arXiv subjects

Mickaël Bourgoin

Publications and source records attributed to Mickaël Bourgoin.

At least 19 recordsLinked to original sources

arXiv2026

Using analogues to investigate error growth and predictability in turbulence

In this study, we revisit Lorenz's pioneering concept of analogues to investigate error growth and predictability in fully developed turbulence using experimental data. By applying the method to a 1D turbulent velocity time series, we successfully identify the three error growth regimes intuited by Lorenz and later formalized by turbulence theory: the chaotic exponential regime, the algebraic regime of spontaneous stochasticity, and the saturation regime. Our analysis reveals that the Lyapunov exponent and the exponent of the algebraic regime depend on the initial error. We interpret this dependence as a statistical bias induced by the intermittency of turbulence, where rare events, characterized by lower Lyapunov exponents and more singular velocity increments, are preferentially sampled when considering larger initial errors. These findings not only validate Lorenz's qualitative intuition but also provide new quantitative insights into the predictability of turbulent flows, paving the way for potential applications in the prediction of extreme events.

physics.flu-dyn↗

arXiv2026

Mixing and sharpening at the interface of a two-layer fluid forced by random jets

Understanding mixing at density interfaces is essential for predicting transport in stratified environmental flows. Laboratory studies have mostly relied on steady, spatially uniform forcing, whereas turbulence in nature is intermittent and heterogeneous. Here, we present experiments on a two-layer salt-stratified fluid forced by random turbulent bursts generated with a randomly actuated synthetic jet array (RASJA). Density fields are recorded with the light attenuation technique, allowing us to resolve the interface evolution. We measure that the upward velocity of the interface decreases with the density jump, in agreement with the power-law found in previous oscillating-grid studies. At large density differences, the interface sharpens during mixing, contrary to the smaller density jump case. Background potential energy analysis demonstrates irreversible mixing in both cases, with comparable energy changes. These results extend classical laboratory observations to a more isotropic forcing, offering new insights into the dynamics of mixing in geophysical settings.

physics.flu-dyn↗

arXiv2026

A spatio-temporal random synthetic turbulent velocity field: The underlying Gaussian structure

We develop, simulate and extend an initial proposition by Chaves et al. concerning a random incompressible vector field able to reproduce key ingredients of three-dimensional turbulence in both space and time. In this article, we focus on the important underlying Gaussian framework. Presently, the statistical spatial structure of this velocity field is consistent with a divergence-free fractional Gaussian vector field that encodes all known properties of homogeneous and isotropic fluid turbulence at a given finite Reynolds number, up to second-order statistics. The temporal structure of the velocity field is introduced through a stochastic evolution of the respective Fourier modes. In the simplest picture, Fourier modes evolve according to an Ornstein-Uhlenbeck process, where the characteristic time scale depends on the wave-vector amplitude. For consistency with direct numerical simulations (DNSs) of the Navier-Stokes equations, this time scale is inversely proportional to the wave vector amplitude. As a consequence, the characteristic velocity that governs the eddies is independent of their size and is related to the velocity standard deviation, which is consistent with some features of the so-called sweeping effect. To ensure differentiability in time while respecting the Markovian nature of the evolution, we use the methodology developed by Viggiano et al. to propose a fully consistent stochastic picture. We finally derive analytically all statistical quantities in a continuous setup and develop precise and efficient numerical schemes of the corresponding periodic framework. Both exact predictions and numerical estimations of the model are compared to DNSs provided by the Johns Hopkins database.

physics.flu-dyn↗

arXiv2023

Turbulent properties of stationary flows in porous media

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.

physics.flu-dyn↗

arXiv2023

Lagrangian modeling of a non-homogeneous turbulent shear flow: Molding homogeneous and isotropic trajectories into a jet

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.

physics.flu-dyn↗

arXiv2023

Influence of the porosity pattern on the aerodynamics of a square plate

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.

physics.flu-dyn↗

arXiv2023

Path instabilities and drag in the settling of single spheres

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 ($Γ$) and Galileo number ($\mathrm{Ga}$), with $Γ\in (1.1, 7.9)$ 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 $Γ$ are varied. Numerically predicted regimes such as Vertical Periodic and Planar Rotating were validated at high $Γ$ 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 $Re_p$.

physics.flu-dyn↗

arXiv2022

Entrainment, diffusion and effective compressibility in a self-similar turbulent jet

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, $\langle \boldsymbol{U_φ} \rangle$, 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 $\boldsymbol{\nabla \cdot} \langle \boldsymbol{U_φ} \rangle \neq 0$ 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 $ν_T$) to entrainment. This results in new practical relations to experimentally determine the non-uniform spatial profiles of $K_T$ and $ν_T$ (and hence of the turbulent Prandtl number $σ_T = ν_T/K_T$) 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.

physics.flu-dyn↗

arXiv2021

Broken mirror symmetry of tracer's trajectories in turbulence

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.

physics.flu-dyn↗

arXiv2021

Mixing and unmixing induced by active camphor particles

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.

physics.flu-dyn↗

arXiv2020

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 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.

physics.flu-dyn↗

arXiv2020

Inertial drag-out problem : sheets and films on a rotating disc

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.

physics.flu-dyn↗

arXiv2020

Preferential concentration of free-falling heavy particles in turbulence

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.

physics.flu-dyn↗

arXiv2020

Analysis of the dissipative range of the energy spectrum in grid turbulence and in direct numerical simulations

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 $α= 0.68 \pm 0.19$. This result corroborates previous DNS studies which found that the spectrum in the near-dissipative range is best modeled by a stretched exponential with $α<1$. Moreover, we here give an estimate for the actual value of $α$, which turns out to be in precise agreement with the theoretical prediction $α=2/3$ from the non-perturbative renormalisation group.

physics.flu-dyn↗

arXiv2019

Pair dispersion in inhomogeneous turbulent thermal convection

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-Bénard 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.

physics.flu-dyn↗

arXiv2019

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

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.

cond-mat.soft↗

arXiv2018

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 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 $\text{Re}_λ$ 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 ($\propto τ^2$), while at larger times, it approaches the diffusive regime where MSD $\propto τ$. 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-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.

physics.flu-dyn↗

arXiv2018

Relative dispersion of particle pairs in turbulent channel flow

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 $Δ_{ij}$ is also presented and particularly the sign and time evolution of the cross-term $Δ_{xy}$ 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.

physics.flu-dyn↗