arXiv subjects

Jérémie Bec

Publications and source records attributed to Jérémie Bec.

18 recordsLinked to original sources

arXiv2025

Harnessing swarms for directed migration of interacting active particles via optimal global control

This study investigates the use of global control strategies to enhance the directed migration of swarms of interacting self-propelled particles confined in a channel. Uncontrolled dynamics naturally leads to wall accumulation, clogging, and band formation due to the interplay between self-organization and confinement. This work explores whether a uniform global control, such as magnetic field acting on all particles, can optimize collective transport. Using a discrete Vicsek-like model, it is found that simple global alignment controls, optimized via reinforcement learning, efficiently suppress unfavorable configurations and significantly increase the net particle flux along a prescribed channel direction. These results highlight that coarse, system-level observations are sufficient to achieve near-optimal control, even in regimes with strong fluctuations or partial ordering.

cond-mat.soft↗

arXiv2025

Surface quasigeostrophic turbulence: The refined study of an active scalar

SQG describes the 2D active transport of a scalar field, such as temperature, which -- when properly rescaled -- shares the same physical dimension of length/time as the advecting velocity field. This duality has motivated analogies with 3D turbulence. In particular, the Kraichnan-Leith-Batchelor similarity theory predicts a Kolmogorov-type inertial range scaling $\propto (\varepsilon \ell)^{1/3}$ for both scalar and velocity fields, and the presence of intermittency was pointed out by Sukhatme & Pierrehumbert ($Chaos$ $\boldsymbol{12}$, 439, 2002) in unforced settings. In this work, we refine these analogies using simulations up to $16,384^2$ collocation points in a steady-state regime dominated by the direct cascade of scalar variance. We show that mixed structure functions, linking velocity increments with powers of scalar differences, exhibit clear scaling, revealing the role of anomalous fluxes of all the scalar moments. However, the usual (unmixed) structure functions do no follow any power-law scaling in any range of scales, neither for the velocity nor for the scalar increments. This specific form of the intermittency phenomenon reflects the specific kinematic properties of SQG turbulence, involving the interplay between long-range interactions, structures and geometry. Revealing the multiscaling in single-field statistics requires to resort to generalised notions of scale invariance, such as extended self-similarity and specific form of refined self-similarity. Our findings emphasise the fundamental entanglement of scalar and velocity fields in SQG turbulence: They evolve hand in hand and any attempt to isolate them destroys scaling in its usual sense. This perspective sheds new lights on the discrepancies in spectra and structure functions, that have been repeatedly observed in SQG numerics for the past 20 years.

physics.flu-dyn↗

arXiv2024

Effects of collective patterns, confinement, and fluid flow on active particle transport

The self-organization of active particles on a two-dimensional single-occupancy lattice is investigated, with an emphasis on the effects of boundary confinement and the influence of an external mean fluid flow. The study examines collective behaviors, particularly the transition from a disordered phase to the formation of orientationally ordered patterns, and their impact on particle transport and flux. In the absence of fluid flow, confinement causes particles to accumulate near the walls, leading to clogs or obstructions that hinder movement, or to the formation of bands aligned with the channel. Although these bands limit the particles ability to freely self-propel, they still result in a net flux along the channel. The introduction of an external Poiseuille fluid flow induces vorticity, shifts the phase transition to higher alignment sensitivities, and promotes particle clustering at the channel center, significantly enhancing overall flux.

cond-mat.soft↗

arXiv2024

Homogeneous turbophoresis of heavy inertial particles in turbulent flow

Heavy particles suspended in turbulent flow possess inertia and are ejected from violent vortical structures by centrifugal forces. Once piled up along particle paths, this small-scale mechanism leads to an effective large-scale drift. This phenomenon, known as turbophoresis, causes particles to leave highly turbulent regions and migrate towards calmer regions, explaining why particles transported by non-homogeneous flows tend to concentrate near the minima of turbulent kinetic energy. It is demonstrated here that turbophoretic effects are just as crucial in statistically homogeneous flows. Although the average turbulent activity is uniform, instantaneous spatial fluctuations are responsible for inertial-range inhomogeneities in the particle distribution. Direct numerical simulations are used to probe particle accelerations, specifically how they correlate to local turbulent activity, yielding an effective coarse-grained dynamics that accounts for particle detachment from the fluid and ejection from excited regions through a space and time-dependent non-Fickian diffusion. This leads to cast fluctuations in particle distributions in terms of a scale-dependent Péclet number $Pe_l$, which measures the importance of turbulent advection compared with inertial turbophoresis at a given scale $l$. Multifractal statistics of energy dissipation indicate that $Pe_l \sim l^δ/τ_{\rm p}$ with $δ\approx 0.84$. Numerical simulations support this behaviour and emphasises the relevance of the turbophoretic Péclet number in characterising how particle distributions, including their radial distribution function, depends on $l$. This approach also explains the presence of voids with inertial-range sizes, and the fact that their volumes has a non-trivial distribution with a power-law tail $p(V) \propto V^{-α}$, with an exponent $α$ that tends to 2 as $Pe_l\to0$.

