and by the average velocity, it is shown that the influence of mean shear becomes important at early stages of dispersion close to the wall but also near the channel centre. The relative dispersion tensor $\Delta_{ij}$ is also presented and particularly the sign and time evolution of the cross-term $\Delta_{xy}$ are discussed. Finally, a ballistic cascade model previously proposed for homogeneous isotropic turbulence is adapted here to turbulent channel flows. Preliminary results are given and compared to the DNS., Comment: Accepted for publication in International Journal of Heat and Fluid Flow (TSFP10 Special Issue), 18 pages, 16 figures

Bubbles play an important role in the transport of chemicals and nutrients in many natural and industrial flows. Their dispersion is crucial to understand the mixing processes in these flows. Here we report on the dispersion of millimetric air bubbles in a homogeneous and isotropic turbulent flow with Reynolds number $\text{Re}_\lambda$ from $110$ to $310$. We find that the mean squared displacement (MSD) of the bubbles far exceeds that of fluid tracers in turbulence. The MSD shows two regimes. At short times, it grows ballistically ($\propto \tau^2$), while at larger times, it approaches the diffusive regime where MSD $\propto \tau$. Strikingly, for the bubbles, the ballistic-to-diffusive transition occurs one decade earlier than for the fluid. We reveal that both the enhanced dispersion and the early transition to the diffusive regime can be traced back to the unsteady wake-induced-motions of the bubbles. Further, the diffusion transition for bubbles is not set by the integral time scale of the turbulence (as it is for fluid tracers and microbubbles), but instead, by a timescale of eddy-crossing of the rising bubbles. The present findings provide a Lagrangian perspective towards understanding mixing in turbulent bubbly flows., Comment: Physical Review Letters (accepted), 6 pages, 4 figures, 1 table

Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of particles in a turbulent flow. To this end, we study how the dispersion of a cloud of phoretic particles is modified when injected in the flow, together with a blob of scalar, whose effect is to transiently bring particles together, or push them away from the center of the blob. The resulting phoretic effect can be quantified by a single dimensionless number. Phenomenological considerations lead to simple predictions for the mean separation between particles, which are consistent with results of direct numerical simulations. Using the numerical results presented here, as well as those from previous studies, we discuss quantitatively the experimental consequences of this work and the possible impact of such phoretic mechanisms in natural systems., Comment: 17 pages, 6 figures

Turbulent flows laden with inertial particles present multiple open questions and are a subject of great interest in current research. Due to their higher density compared to the carrier fluid, inertial particles tend to form high concentration regions, i.e. clusters, and low concentration regions, i.e. voids, due to the interaction with the turbulence. In this work, we present an experimental investigation of the clustering phenomenon of heavy sub-Kolmogorov particles in homogeneous isotropic turbulent flows. Three control parameters have been varied over significant ranges: $Re_{\lambda} \in [170 - 450]$, $St\in [0.1 - 5]$ and volume fraction $\phi_v\in [2\times 10^{-6} - 2\times 10^{-5}]$. The scaling of clustering characteristics, such as the distribution of Vorono\"i areas and the dimensions of cluster and void regions, with the three parameters are discussed. In particular, for the polydispersed size distributions considered here, clustering is found to be enhanced strongly (quasi-linearly) by $Re_{\lambda}$ and noticeably (with a square-root dependency) with $\phi_v$, while the cluster and void sizes, scaled with the Kolmogorov lengthscale $\eta$, are driven primarily by $Re_{\lambda}$. Cluster length $\sqrt{\langle A_c \rangle}$ scales up to $\approx 100 {\eta}$, measured at the highest $Re_{\lambda}$, while void length $\sqrt{\langle A_v \rangle}$ scaled also with $\eta$ is typically two times larger ($\approx 200 {\eta}$). The lack of sensitivity of the above characteristics to the Stokes number lends support to the "sweep-stick" particle accumulation scenario. The non-negligible influence of the volume fraction, however, is not considered by that model and can be connected with collective effects.

