arXiv subjects

Mickael Bourgoin

Publications and source records attributed to Mickael Bourgoin.

At least 19 recordsLinked to original sources

arXiv2025

Lagrangian flow statistics in experimental homogeneous isotropic turbulence

We report on Lagrangian flow statistics from experimental measurements of homogeneous isotropic turbulence. The investigated flow is driven by 12 impellers inside an icosahedral volume. Seven impeller rotation rates are considered resulting in seven Reynolds numbers with $205 \leq \text{Re}_λ\leq 602$. We perform high-speed imaging using 3 cameras to record a total of $8.2\times10^6$ frames, and using high resolution three dimensional (3D) particle tracking velocimetry position, velocity, and acceleration of particle tracks are obtained in the vicinity of the center of the device. From these tracks, we obtain the Eulerian and Lagrangian flow statistics, mainly based on second-order structure functions and autocorrelation functions. The universal constants $C_0^*$ (for the Lagrangian second order structure function), $C_\varepsilon$ (for the energy injection rate) and $a_0$ (for the acceleration fluctuations) are determined, as well as all the relevant Lagrangian and Eulerian flow time scales. Analytical relations between these constants and time scales are experimentally verified.

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arXiv2023

Suspension of large inertial particles in a turbulent swirling flow

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.

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arXiv2021

Lagrangian diffusion properties of a free shear turbulent jet

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 $\mathcal R_λ\simeq 230$. 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.

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arXiv2020

Multi-scale energy budget of inertially driven turbulence in normal and superfluid helium

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 Voronoï 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.

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arXiv2020

Modelling Lagrangian velocity and acceleration in turbulent flows as infinitely differentiable stochastic processes

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.

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arXiv2020

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

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arXiv2019

Kolmogorovian active turbulence of a sparse assembly of interacting swimmers

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.

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arXiv2018

Advection and diffusion in a chemically induced compressible flow

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.

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arXiv2016

Preferential concentration of inertial sub-kolmogorov particles. The roles of mass loading of particles, Stokes and Reynolds numbers

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: $Re_λ \in [170 - 450]$, $St\in [0.1 - 5]$ and volume fraction $ϕ_v\in [2\times 10^{-6} - 2\times 10^{-5}]$. The scaling of clustering characteristics, such as the distribution of Voronoï 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 $Re_λ$ and noticeably (with a square-root dependency) with $ϕ_v$, while the cluster and void sizes, scaled with the Kolmogorov lengthscale $η$, are driven primarily by $Re_λ$. Cluster length $\sqrt{\langle A_c \rangle}$ scales up to $\approx 100 η$, measured at the highest $Re_λ$, while void length $\sqrt{\langle A_v \rangle}$ scaled also with $η$ is typically two times larger ($\approx 200 η$). 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.

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arXiv2016

Improvements on Particle Tracking Velocimetry: model-free calibration and noiseless measurement of second order statistics of the velocity field

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.

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arXiv2015

Turbulent pair dispersion as a ballistic cascade phenomenology

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.

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arXiv2014

Chaotic mixing in effective compressible flows

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 $σ^2=\langle C^2 \rangle - \langle C \rangle^2$. 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.

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arXiv2014

Robust estimate of dynamo thresholds in the von Kármán sodium experiment using the Extreme Value Theory

We apply a new threshold detection method based on the extreme value theory to the von Kármán 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.

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arXiv2014

Long-term memory in experiments and numerical simulations of hydrodynamic and magnetohydrodynamic turbulence

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 Kármán 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 Kármán flow, and in the dynamo case associated with slow magnetohydrodynamic behavior of the large scale magnetic field.

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arXiv2013

Large spheres motion in a non homogeneous turbulent flow

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.

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arXiv2012

On the clustering of finite-size particles in turbulence

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.

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arXiv2012

Do finite size neutrally buoyant particles cluster?

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.

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arXiv2010

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 provide evidence of a lift force acting on the particle.

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