physics.flu-dyn↗

arXiv2024

Reduction of dust radial drift by turbulence in protoplanetary disks

Dust particles in protoplanetary disks, lacking support from pressure, rotate at velocities exceeding those of the surrounding gas. Consequently, they experience a head-wind from the gas that drives them toward the central star. Radial drift occurs on timescales much shorter than those inferred from disk observations or those required for dust to aggregate and form planets. Additionally, turbulence is often assumed to amplify the radial drift of dust in planet-forming disks when modeled through an effective viscous transport. However, the local interactions between turbulent eddies and particles are known to be significantly more intricate than in a viscous fluid. Our objective is to elucidate and characterize the dynamic effects of Keplerian turbulence on the mean radial and azimuthal velocities of dust particles. We employ 2D shearing-box incompressible simulations of the gas, which is maintained in a developed turbulent state while rotating at a sub-Keplerian speed. Dust is modeled as Lagrangian particles set at a Keplerian velocity, therefore experiencing a radial force toward the star through drag. Turbulent eddies are found to reduce the radial drift, while simultaneously enhancing the azimuthal velocities of small particles. This dynamic behavior arises from the modification of dust trajectories due to turbulent eddies.

astro-ph.EP↗

arXiv2023

Clusters of heavy particles in two-dimensional Keplerian turbulence

Protoplanetary disks are gaseous systems in Keplerian rotation around young stars, known to be turbulent. They include a small fraction of dust from which planets form. In the incremental scenario for planet growth, the formation of kilometer-size objects (planetesimals) from pebbles is a major open question. Clustering of particles is necessary for solids to undergo a local gravitational collapse. To address this question, the dynamic of inertial particles in turbulent flows with Keplerian rotation and shear is studied. Two-dimensional direct numerical simulations are performed to explore systematically two physical parameters: the rotation rate, which depends on the distance to the star, and the particle response time, which relates to their size. Shear is found to drastically affect the characteristics of the turbulent flow destroying cyclones and favoring the survival of anticyclones. Faster Keplerian rotation enhances clustering of particles. For intermediate sizes, particles concentrate in anticyclones. These clusters form in a hierarchical manner and merge together with time. For other parameter values, solids concentrate on fractal sets that get more singular with rotation. The mass distribution of particles is then found to be multifractal with small dimensions at large orders, intriguing for triggering their gravitational collapse. Such results are promising for a precise description and better understanding of planetesimal formation.

astro-ph.EP↗

arXiv2021

Machine learning strategies for path-planning microswimmers in turbulent flows

We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D). We show that this scheme allows microswimmers to find non-trivial paths, which enable them to reach a target on average in less time than a naive microswimmer, which tries, at any instant of time and at a given position in space, to swim in the direction of the target. We use pseudospectral direct numerical simulations (DNSs) of the 2D and 3D (incompressible) Navier-Stokes equations to obtain the turbulent flows. We then introduce passive microswimmers that try to swim along a given direction in these flows; the microswimmers do not affect the flow, but they are advected by it.

physics.flu-dyn↗

arXiv2020

From the butterfly effect to intrinsic randomness: the spontaneous growth of singular shear flows

The butterfly effect is today commonly identified with the sensitive dependence of deterministic chaotic systems upon initial conditions. However, this is only one facet of the notion of unpredictability pioneered by Lorenz, who actually predicted that multiscale fluid flows could spontaneously lose their deterministic nature and become intrinsically random. This effect, which is radically different from chaos, have remained out of reach for detailed physical observations. Here, we substantiate this scenario by showing that it is inherent to the elementary Kelvin--Helmholtz hydrodynamical instability of an initially singular shear layer. We moreover provide evidence that the resulting macroscopic flow displays universal statistical properties that are triggered by, but independent of specific physical properties at micro-scales. This spontaneous stochasticity is interpreted as an Eulerian counterpart to Richardson's relative dispersion of Lagrangian particles, giving substance to the intrinsic nature of randomness in turbulence.