The settling of heavy spherical particles in a column of quiescent fluid is investigated. The performed experiments cover a range of Galileo numbers ($110 \leq \text{Ga} \leq 310$) for a fixed density ratio of $\Gamma = \rho_p/\rho_f = 2.5$. In this regime the particles are known (M. Jenny, J. Du\v{s}ek and G. Bouchet, Journal of Fluid Mechanics 508, 201 (2004).) to show a variety of motions. It is known that the wake undergoes several transitions for increasing $\text{Ga}$ resulting in particle motions that are successively: vertical, oblique, oblique oscillating, and finally chaotic. Not only does this change the trajectory of single, isolated, settling particles, but it also changes the dynamics of a swarm of particles as collective effects become important even for dilute suspensions, with volume fraction up to $\Phi_V = \mathcal{O}\left(10^{-3}\right)$, which are investigated in this work. Multi-camera recordings of settling particles are recorded and tracked over time in 3 dimensions. A variety of analysis are performed and show a strong clustering behavior. The distribution of the cell areas of the Vorono\"i tessellation in the horizontal plane are compared to that of a random distribution of particles and shows clear clustering. Moreover, a negative correlation was found between the Vorono\"i area and the particle velocity; clustered particles fall faster. In addition, the angle between two adjacent particles and the vertical is calculated and compared to a homogeneous distribution of particles, clear evidence of vertical alignment of particles is found. The experimental findings are compared to simulations., Comment: 8 pages, 6 figures

This article describes two independent developments aimed at improving the Particle Tracking Method for measurements of flow or particle velocities. First, a stereoscopic multicamera calibration method that does not require any optical model is described and evaluated. We show that this new calibration method gives better results than the most commonly-used technique, based on the Tsai camera/optics model. Additionally, the methods uses a simple interpolant to compute the transformation matrix and it is trivial to apply for any experimental fluid dynamics visualization set up. The second contribution proposes a solution to remove noise from Eulerian measurements of velocity statistics obtained from Particle Tracking velocimetry, without the need of filtering and/or windowing. The novel method presented here is based on recomputing particle displacement measurements from two consecutive frames for multiple different time-step values between frames. We show the successful application of this new technique to recover the second order velocity structure function of the flow. Increased accuracy is demonstrated by comparing the dissipation rate of turbulent kinetic energy measured from the second order structure function against previously validated measurements. These two techniques for improvement of experimental fluid/particle velocity measurements can be combined to provide high accuracy 3D particle and/or flow velocity statistics and derived variables needed to characterize a turbulent flow.

Since the pioneering work of Richardson in 1926, later refined by Batchelor and Obukhov in 1950, it is predicted that the rate of separation of pairs of fluid elements in turbulent flows with initial separation at inertial scales, grows ballistically first (Batchelor regime), before undergoing a transition towards a super-diffusive regime where the mean-square separation grows as t^3 (Richardson regime). Richardson empirically interpreted this super-diffusive regime in terms of a non-Fickian process with a scale dependent diffusion coefficient (the celebrated Richardson's "4/3rd" law). However, the actual physical mechanism at the origin of such a scale dependent diffusion coefficient remains unclear. The present article proposes a simple physical phenomenology for the time evolution of the mean square relative separation in turbulent flows, based on a scale dependent ballistic scenario rather than a scale dependent diffusive. This phenomenology accurately retrieves most of the known features of relative dispersion ; among others : (i) it is quantitatively consistent with recent numerical simulations and experiments (both for the short term Batchelor regime and the long term Richardson regime, and for all initial separations at inertial scales), (ii) it gives a simple physical explanation of the origin of the super diffusive t^3 Richardson regime which naturally builts itself as an iterative process of elementary short-term-scale-dependent ballistic steps, (iii) it shows that the Richardson constant is directly related to the Kolmogorov constant (and eventually to a ballistic persistence parameter) and (iv) in a further extension of the phenomenology, taking into account third order corrections, it robustly describes the temporal asymmetry between forward and backward dispersion, with an explicit connection to the cascade of energy flux across scales.

The von-Karman plasma experiment is a novel versatile experimental device designed to explore the dynamics of basic magnetic induction processes and the dynamics of flows driven in weakly magnetized plasmas. A high-density plasma column (10^16 - 10^19 particles.m^-3) is created by two radio-frequency plasma sources located at each end of a 1 m long linear device. Flows are driven through JxB azimuthal torques created from independently controlled emissive cathodes. The device has been designed such that magnetic induction processes and turbulent plasma dynamics can be studied from a variety of time-averaged axisymmetric flows in a cylinder. MHD simulations implementing volume-penalization support the experimental development to design the most efficient flow-driving schemes and understand the flow dynamics. Preliminary experimental results show that a rotating motion of up to nearly 1 km/s is controlled by the JxB azimuthal torque.

