arXiv subjects

Jeremie Bec

Publications and source records attributed to Jeremie Bec.

At least 19 recordsLinked to original sources

arXiv2026

Contrasting Eulerian and Lagrangian organization of turbulent dissipation

The dissipation of turbulent kinetic energy is conventionally attributed to a scale-invariant spatial multiplicative cascade, with Lagrangian statistics inferred through bridge relations. Direct numerical simulations with tracers reveal instead that Eulerian coarse-grained dissipation has a squared-logarithmic cascade depth and scale-dependent multipliers, whereas time-averaged dissipation along trajectories displays multifractal scaling and an approximately scale-invariant temporal cascade. The classical bridge fails at the level of individual trajectories. Eulerian multipliers nevertheless possess a multifractal organization whose accumulation accounts for the squared-logarithmic spatial statistics. This contrast motivates a material-inheritance picture in which Eulerian dissipation statistics reflect the spatial assembly, deformation, and mixing of distinct Lagrangian histories. The results therefore distinguish the temporal cascade organization revealed along fluid trajectories from the non-stationary spatial refinement observed in the Eulerian frame.

physics.flu-dyn↗

arXiv2026

Long rigid fibres in a turbulent channel flow: comparison between experiments and simulations

The dynamics of long rigid fibres transported by turbulent channel flow are investigated experimentally and numerically. Experiments use polystyrene fibres of three lengths, $\ell/h=0.25$, $0.5$ and $1$, with moderate inertia, $St^+\approx20$. Their settling velocity is comparable to the friction velocity, causing accumulation near the bottom wall. Measurements are compared systematically with simulations based on a rigid slender-body model. Statistics conditioned on the distance from the wall are used to characterise the effects of fibre length and confinement on translation, orientation and tumbling. Away from the wall, the experimental fibres lag the fluid, with no clear dependence of the velocity deficit on length. Near the wall, the shortest fibres move faster than the local mean flow, whereas longer fibres remain slower, indicating length-dependent sampling of near-wall turbulence. Confinement also strongly constrains orientation and rotation. Fibres close to the wall predominantly undergo "kayaking" motion, tumbling in planes approximately parallel to it. Orientation statistics collapse when wall distance is normalised by fibre length, identifying $y^+/\ell^+$ as the relevant geometrical variable. Where fibres can acquire a significant wall-normal orientation, "pole-vaulting" events produce a local tumbling-rate maximum at $y^+\approx\ell^+/2$. Its magnitude decreases approximately as $(\ell^+)^{-2}$, consistently with a dimensional estimate based on the near-wall velocity variation sampled along the fibre. Experiments and simulations agree well for orientation and tumbling but differ more for translational velocity. The discrepancies highlight the effect of settling, finite fibre thickness and finite slip Reynolds number that are not fully represented by the model.

physics.flu-dyn↗

arXiv2023

Velocity and acceleration statistics of heavy spheroidal particles in turbulence

Non-spherical particles transported by turbulent flow have a rich dynamics that combines their translational and rotational motions. Here, the focus is on small, heavy, inertial particles with a spheroidal shape fully prescribed by their aspect ratio. Such particles undergo an anisotropic, orientation-dependent viscous drag with the carrier fluid flow whose associated torque is given by the Jeffery equations. Direct numerical simulations of homogeneous, isotropic turbulence are performed to study systematically how the translational motion of such spheroidal particles depends on their shape and size. Surprisingly, it is found that the Lagrangian statistics of both velocity and acceleration can be thoroughly described in terms of an effective Stokes number obtained as an isotropic average over angles of the particle's orientation. Corrections to the translational motion of particles due to their non-sphericity and rotation can hence be fully recast as an effective radius obtained from such a mean.

physics.flu-dyn↗

arXiv2023

Enhanced transport of flexible fibers by pole vaulting in turbulent wall-bounded flow

Long, flexible fibers transported by a turbulent channel flow sample non-linear variations of the fluid velocity along their length. As the fibers tumble and collide with the boundaries, they bounce off with an impulse that propels them toward the center of the flow, similar to pole vaulting. As a result, the fibers migrate away from the walls, leading to depleted regions near the boundaries and more concentrated regions in the bulk. These higher concentrations in the center of the channel result in a greater net flux of fibers than what was initially imposed by the fluid. This effect becomes more pronounced as fiber length increases, especially when it approaches the channel height.

