Chaotic saddles in a gravitational field: The case of inertial particles in finite domains

Drótos, Gábor; Tél, Tamás

doi:10.1103/physreve.83.056203

Cited by 6 publications

(5 citation statements)

References 38 publications

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“…The initially columnar shape is deformed into a Gaussian one that spreads as its center moves downwards. This behavior was also observed in a simple cloud model with aerosol particles (Drótos and Tél, 2011). It is remarkable, however, that after the center of the Gaussian distribution reaches the surface, and the majority of the particles is deposited, the small fraction of particles remaining aloft is distributed widely in the different layers.…”

Section: A Case Studysupporting

confidence: 60%

Escape rate: a Lagrangian measure of particle deposition from the atmosphere

Haszpra

Tél

2013

Nonlin. Processes Geophys.

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Abstract. Due to rising or descending air and due to gravity, aerosol particles carry out a complicated, chaotic motion and move downwards on average. We simulate the motion of aerosol particles with an atmospheric dispersion model called the Real Particle Lagrangian Trajectory (RePLaT) model, i.e., by solving Newton's equation and by taking into account the impacts of precipitation and turbulent diffusion where necessary, particularly in the planetary boundary layer. Particles reaching the surface are considered to have escaped from the atmosphere. The number of non-escaped particles decreases with time. The short-term and long-term decay are found to be exponential and are characterized by escape rates. The reciprocal values of the short-term and long-term escape rates provide estimates of the average residence time of typical particles, and of exceptional ones that become convected or remain in the free atmosphere for an extremely long time, respectively. The escape rates of particles of different sizes are determined and found to vary in a broad range. The increase is roughly exponential with the particle size. These investigations provide a Lagrangian foundation for the concept of deposition rates.

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Section: A Case Studysupporting

confidence: 60%

Escape rate: a Lagrangian measure of particle deposition from the atmosphere

Haszpra

Tél

2013

Nonlin. Processes Geophys.

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“…In the same vein, particle collisions, which were neglected in the present study, are known to influence the trapping process [40,61]. In addition, it would be interesting to consider particles with density comparable with the fluid density and investigate the effect of the Boussinesq-Basset, added-mass, and lift forces on the trapping process (see, for example, [16], [51], [17], and [19]). Such an extended analysis of inertial particle dynamics is among the topics for future exploration that we hope our results will encourage researchers to pursue.…”

Section: Discussionmentioning

confidence: 95%

Inertial particle trapping in an open vortical flow

Angilella¹,

Vilela

Motter

2014

J. Fluid Mech.

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Recent numerical results on advection dynamics have shown that particles denser than the fluid can remain trapped indefinitely in a bounded region of an open fluid flow. Here, we investigate this counterintuitive phenomenon both numerically and analytically to establish the conditions under which the underlying particle-trapping attractors can form. We focus on a two-dimensional open flow composed of a pair of vortices and its specular image, which is a system we represent as a vortex pair plus a wall along the symmetry line. Considering particles that are much denser than the fluid, we show that two point attractors form in the neighborhood of the vortex pair provided that the particle Stokes number is smaller than a critical value of order unity. In the absence of the wall, the boundaries of the basins of the attracting points are smooth. When the wall is present, the point attractors describe counter-rotating ellipses in this frame, with a period equal to half the period of one isolated vortex pair. However, their boundaries are shown to become fractal if the distance to the wall is smaller than a critical distance that scales with the inverse square root of the Stokes number. This transformation is related to the breakdown of a separatrix that gives rise to a heteroclinic tangle close to the vortices, which we describe using a Melnikov function. For an even smaller distance to the wall, we demonstrate that a second separatrix breaks down and a new heteroclinic tangle forms farther away from the vortices. Particles released in the open part of the flow can approach the attractors and be trapped permanently provided that they cross the two separatrices. Furthermore, the trapping of heavy particles from the open flow is shown to be robust to the presence of gravity, viscosity, and noise

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“…For clarity, we choose this velocity field to have zero mean integrated over space. Note, however, that as long as the spatial distribution of the particles is inhomogeneous, the vertical velocity averaged over all particles will be different from −W due to the inhomogeneities of the velocity field 27 .…”

Section: A Model Flowmentioning

confidence: 99%

Inhomogeneities and caustics in the sedimentation of noninertial particles in incompressible flows

Drótos

Monroy

Hernández-Garcı́a

et al. 2019

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In an incompressible flow, fluid density remains invariant along fluid element trajectories. This implies that the spatial distribution of non-interacting noninertial particles in such flows cannot develop density inhomogeneities beyond those that are already introduced in the initial condition. However, in certain practical situations, density is measured or accumulated on (hyper-) surfaces of dimensionality lower than the full dimensionality of the flow in which the particles move. An example is the observation of particle distributions sedimented on the floor of the ocean. In such cases, even if the initial distribution of noninertial particles is uniform within a finite support in an incompressible flow, advection in the flow will give rise to inhomogeneities in the observed density. In this paper we analytically derive, in the framework of an initially homogeneous particle sheet sedimenting towards a bottom surface, the relationship between the geometry of the flow and the emerging distribution. From a physical point of view, we identify the two processes that generate inhomogeneities to be the stretching within the sheet, and the projection of the deformed sheet onto the target surface. We point out that an extreme form of inhomogeneity, caustics, can develop for sheets. We exemplify our geometrical results with simulations of particle advection in a simple kinematic flow, study the dependence on various parameters involved, and illustrate that the basic mechanisms work similarly if the initial (homogeneous) distribution occupies a more general region of finite extension rather than a sheet. a) gabor@ifisc.uib-csic.es 1 Sedimentation of small particles in complex flows is an outstanding problem in science and technology. In particular, the sinking of biogenic particles from the marine surface to the bottom is a fundamental process of the biological carbon pump, playing a key role in the global carbon cycle. A complete understanding of this problem is still lacking. It has been recently shown that despite fluid incompressibility, sedimenting particles moving as noninertial particles in the ocean on large scales show density inhomogeneities when accumulated on some bottom surface. Here, we analytically derive the relation between the geometry of the flow and the emerging distribution for an initially homogeneous sheet of particles. From a physical point of view, we identify the two processes that generate inhomogeneities to be the stretching within the sheet, and the projection of the deformed sheet onto the target surface. We point out conditions under which an extreme form of inhomogeneity, caustics, can develop.

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Chaotic saddles in a gravitational field: The case of inertial particles in finite domains

Cited by 6 publications

References 38 publications

Escape rate: a Lagrangian measure of particle deposition from the atmosphere

Escape rate: a Lagrangian measure of particle deposition from the atmosphere

Inertial particle trapping in an open vortical flow

Inhomogeneities and caustics in the sedimentation of noninertial particles in incompressible flows

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