physics.flu-dyn↗

arXiv2019

Dynamics and fragmentation of small inextensible fibers in turbulence

The fragmentation of small, brittle, flexible, inextensible fibers is investigated in a fully-developed, homogeneous, isotropic turbulent flow. Such small fibers spend most of their time fully stretched and their dynamics follows that of stiff rods. They can then break through tensile failure, i.e. when the tension is higher than a given threshold. Fibers bend when experiencing a strong compression. During these rare and intermittent buckling events, they can break under flexural failure, i.e. when the curvature exceeds a threshold. Fine-scale massive simulations of both the fluid flow and the fiber dynamics are performed to provide statistics on these two fragmentation processes. This gives ingredients for the development of accurate macroscopic models, namely the fragmentation rate and daughter-size distributions, which can be used to predict the time evolution of the fiber size distribution. Evidence is provided for the generic nature of turbulent fragmentation and of the resulting population dynamics. It is indeed shown that the statistics of breakup is fully determined by the probability distribution of Lagrangian fluid velocity gradients. This approach singles out that the only relevant dimensionless parameter is a local flexibility which balances flow stretching to the fiber elastic forces.

cond-mat.soft↗

arXiv2019

Turbulence of generalised flows in two dimensions

This paper discusses the generalised least-action principle introduced by Brenier (J. Am. Math. Soc, 1989), from the perspective of turbulence modelling. In essence, Brenier's least-action principle extends to a probabilistic setting Arnold's geometric interpretation of ideal fluid mechanics, whereby strong solutions to the Euler equations are deduced from minimising an action over Lagrangian maps. While Arnold's framework relies on the deterministic concept of Lagrangian flow, Brenier's least-action principle describes solutions to the Euler equations in terms of non-deterministic "generalised flows", namely probability measures over sets of Lagrangian trajectories. Generalised flows seem naturally fit to describe turbulent Lagrangian trajectories in terms of stochastic processes, an approach that originates from Richardson's seminal work on turbulent dispersion. In particular, they seem suited to address cases when the concept of Lagrangian flow breaks down, due to Lagrangian trajectories becoming spontaneously stochastic. The purpose of the present paper is therefore to give a physical perspective on Brenier's principle, and provide a qualitative description of the hydrodynamical features of generalised flows. Using Monte-Carlo techniques, we analyse the statistical features of three classes of two-dimensional generalised flows, ranging from solid rotation and cellular flows to to freely decaying two-dimensional turbulence. Our results suggest that generalised variational formulations, if carefully used, may provide new tools to coarse-grain multi-scale hydrodynamics.

physics.flu-dyn↗

arXiv2018

Tumbling dynamics of inertial chains in extensional flow

The dynamics of elongated inertial particles in an extensional flow is studied numerically by performing simulations of freely jointed bead-rod chains. The coil-stretch transition and the tumbling instability are characterized as a function of three parameters: The Peclet number, the Stokes number and the chain length. Numerical results show that in the limit of infinite chain length, particles are trapped in a coiled or stretched state. The coil-stretch transition is also shown to depend non-linearly on the Stokes and Peclet number. Results also reveal that tumbling occurs close to the coil-stretch transition and that the persistence time is a non-linear function of Stokes and Peclet numbers.

physics.flu-dyn↗

arXiv2017

Inelastic accretion of inertial particles by a towed sphere

The problem of accretion of small particles by a sphere embedded in a mean flow is studied in the case where the particles undergo inelastic collisions with the solid object. The collision efficiency, which gives the flux of particles experiencing at least one bounce on the sphere, is found to depend upon the sphere Reynolds number only through the value of the critical Stokes number below which no collision occurs. In the absence of molecular diffusion, it is demonstrated that multiple bounces do not provide enough energy dissipation for the particles to stick to the surface within a finite time. This excludes the possibility of any kind of inelastic collapse, so that determining an accretion efficiency requires modelling more precisely particle-surface microphysical interactions. A straightforward choice is to assume that the particles stick when their kinetic energy at impact is below a threshold. In this view, numerical simulations are performed in order to describe the statistics of impact velocities at various values of the Reynolds number. Successive bounces are shown to enhance accretion. These results are put together in order to provide a general qualitative picture on how the accretion efficiency depends upon the non dimensional parameters of the problem.

physics.flu-dyn↗

arXiv2017

Dusty turbulence

The feedback forces exerted by particles suspended in a turbulent flow is shown to lead to a new scaling law for velocity fluctuations associated to a power-spectra $\propto k^{-2}$. The mechanism at play relies on a direct transfer of kinetic energy to small scales through Kelvin--Helmholtz instabilities occurring in regions of high particle density contrast. This finding is confirmed by two-dimensional direct numerical simulations.

physics.flu-dyn↗

arXiv2016

Extreme fluctuations of the relative velocities between droplets in turbulent airflow

