Turbulent Properties of Stationary Flows in Porous Media.

In this study, we investigate 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 (Re=[124,169,203,211]). We discover that even though the flow is stationary at the larger scales, it exhibits complex multiscale spatial dynamics reminiscent of those observed in classical turbulence. We find evidence of the presence of an inertial range and a direct energy cascade, and are able to obtain a value for a "porous" Kolmogorov constant of C_{2}=3.1±0.3. This analogy with turbulence opens up new possibilities for understanding mixing and global transport properties in porous media.

Capillary washboarding during slow drainage of a frictional fluid.

Numerous natural and industrial processes involve the mixed displacement of liquids, gases and granular materials through confining structures. However, understanding such three-phase flows remains a formidable challenge, despite their tremendous economic and environmental impact. To unveil the complex interplay of capillary and granular stresses in such flows, we consider here a model configuration where a frictional fluid (an immersed sedimented granular layer) is slowly drained out of a horizontal capillary. Analyzing how liquid/air menisci displace particles from such granular beds, we reveal various drainage patterns, notably the periodic formation of dunes, analogous to road washboard instability. Considering the competitive role of friction and capillarity, a 2D theoretical approach supported by numerical simulations of a meniscus bulldozing a front of particles provides quantitative criteria for the emergence of those dunes. A key element is the strong increase of the frictional forces, as the bulldozed particles accumulate and bend the meniscus horizontally. Interestingly, this frictional enhancement with the attack angle is also crucial in small-legged animals' locomotion over granular media.

Rare Event-Triggered Transitions in Aerodynamic Bifurcation.

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 4 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.

Two-dimensional numerical model of Marangoni surfers: From single swimmer to crystallization.

We numerically study the dynamics of an ensemble of Marangoni surfers in a two-dimensional and unconfined space. The swimmers are modeled as Gaussian sources of surfactant generating surface tension gradients and are shown to follow the Marangoni flow filtered at their spatial scale in the lubrication regime, an unstable situation leading to spontaneous motion as soon as the Marangoni effect is intense enough. As the system is fully unconstrained, it is possible to study the various dynamical regimes from single swimmer, two-body interaction, to the many-particles case characterized by an efficient particle dispersion. We show that, although the present model is very simple, it reproduces the experimentally observed transition between a regime of dispersion by random agitation when the number of swimmers is moderate to the regime of crystallization with imperfect hexagonal lattice at high density.

Using ray-traversal for 3D particle matching in the context of particle tracking velocimetry in fluid mechanics.

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 the 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 do 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 numbers 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 (µm)-O (cm). The method, however, does not impose a size limit on the particles.

Sedimentation of a suspension of paramagnetic particles in an external magnetic field.

We investigate the sedimentation of initially packed paramagnetic particles in the 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 attractive 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, however, found to remain marginal.

Stability of a Liquid Jet Impinging on Confined Saturated Sand.

This Letter focuses on the dynamics of a liquid jet impacting the surface of a confined, immersed granular bed. Although previous works have considered the erosion process and surface morphology, less attention has been given to the jet hydrodynamics. Based on laboratory experiments, we show that when the liquid jet forms a crater, two situations arise. For weak or no erosion and for open craters, the jet is stationary. For vertical or overhanging crater walls, the jet displays a wide range of behaviors, from quasiperiodic oscillations to symmetry breaking and exploration of different states in time. An analysis of the different system states leads to the emergence of a bifurcation diagram depending on a dimensionless parameter, J, comparing the jet impact force to the force necessary to eject a grain. The frequency of the jet oscillations depends on the inertial velocity, the jet dispersion and the ratio between the injector cross section and the confinement length.

Dispersion of Air Bubbles in Isotropic Turbulence.

Bubbles play an important role in the transport of chemicals and nutrients in many natural and industrial flows. Their dispersion is crucial to understanding the mixing processes in these flows. Here we report on the dispersion of millimetric air bubbles in a homogeneous and isotropic turbulent flow with a Taylor Reynolds number 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 (∝τ^{2}), while at larger times, it approaches the diffusive regime where the MSD∝τ. 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 motion of the bubbles. Further, the diffusion transition for bubbles is not set by the integral timescale 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.

Stochastic reversal dynamics of two interacting magnetic dipoles: A simple model experiment.

We report an experimental study of the dynamics of two coupled magnetic dipoles. The experiment consists in two coplanar permanent disk magnets separated by a distance d, each allowed to rotate on a fixed parallel axis-each magnet's axis being perpendicular to its dipolar moment vector. A torque of adjustable strength can be externally applied to one of the magnets, the other magnet being free. The driving torque may be time-independent or temporally fluctuating. We study the influence of the parameters of the driving torque on the dynamics of the coupled system, in particular the emergence of dynamical regimes such as stochastic reversals. We report transitions between stationary and stochastic reversal regimes. All the observed features can be understood by a simple mechanical dynamical model. The transition between statistically stationary regimes and reversals is explained introducing an effective potential energy incorporating both the coupling between magnets and the external driving. Relations between this simple experimental model with macroscopic models of magnetic spin coupling, as well as with chaotic reversals of turbulent dynamos, are discussed.