physics.flu-dyn↗

arXiv2023

Steering undulatory micro-swimmers in a fluid flow through reinforcement learning

This work aims at finding optimal navigation policies for thin, deformable microswimmers that progress in a viscous fluid by propagating a sinusoidal undulation along their slender body. These active filaments are embedded in a prescribed, non-homogeneous flow, in which their swimming undulations have to compete with the drifts, strains, and deformations inflicted by the outer velocity field. Such an intricate situation, where swimming and navigation are tightly bonded, is addressed using various methods of reinforcement learning. Each swimmer has only access to restricted information on its configuration and has to select accordingly an action among a limited set. The optimisation problem then consists in finding the policy leading to the most efficient displacement in a given direction. It is found that usual methods do not converge and this pitfall is interpreted as a combined consequence of the non-Markovianity of the decision process, together with the highly chaotic nature of the dynamics, which is responsible for high variability in learning efficiencies. Still, we provide an alternative method to construct efficient policies, which is based on running several independent realisations of Q-learning. This allows the construction of a set of admissible policies whose properties can be studied in detail and compared to assess their efficiency and robustness.

physics.flu-dyn↗

arXiv2022

Stochastic model for the alignment and tumbling of rigid fibres in two-dimensional turbulent shear flow

Non-spherical particles transported by an anisotropic turbulent flow preferentially align with the mean shear and intermittently tumble when the local strain fluctuates. Such an intricate behaviour is here studied for inertialess, rod-shaped particles embedded in a two-dimensional turbulent flow with homogeneous shear. A Lagrangian stochastic model for the rods angular dynamics is introduced and compared to the results of direct numerical simulations. The model consists in superposing a short-correlated random component to the steady large-scale mean shear, and can thereby be integrated analytically. To reproduce the single-time orientation statistics obtained numerically, it is found that one has to properly account for the combined effect of the mean shear, for anisotropic velocity gradient fluctuations, and for the presence of persistent rotating structures in the flow that bias Lagrangian statistics. The model is then used to address two-time statistics. The notion of tumbling rate is extended to diffusive dynamics by introducing the stationary probability flux of the rods unfolded angle. The model is found to reproduce the long-term effects of an average shear on the mean and the variance of the fibres angular increment. Still, it does not reproduce an intricate behaviour observed in numerics for intermediate times: the unfolded angle is there very similar to a Lévy walk with distributions of increments displaying intermediate power-law tails.

cond-mat.soft↗

arXiv2022

Anomalous dissipation and spontaneous stochasticity in deterministic surface quasi-geostrophic flow

Surface quasi geostrophy (SQG) describes the two-dimensional active transport of a temperature field in a strongly stratified and rotating environment. Besides its relevance to geophysics, SQG bears formal resemblance with various flows of interest for turbulence studies, from passive scalar and Burgers to incompressible fluids in two and three dimensions. This analogy is here substantiated by considering the turbulent SQG regime emerging from deterministic and smooth initial data prescribed by the superposition of a few Fourier modes. While still unsettled in the inviscid case, the initial value problem is known to be mathematically well-posed when regularised by a small viscosity. In practice, numerics reveal that in the presence of viscosity, a turbulent regime appears in finite time, which features three of the distinctive anomalies usually observed in three-dimensional developed turbulence: (i) dissipative anomaly, (ii) multifractal scaling, and (iii) super-diffusive separation of fluid particles, both backward and forward in time. These three anomalies point towards three spontaneously broken symmetries in the vanishing viscosity limit: scale invariance, time reversal and uniqueness of the Lagrangian flow, a fascinating phenomenon that Krzysztof Gawedzki dubbed spontaneous stochasticity. In the light of Gawedzki's work on the passive scalar problem, we argue that spontaneous stochasticity and irreversibility are intertwined in SQG, and provide numerical evidence for this connection. Our numerics, though, reveal that the deterministic SQG setting only features a tempered version of spontaneous stochasticity, characterised in particular by non-universal statistics.

physics.flu-dyn↗

arXiv2020

Effect of gravitational settling on the collisions of small inertial particles with a sphere