We study numerically joint mixing of salt and colloids by a chaotic velocity field $\mathbf{V}$, and how salt inhomogeneities accelerate or delay colloid mixing by inducing a velocity drift $\mathbf{V}_{\rm dp}$ between colloids and fluid particles as proposed in recent experiments \cite{Deseigne2013}. We demonstrate that because the drift velocity is no longer divergence free, small variations to the total velocity field drastically affect the evolution of colloid variance $\sigma^2=\langle C^2 \rangle - \langle C \rangle^2$. A consequence is that mixing strongly depends on the mutual coherence between colloid and salt concentration fields, the short time evolution of scalar variance being governed by a new variance production term $P=- \langle C^2 \nabla \cdot \mathbf{V}_{\rm dp} \rangle/2$ when scalar gradients are not developed yet so that dissipation is weak. Depending on initial conditions, mixing is then delayed or enhanced, and it is possible to find examples for which the two regimes (fast mixing followed by slow mixing) are observed consecutively when the variance source term reverses its sign. This is indeed the case for localized patches modeled as gaussian concentration profiles.

We apply a new threshold detection method based on the extreme value theory to the von K\'arm\'an sodium (VKS) experiment data. The VKS experiment is a successful attempt to get a dynamo magnetic field in a laboratory liquid-metal experiment. We first show that the dynamo threshold is associated to a change of the probability density function of the extreme values of the magnetic field. This method does not require the measurement of response functions from applied external perturbations, and thus provides a simple threshold estimate. We apply our method to different configurations in the VKS experiment showing that it yields a robust indication of the dynamo threshold as well as evidence of hysteretic behaviors. Moreover, for the experimental configurations in which a dynamo transition is not observed, the method provides a way to extrapolate an interval of possible threshold values., Comment: 10 pages, 7 figures

We analyze time series stemming from experiments and direct numerical simulations of hydrodynamic and magnetohydrodynamic turbulence. Simulations are done in periodic boxes, but with a volumetric forcing chosen to mimic the geometry of the flow in the experiments, the von K\'arm\'an swirling flow between two counter-rotating impellers. Parameters in the simulations are chosen to (within computational limitations) allow comparisons between the experiments and the numerical results. Conducting fluids are considered in all cases. Two different configurations are considered: a case with a weak externally imposed magnetic field, and a case with self-sustained magnetic fields. Evidence of long-term memory and $1/f$ noise is observed in experiments and simulations, in the case with weak magnetic field associated with the hydrodynamic behavior of the shear layer in the von K\'arm\'an flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large scale magnetic field., Comment: 10 pages, 9 figures

We investigate the dynamics of very large particles freely advected in a turbulent von Karman flow. Contrary to other experiments for which the particle dynamics is generally studied near the geometrical center of the flow, we track the particles in the whole experiment volume. We observe a strong influence of the mean structure of the flow that generates an unexpected large-scale sampling effect for the larger particles studied; contrary to neutrally buoyant particles of smaller yet finite sizes that exhibit no preferential concentration in homogeneous and isotropic turbulence (Fiabane et al., Phys. Rev. E 86(3), 2012). We find that particles whose diameter approaches the flow integral length scale explore the von Karman flow non-uniformly, with a higher probability to move in the vicinity of two tori situated near the poloidal neutral lines. This preferential sampling is quite robust with respect to changes of any varied parameters: Reynolds number, particle density and particle surface roughness.

We investigate experimentally the spatial distributions of heavy and neutrally buoyant particles of finite size in a fully turbulent flow. As their Stokes number (i.e. ratio of the particle viscous relaxation time to a typical flow time scale) is close to 1, one may expect both classes of particles to aggregate in specific flow regions. This is not observed. Using a Voronoi analysis we show that neutrally buoyant particles sample turbulence homogeneously, whereas heavy particles do cluster. One implication for the understanding and modeling of particle laden flows, is that the Stokes number cannot be the sole key parameter as soon as the dynamics of finite-size objects is considered., Comment: accepted for publication in Physical Review E

We investigate the preferential concentration of particles which are neutrally buoyant but with a diameter significantly larger than the dissipation scale of the carrier flow. Such particles are known not to behave as flow tracers (Qureshi et al., Phys. Re. Lett. 2007) but whether they do cluster or not remains an open question. For this purpose, we take advantage of a new turbulence generating apparatus, the Lagrangian Exploration Module which produces homogeneous and isotropic turbulence in a closed water flow. The flow is seeded with neutrally buoyant particles with diameter 700\mum, corresponding to 4.4 to 17 times the turbulent dissipation scale when the rotation frequency of the impellers driving the flow goes from 2 Hz to 12 Hz, and spanning a range of Stokes numbers from 1.6 to 24.2. The spatial structuration of these inclusions is then investigated by a Voronoi tesselation analysis, as recently proposed by Monchaux et al. (Phys. Fluids 2010), from images of particle concentration field taken in a laser sheet at the center of the flow. No matter the rotating frequency and subsequently the Reynolds and Stokes numbers, the particles are found not to cluster. The Stokes number by itself is therefore shown to be an insufficient indicator of the clustering trend in particles laden flows.