Dynamo efficiency controlled by hydrodynamic bistability.

Hydrodynamic and magnetic behaviors in a modified experimental setup of the von Kármán sodium flow-where one disk has been replaced by a propeller-are investigated. When the rotation frequencies of the disk and the propeller are different, we show that the fully turbulent hydrodynamic flow undergoes a global bifurcation between two configurations. The bistability of these flow configurations is associated with the dynamics of the central shear layer. The bistable flows are shown to have different dynamo efficiencies; thus for a given rotation rate of the soft-iron disk, two distinct magnetic behaviors are observed depending on the flow configuration. The hydrodynamic transition controls the magnetic field behavior, and bifurcations between high and low magnetic field branches are investigated.

Dynamo threshold detection in the von Kármán sodium experiment.

Predicting dynamo self-generation in liquid metal experiments has been an ongoing question for many years. In contrast to simple dynamical systems for which reliable techniques have been developed, the ability to predict the dynamo capacity of a flow and the estimate of the corresponding critical value of the magnetic Reynolds number (the control parameter of the instability) has been elusive, partly due to the high level of turbulent fluctuations of flows in such experiments (with kinetic Reynolds numbers in excess of 10(6)). We address these issues here, using the von Kármán sodium experiment and studying its response to an externally applied magnetic field. We first show that a dynamo threshold can be estimated from analysis related to critical slowing down and susceptibility divergence, in configurations for which dynamo action is indeed observed. These approaches are then applied to flow configurations that have failed to self-generate magnetic fields within operational limits, and we quantify the dynamo capacity of these configurations.

Rotational intermittency and turbulence induced lift experienced by large particles in a turbulent flow.

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, provides evidence of a lift force acting on the particle.

Tracking the dynamics of translation and absolute orientation of a sphere in a turbulent flow.

We study the six-dimensional dynamics--position and orientation--of a large sphere advected by a turbulent flow. The movement of the sphere is recorded with two 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 inertial range, close to the integral scale of the underlying turbulent flow.

The Lagrangian exploration module: an apparatus for the study of statistically homogeneous and isotropic turbulence.

We present an apparatus that generates statistically homogeneous and isotropic turbulence with a mean flow that is less than 10% of the fluctuating velocity in a volume of the size of the integral length scale. The apparatus is shaped as an icosahedron where at each of the 12 vertices the flow is driven by independently controlled propellers. By adjusting the driving of the different propellers the isotropy and homogeneity of the flow can be tuned, while keeping the mean flow weak.

Turbulent transport of material particles: an experimental study of finite size effects.

We present experimental Lagrangian statistics of finite sized, neutrally bouyant, particles transported in an isotropic turbulent flow. The particle's diameter is varied over turbulent inertial scales. Finite size effects are shown not to be trivially related to velocity intermittency. The global shape of the particle's acceleration probability density functions is not found to depend significantly on its size while the particle's acceleration variance decreases as it becomes larger in quantitative agreement with the classical k(-7/3) scaling for the spectrum of Eulerian pressure fluctuations in the carrier flow.

High order Lagrangian velocity statistics in turbulence.

We report measurements of the Lagrangian velocity structure functions of orders 1 through 10 in a high Reynolds number (Taylor microscale Reynolds numbers of up to R(lambda) = 815 ) turbulence experiment. Passive tracer particles are tracked optically in three dimensions and in time, and velocities are calculated from the particle tracks. The structure function anomalous scaling exponents are measured both directly and using extended self-similarity and are found to be more intermittent than their Eulerian counterparts. Classical Kolmogorov inertial range scaling is also found for all structure function orders at times that trend downward as the order increases. The temporal shift of this classical scaling behavior is observed to saturate as the structure function order increases at times shorter than the Kolmogorov time scale.

The role of pair dispersion in turbulent flow.

Mixing and transport in turbulent flows-which have strong local concentration fluctuations-are essential in many natural and industrial systems including reactions in chemical mixers, combustion in engines and burners, droplet formation in warm clouds, and biological odor detection and chemotaxis. Local concentration fluctuations, in turn, are intimately tied to the problem of the separation of pairs of fluid elements. We have measured this separation rate in an intensely turbulent laboratory flow and have found, in quantitative agreement with the seminal predictions of Batchelor, that the initial separation of the pair plays an important role in the subsequent spreading of the fluid elements. These results have surprising consequences for the decay of concentration fluctuations and have applications to biological and chemical systems.