We compare experiments and direct numerical simulations to evaluate the accuracy of the Stokes-drag model, which is used widely in studies of inertial particles in turbulence. We focus on statistics at the dissipation scale and on extreme values of relative particle velocities for moderately inertial particles (St < 1). The probability distributions of relative velocities in the simulations were qualitatively similar to those in the experiments. The agreement improved with increasing Stokes number and decreasing relative velocity. Simulations underestimated the probability of extreme events, which suggests that the Stokes drag model misses important dynamics. Nevertheless, the scaling behavior of the extreme events in both the experiments and the simulations can be captured by the same multi-fractal model.

physics.flu-dyn↗

arXiv2015

A lattice model for the Eulerian description of heavy particle suspensions

Modeling dispersed solid phases in fluids still represents a computational challenge when considering a small-scale coupling in wide systems, such as the atmosphere or industrial processes at high Reynolds numbers. A numerical method is here introduced for simulating the dynamics of diffusive heavy inertial particles in turbulent flows. The approach is based on the position/velocity phase-space particle distribution. The discretization of velocities is inspired from lattice Boltzmann methods and is chosen to match discrete displacements between two time steps. For each spatial position, the time evolution of particles momentum is approximated by a finite-volume approach. The proposed method is tested for particles experiencing a Stokes viscous drag with a prescribed fluid velocity field in one dimension using a random flow, and in two dimensions with the solution to the forced incompressible Navier-Stokes equations. Results show good agreements between Lagrangian and Eulerian dynamics for both spatial clustering and the dispersion in particle velocities. This demonstrates the suitability of the proposed approach at large Stokes numbers or for situations where details of collision processes are important.

physics.flu-dyn↗

arXiv2015

Concentrations of inertial particles in the turbulent wake of an immobile sphere

Direct numerical simulations are used to study the interaction of a stream of small heavy inertial particles with the laminar and turbulent wakes of an immobile sphere facing an incompressible uniform inflow. Particles that do not collide with the obstacle but move past it, are found to form preferential concentrations both in the sphere boundary layer and in its wake. In the laminar case, the upstream diverging flow pattern is responsible for particle clustering on a cylinder that extends far downstream the sphere. The interior of this surface contains no particles and can be seen as a shadow of the large obstacle. Such concentration profiles are also present in the case of turbulent wakes but show a finite extension. The sphere shadow is followed by a region around the axis of symmetry where the concentration is higher than the average. It originates from a resonant centrifugal expulsion of particles from shed vortices. The consequence of this concentration mechanism on monodisperse inter-particle collisions is also briefly discussed. They are enhanced by both the increased concentration and the presence of large velocity differences between particles in the wake.

physics.flu-dyn↗

arXiv2013

Effect of turbulent fluctuations on the drag and lift forces on a towed sphere and its boundary layer

The impact of turbulent fluctuations on the forces exerted by a fluid on a towed spherical particle is investigated by means of high-resolution direct numerical simulations. The measurements are carried out using a novel scheme to integrate the two-way coupling between the particle and the incompressible surrounding fluid flow maintained in a high-Reynolds-number turbulent regime. The main idea consists in combining a Fourier pseudo-spectral method for the fluid with an immersed-boundary technique to impose the no-slip boundary condition on the surface of the particle. Benchmarking of the code shows a good agreement with experimental and numerical measurements from other groups. A study of the turbulent wake downstream the sphere is also reported. The mean velocity deficit is shown to behave as the inverse of the distance from the particle, as predicted from classical similarity analysis. This law is reinterpreted in terms of the principle of "permanence of large eddies" that relates infrared asymptotic self-similarity to the law of decay of energy in homogeneous turbulence. The developed method is then used to attack the problem of an upstream flow that is in a developed turbulent regime. It is shown that the average drag force increases as a function of the turbulent intensity and the particle Reynolds number. This increase is significantly larger than predicted by standard drag correlations based on laminar upstream flows. It is found that the relevant parameter is the ratio of the viscous boundary layer thickness to the dissipation scale of the ambient turbulent flow. The drag enhancement can be motivated by the modification of the mean velocity and pressure profile around the sphere by small scale turbulent fluctuations.

physics.flu-dyn↗

arXiv2012

Timescales of Turbulent Relative Dispersion

Tracers in a turbulent flow separate according to the celebrated $t^{3/2}$ Richardson--Obukhov law, which is usually explained by a scale-dependent effective diffusivity. Here, supported by state-of-the-art numerics, we revisit this argument. The Lagrangian correlation time of velocity differences is found to increase too quickly for validating this approach, but acceleration differences decorrelate on dissipative timescales. This results in an asymptotic diffusion $\propto t^{1/2}$ of velocity differences, so that the long-time behavior of distances is that of the integral of Brownian motion. The time of convergence to this regime is shown to be that of deviations from Batchelor's initial ballistic regime, given by a scale-dependent energy dissipation time rather than the usual turnover time. It is finally argued that the fluid flow intermittency should not affect this long-time behavior of relative

physics.flu-dyn↗