The motion of a large, neutrally buoyant, particle, freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a manifestation of intermittency. The orientation of the angular velocity with respect to the trajectory, as well as the translational acceleration conditioned on the spinning velocity provide evidence of a lift force acting on the particle., Comment: 4 page, 4 figures

We study the 6-dimensional dynamics -- position and orientation -- of a large sphere advected by a turbulent flow. The movement of the sphere is recorded with 2 high-speed cameras. Its orientation is tracked using a novel, efficient algorithm; it is based on the identification of possible orientation `candidates' at each time step, with the dynamics later obtained from maximization of a likelihood function. Analysis of the resulting linear and angular velocities and accelerations reveal a surprising intermittency for an object whose size lies in the integral range, close to the integral scale of the underlying turbulent flow.

We study magnetohydrodynamics in a von K\'arm\'an flow driven by the rotation of impellers made of material with varying electrical conductivity and magnetic permeability. Gallium is the working fluid and magnetic Reynolds numbers of order unity are achieved. We find that specific induction effects arise when the impeller's electric and magnetic characteristics differ from that of the fluid. Implications in regards to the VKS dynamo are discussed., Comment: 14 pages, 7 figures

A synthetic fluid dynamo built in the spirit of the Bullard device [E. C. Bullard, Proc. Camb. Phil. Soc., 51, 744 (1955)] is investigated. It is a two-step dynamo in which one process stems from the fluid turbulence, while the other part is an alpha effect achieved by a linear amplification of currents in external coils [M. Bourgoin et al., New J. Phys., 8, 329 (2006)]. Modifications in the forcing are introduced in order to change the dynamics of the flow, and hence the dynamo behavior. Some features, such as on-off intermittency at onset of dynamo action, are very robust. Large scales fluctuations have a significant impact on the resulting dynamo, in particular in the observation of magnetic field reversals.

The dynamics of particles in turbulence when the particle-size is larger than the dissipative scale of the carrier flow is studied. Recent experiments have highlighted signatures of particles finiteness on their statistical properties, namely a decrease of their acceleration variance, an increase of correlation times -at increasing the particles size- and an independence of the probability density function of the acceleration once normalized to their variance. These effects are not captured by point particle models. By means of a detailed comparison between numerical simulations and experimental data, we show that a more accurate model is obtained once Faxen corrections are included., Comment: 10 pages, 4 figures

Being able to accurately model and predict the dynamics of dispersed inclusions transported by a turbulent flow, remains a challenge with important scientific, environmental and economical issues. One critical and difficult point is to correctly describe the dynamics of particles over a wide range of sizes and densities. Our measurements show that acceleration statistics of particles dispersed in a turbulent flow do exhibit specific size and density effects but that they preserve an extremely robust turbulent signature with lognormal fluctuations, regardless of particles size and density. This has important consequences in terms of modelling of the turbulent transport of dispersed inclusions.

We use an acoustic Lagrangian tracking technique, particularly adapted to measurements in open flows, and a versatile material particles generator (in the form of soap bubbles with adjustable size and density) to characterize Lagrangian statistics of finite sized, neutrally bouyant, particles transported in an isotropic turbulent flow of air. We vary the size of the particles in a range corresponding to turbulent inertial scales and explore how the turbulent forcing experienced by the particles depends on their size. We show that, while the global shape of the intermittent acceleration probability density function does not depend significantly on particle size, the acceleration variance of the particles decreases as they become larger in agreement with the classical scaling for the spectrum of Eulerian pressure fluctuations in the carrier flow.

Turbulent mixing of liquids and gasses is ubiquitous in nature. It is the basis of all industrial fluid mixing processes, and it determines the spread of pollutants or bioagents in the atmosphere and oceans. Biological organisms even use it to survive in marine ecosystems. A fundamental component of turbulent mixing is the separation of two nearby fluid elements, i.e., pair dispersion. Despite almost eighty years of intense scientific inquiry, no clear understanding of this fundamental aspect of turbulence has emerged. One critical unresolved question is the extent to which the initial separation of the fluid particles influences their subsequent motion. Surprisingly, our measurements in a laboratory water flow at very high turbulence levels (Taylor microscale Reynolds numbers up to R_lambda = 815) suggest that the initial separation remains important for all but the most violent flows on Earth. This observation has important consequences for such varied problems as pollution control, combustion modelling, hazardous chemical control, and even the understanding of how animals locate food, predators, and mates., Comment: 11 pages, 3 figures