The rate at which small inertial particles collide with a moderate-Reynolds-number spherical body is found to be strongly affected when the formers are also settling under the effect of gravity. The sedimentation of small particles indeed changes the critical Stokes number above which collisions occur. This is explained by the presence of a shielding effect caused by the unstable manifolds of a stagnation-saddle point of an effective velocity field perceived by the small particles. It is also found that there exists a secondary critical Stokes number above which no collisions occur. This is due to the fact that large-Stokes number particles settle faster, making it more difficult for the larger one to catch them up. Still, in this regime, the flow disturbances create a complicated particle distribution in the wake of the collector, sometimes allowing for collisions from the back. This can lead to collision efficiencies higher than unity at large values of the Froude number.

physics.flu-dyn↗

arXiv2018

Stretching and buckling of small elastic fibers in turbulence

Small flexible fibers in a turbulent flow are found to be most of the time as straight as stiff rods. This is due to the cooperative action of flexural rigidity and fluid stretching. However, fibers might bend and buckle when they tumble and experience a strong-enough local compressive shear. Such events are similar to an activation process, where the role of temperature is played by the inverse of Young's modulus. Numerical simulations show that buckling occurs very intermittently in time. This results from unexpected long-range Lagrangian correlations of the turbulent shear.

physics.flu-dyn↗

arXiv2016

Statistical steady state in turbulent droplet condensation

Motivated by systems in which droplets grow and shrink in a turbulence-driven supersaturation field, we investigate the problem of turbulent condensation in a general manner. Using direct numerical simulations we show that the turbulent fluctuations of the supersaturation field offer different conditions for the growth of droplets which evolve in time due to turbulent transport and mixing. Based on that, we propose a Lagrangian stochastic model for condensation and evaporation of small droplets in turbulent flows. It consists of a set of stochastic integro-differential equations for the joint evolution of the squared radius and the supersaturation along the droplet trajectories. The model has two parameters fixed by the total amount of water and the thermodynamic properties, as well as the Lagrangian integral timescale of the turbulent supersaturation. The model reproduces very well the droplet size distributions obtained from direct numerical simulations and their time evolution. A noticeable result is that, after a stage where the squared radius simply diffuses, the system converges exponentially fast to a statistical steady state independent of the initial conditions. The main mechanism involved in this convergence is a loss of memory induced by a significant number of droplets undergoing a complete evaporation before growing again. The statistical steady state is characterised by an exponential tail in the droplet mass distribution. These results reconcile those of earlier numerical studies, once these various regimes are considered.

physics.flu-dyn↗

arXiv2015

Abrupt growth of large aggregates by correlated coalescences in turbulent flow

Smoluchowski's coagulation kinetics is here shown to fail when the coalescing species are dilute and transported by a turbulent flow. The intermittent Lagrangian motion involves correlated violent events that lead to an unexpected rapid occurrence of the largest particles. This new phenomena is here quantified in terms of the anomalous scaling of turbulent three-point motion, leading to significant corrections in macroscopic processes that are critically sensitive to the early-stage emergence of large embryonic aggregates, as in planet formation or rain precipitation.

physics.flu-dyn↗

arXiv2015

Turbulence attenuation by large neutrally buoyant particles

Turbulence modulation by inertial-range-size, neutrally-buoyant particles is investigated experimentally in a von Kármán flow. Increasing the particle volume fraction $Φ_\mathrm{v}$, maintaining constant impellers Reynolds number attenuates the fluid turbulence. The inertial-range energy transfer rate decreases as $\proptoΦ_\mathrm{v}^{2/3}$, suggesting that only particles located on a surface affect the flow. Small-scale turbulent properties, such as structure functions or acceleration distribution, are unchanged. Finally, measurements hint at the existence of a transition between two different regimes occurring when the average distance between large particles is of the order of the thickness of their boundary layers.

physics.flu-dyn↗

arXiv2014

Turbulent pair dispersion as a continuous-time random walk

The phenomenology of turbulent relative dispersion is revisited. A heuristic scenario is proposed, in which pairs of tracers undergo a succession of independent ballistic separations during time intervals whose lengths fluctuate. This approach suggests that the logarithm of the distance between tracers self-averages and performs a continuous-time random walk. This leads to specific predictions for the probability distribution of separations, that differ from those obtained using scale-dependent eddy-diffusivity models (e.g. in the framework of Richardson's approach). Such predictions are tested against high-resolution simulations and shed new lights on the explosive separation between tracers.

