arXiv subjects

Jean-Régis Angilella

Publications and source records attributed to Jean-Régis Angilella.

8 recordsLinked to original sources

arXiv2026

Particle trapping in vortex crystals

We study the motion of inertial particles in two-dimensional inviscid and viscous vortex crystals, where vortices are placed at the tips of a regular polygon, and determine the conditions under which long-term trapping of particles can occur. In crystals with a central vortex, we find that trapping points in addition to those found in a previous analysis may exist finding, furthermore, that particle trajectories may approach a limit-cycle which can be described by means of asymptotic methods. We show that these newly discovered fixed points persist temporarily in the presence of viscosity, and study the different transitions following viscous vortex mergers. We find that for moderate Reynolds numbers, the annular merger of the vortex crystal form an annular vortex layer that can keep particles trapped within a disk centered at the origin. For larger Reynolds numbers, pairwise vortex merger leads to crystals with a smaller number of vortices, with particles clustering at the fixed points of the newly formed vortex crystal.

physics.flu-dyn↗

arXiv2024

Mass crystals and cage effect in vorticity crystals

We study the motion of tiny heavy inertial particles advected by a two dimensional inviscid fluid flow composed of $N$ identical point vortices regularly placed on a ring, and forming a crystal. In the limit of weak particle inertia, we show asymptotically that, in the reference frame of the crystal, inertial particles have $N$ asymptotically stable equilibrium positions located outside the crystal, in agreement with numerical observations by Ravichandran et al. (Sadhana 42, 2017). In addition to these "satellite" attracting points, we observe that for $N \ge 3$ the center of the ring, though degenerate, is a stable equilibrium position for inertial particles. This creates a kind of cage effect, where inclusions slowly drift towards the center under the effect of the surrounding vortices. This cage effect is observed to persist even at larger Stokes numbers, in contrast with the satellite attracting points that vanish when the Stokes number is above some critical value.

physics.flu-dyn↗

arXiv2024

Chaotic advection in a steady three-dimensional MHD flow

We investigate the 3D stationary flow of a weakly conducting fluid in a cubic cavity, driven by the Lorentz force created by two permanent magnets and a weak constant current. Our goal is to determine the conditions leading to efficient mixing within the cavity. The flow is composed of a large recirculation cell created by one side magnet, superposed to two recirculation cells created by a central magnet perpendicular to the first one. The overall structure of this flow, obtained here by solving the Stokes equations with Lorentz forcing, is similar to the tri-cellular model flow studied by Toussaint et. al. (Phys. Fluids. 7, 1995). Chaotic advection in this flow is analyzed by means of Poincar\'e sections, Lyapunov exponents and expansion entropies. In addition, we quantify the quality of mixing by computing contamination rates, homogeneity, as well as mixing times. Though individual vortices have poor mixing properties, the superposition of both flows creates chaotic streamlines and efficient mixing.

physics.flu-dyn↗

arXiv2020

Separatrix crossing due to multiplicative colored noise

The effect of weak multiplicative colored noise on the dynamics of a Hamiltonian system is studied by means of asymptotic methods, in the vicinity of homoclinic or heteroclinic trajectories. A general expression for the probability of noise-induced separatrix crossing is obtained, and is illustrated by means of a two-well Duffing oscillator. It shows how weak noise can significantly affect the dynamics near separatrices. In addition, the influence of the degree of non-linearity of the noise amplitude is discussed.

nlin.CD↗

arXiv2019

Probability of noise-induced separatrix crossing for inertial particles in flows

The motion of weakly inertial Brownian particles, transported by steady two-dimensional fluid flows, is investigated by means of asymptotic methods. We focus on the phenomenon of noise-induced separatrix crossing, which can force particles to enter or exit recirculation cells in an unpredictable manner. An analytical expression for the probability of separatrix crossing is obtained. It can be applied to a wide variety of flows, provided some elementary kinematical quantities of the fluid flow are known. It does not require to solve particle trajectories.

physics.flu-dyn↗

arXiv2019

The effect of colored noise on heteroclinic orbits

The dynamics of a weakly dissipative Hamiltonian system submitted to stochastic perturbations has been investigated by means of asymptotic methods. The probability of noise-induced separatrix crossing, which drastically changes the fate of the system, is derived analytically in the case where noise is an additive Kubo-Anderson process. This theory shows how the geometry of the separatrix, as well as the noise intensity and correlation time, affect the statistics of crossing. Results can be applied to a wide variety of systems, and are valid in the limit where the noise correlation time scale is much smaller than the time scale of the undisturbed Hamiltonian dynamics.

physics.class-ph↗

arXiv2016

Chaotic sedimentation of particle pairs in a vertical channel at low Reynolds number: multiple states and routes to chaos

The sedimentation of a pair of rigid circular particles in a two-dimensional vertical channel containing a Newtonian fluid is investigated numerically, for terminal particle Reynolds numbers ranging from 1 to 10, and for a confinement ratio equal to 4. While it is widely admitted that sufficiently inertial pairs should sediment by performing a regular DKT oscillation (Drafting-Kissing-Tumbling), the present analysis shows in contrast that a chaotic regime can also exist for such particles, leading to a much slower sedimentation velocity. It consists of a nearly horizontal pair, corresponding to a maximum effective blockage ratio, and performing a quasiperiodic transition to chaos under increasing the particle weight. For less inertial regimes, the classical oblique doublet structure and its complex behavior (multiple stable states and hysteresis, period-doubling cascade and chaotic attractor) are recovered, in agreement with previous work [Aidun & Ding, Physics of Fluids 15(6), 2003]. As a consequence of these various behaviors, the link between the terminal Reynolds number and the non-dimensional driving force is complex: it contains several branches displaying hysteresis as well as various bifurcations. For the range of Reynolds number considered here, a global bifurcation diagram is given.

physics.flu-dyn↗

arXiv2016

Critical Stokes number for the capture of inertial particles by recirculation cells in 2D quasi-steady flows

Inertial particles are often observed to be trapped, temporarily or permanently, by recirculation cells which are ubiquitous in natural or industrial flows. In the limit of small particle inertia, determining the conditions of trapping is a challenging task, as it requires a large number of numerical simulations or experiments to test various particle sizes or densities. Here, we investigate this phenomenon analytically and numerically in the case of heavy particles (e.g. aerosols) at low Reynolds number, to derive a trapping criterion that can be used both in analytical and numerical velocity fields. The resulting criterion allows to predict the characteristics of trapped particles as soon as single-phase simulations of the flow are performed. Our analysis is valid for two-dimensional particle-laden flows in the vertical plane, in the limit where the particle inertia, the free-fall terminal velocity, and the flow unsteadiness can be treated as perturbations. The weak unsteadiness of the flow generally induces a chaotic tangle near heteroclinic or homoclinic cycles if any, leading to the apparent diffusion of fluid elements through the boundary of the cell. The critical particle Stokes number Stc below which aerosols also enter and exit the cell in a complex manner has been derived analytically, in terms of the flow characteristics. It involves the non-dimensional curvature-weighted integral of the squared velocity of the steady fluid flow along the dividing streamline of the recirculation cell. When the flow is unsteady and St > Stc, a regular motion takes place due to gravity and centrifugal effects, like in the steady case. Particles driven towards the interior of the cell are trapped permanently. In contrast, when the flow is unsteady and St < Stc, particles wander in a chaotic manner in the vicinity of the border of the cell, and can escape the cell.

physics.flu-dyn↗