physics.flu-dyn↗

arXiv2014

Clustering, fronts, and heat transfer in turbulent suspensions of heavy particles

Heavy inertial particles transported by a turbulent flow are shown to concentrate in the regions where an advected passive scalar, such as temperature, displays very strong front-like discontinuities. This novel effect is responsible for extremely high levels of fluctuations for the passive field sampled by the particles that impacts the heat fluxes exchanged between the particles and the surrounding fluid. Instantaneous and averaged heat fluxes are shown to follow strongly intermittent statistics and anomalous scaling laws.

physics.flu-dyn↗

arXiv2014

Gravity-driven enhancement of heavy particle clustering in turbulent flow

Heavy particles suspended in a turbulent flow settle faster than in a still fluid. This effect stems from a preferential sampling of the regions where the fluid flows downward and is quantified here as a function of the level of turbulence, of particle inertia, and of the ratio between gravity and turbulent accelerations. By using analytical methods and detailed, state-of-the-art numerical simulations, settling is shown to induce an effective horizontal two-dimensional dynamics that increases clustering and reduce relative velocities between particles. These two competing effects can either increase or decrease the geometrical collision rates between same-size particles and are crucial for realistic modeling of coalescing particles.

physics.flu-dyn↗

arXiv2013

Effective rates in dilute reaction-advection systems for the annihilation process $A + A \to \varnothing$

A dilute system of reacting particles transported by fluid flows is considered. The particles react as $A + A \to \varnothing$ with a given rate when they are within a finite radius of interaction. The system is described in terms of the joint n-point number spatial density that it is shown to obey a hierarchy of transport equations. An analytic solution is obtained in either the dilute or the long-time limit by using a Lagrangian approach where statistical averages are performed along non- reacting trajectories. In this limit, it is shown that the moments of the number of particles have an exponential decay rather than the algebraic prediction of standard mean-field approaches. The effective reaction rate is then related to Lagrangian pair statistics by a large-deviation principle. A phenomenological model is introduced to study the qualitative behavior of the effective rate as a function of the interaction length, the degree of chaoticity of the dynamics and the compressibility of the carrier flow. Exact computations, obtained via a Feynman-Kac approach, in a smooth, compressible, random delta-correlated-in-time Gaussian velocity field support the proposed heuristic approach.

nlin.CD↗

arXiv2013

Slipping motion of large neutrally-buoyant particles in turbulence

Direct numerical simulations are used to investigate the individual dynamics of large spherical particles suspended in a developed homogeneous turbulent flow. A definition of the direction of the particle motion relative to the surrounding flow is introduced and used to construct the mean fluid velocity profile around the particle. This leads to an estimate of the particle slipping velocity and its associated Reynolds number. The flow modifications due to the particle are then studied. The particle is responsible for a shadowing effect that occurs in the wake up to distances of the order of its diameter: the particle pacifies turbulent fluctuations and reduces the energy dissipation rate compared to its average value in the bulk. Dimensional arguments are presented to draw an analogy between particle effects on turbulence and wall flows. Evidence is obtained on the presence of a logarithmic sublayer at distances between the thickness of the viscous boundary layer and the particle diameter $\Dp$. Finally, asymptotic arguments are used to relate the viscous sublayer quantities to the particle size and the properties of the outer turbulence. It is shown in particular that the skin-friction Reynolds number behaves as $Re_τ\propto (\Dp/η)^{4/3}$.

physics.flu-dyn↗

arXiv2012

Sticky elastic collisions

The effects of purely elastic collisions on the dynamics of heavy inertial particles is investigated in a three-dimensional random incompressible flow. It is shown that the statistical properties of inter-particle separations and relative velocities are strongly influenced by the occurrence of sticky elastic collisions - particle pairs undergo a large number of collisions against each other during a small time interval over which, hence, they remain close to each other. A theoretical framework is provided for describing and quantifying this phenomenon and it is substantiated by numerical simulations. Furthermore, the impact of hydrodynamic interactions is discussed for such a system of colliding particles.

physics.flu-dyn↗