Relative velocity of inertial particles in turbulent flows

Pan, Liubin; Padoan, Paolo

doi:10.1017/s0022112010002855

Cited by 80 publications

(93 citation statements)

References 49 publications

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“…Recently, some numerical works have tested the analytically derived collision velocities and started to derive distributions of collision velocities, e.g. Carballido et al (2010); Pan and Padoan (2010); Hubbard (2012); Pan and Padoan (2013). We will come back to the treatment of grain velocities in the context of global disk models in § 4.2.…”

Section: Relative Velocitiesmentioning

confidence: 99%

Dust Evolution in Protoplanetary Disks

Testi¹,

Birnstiel²,

Ricci³

et al. 2014

Protostars and Planets VI

291

271

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In the core accretion scenario for the formation of planetary rocky cores, the first step toward planet formation is the growth of dust grains into larger and larger aggregates and eventually planetesimals. Although dust grains are thought to grow from the submicron sizes typical of interstellar dust to micron size particles in the dense regions of molecular clouds and cores, the growth from micron size particles to pebbles and kilometre size bodies must occur in the high densities reached in the mid-plane of protoplanetary disks. This critical step in the formation of planetary systems is the last stage of solids evolution that can be observed directly in young extrasolar systems before the appearance of large planetary-size bodies.Tracing the properties of dust in the disk mid-plane, where the bulk of the material for planet formation resides, requires sensitive observations at long wavelengths (sub-mm through cm waves). At these wavelengths, the observed emission can be related to the dust opacity, which in turns depend on to the grain size distribution. In recent years the upgrade of the existing (sub-)mm arrays, the start of ALMA Early Science operations and the upgrade of the VLA have significantly improved the observational constraints on models of dust evolution in protoplanetary disks. Laboratory experiments and numerical simulations led to a substantial improvement in the understanding of the physical processes of grain-grain collisions, which are the foundation for the models of dust evolution in disks.In this chapter we review the constraints on the physics of grain-grain collisions as they have emerged from laboratory experiments and numerical computations. We then review the current theoretical understanding of the global processes governing the evolution of solids in protoplanetary disks, including dust settling, growth, and radial transport. The predicted observational signatures of these processes are summarized.We discuss the recent developments in the study of grain growth in molecular cloud cores and in collapsing envelopes of protostars as these likely provide the initial conditions for the dust in protoplanetary disks. We then discuss the current observational evidence for the growth of grains in young protoplanetary disks from millimeter surveys, as well as the very recent evidence of radial variations of the dust properties in disks. We also include a brief discussion of the constraints on the small end of the grain size distribution and on dust settling as derived from optical, near-, and mid-IR observations. The observations are discussed in the context of global dust evolution models, in particular we focus on the emerging evidence for a very efficient early growth of grains in disks and the radial distribution of maximum grain sizes as the result of growth barriers in disks. We will also highlight the limits of the current models of dust evolution in disks including the need to slow the radial drift of grains to overcome the migration/fragmentation barrier.

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Section: Relative Velocitiesmentioning

confidence: 99%

Dust Evolution in Protoplanetary Disks

Testi¹,

Birnstiel²,

Ricci³

et al. 2014

Protostars and Planets VI

291

271

View full text Add to dashboard Cite

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“…The large or integral scale L, which contains the energy in this flow, is thus apparently much larger than the vertical distance of the sensor from the boundary (h = 2 m) and plausibly the same as the longitudinal integral scale given as L = 180 m [2], see also [13], thus L/⌘ ⇡ 10 5 . In cascade applications, it may be more meaningful to assess the scale dependence of p(m) at large scales not in terms of multiples of ⌘ as in [8] and most other work [e.g., 20], but in terms of fractions of L. We will also express scale fractions l/L in terms of cascade bifurcation levels N needed to achieve equidimensional volumes l on a side:…”

Section: Figmentioning

confidence: 99%

“…Theories by Zaichik and Alipchenkov [11] et seq., and Pan and Padoan [8] et seq. have been shown to be promising in explaining the cause of particle clustering in terms of history effects, with helpful contributions from the traditional local centrifugation mechanism [2,4,10,13].…”

Section: Background and Introductionmentioning

confidence: 98%

Scale dependence of multiplier distributions for particle concentration, enstrophy, and dissipation in the inertial range of homogeneous turbulence

2017

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Turbulent flows preferentially concentrate inertial particles depending on their stopping time or Stokes number, which can lead to significant spatial variations in the particle concentration. Cascade models are one way to describe this process in statistical terms. Here, we use a direct numerical simulation (DNS) dataset of homogeneous, isotropic turbulence to determine probability distribution functions (PDFs) for cascade multipliers, which determine the ratio by which a property is partitioned into sub-volumes as an eddy is envisioned to decay into smaller eddies. We present a technique for correcting effects of small particle numbers in the statistics. We determine multiplier PDFs for particle number, flow dissipation, and enstrophy, all of which are shown to be scale dependent. However, the particle multiplier PDFs collapse when scaled with an appropriately defined local Stokes number. As anticipated from earlier works, dissipation and enstrophy multiplier PDFs reach an asymptote for sufficiently small spatial scales. From the DNS measurements, we derive a cascade model that is used it to make predictions for the radial distribution function (RDF) for arbitrarily high Reynolds numbers, Re, finding good agreement with the asymptotic, infinite Re inertial range theory of Zaichik & Alipchenkov [New Journal of Physics 11, 103018 (2009)]. We discuss implications of these results for the statistical modeling of the turbulent clustering process in the inertial range for high Reynolds numbers inaccessible to numerical simulations.

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“…Thus, a fluid description for these particles would not be sufficient. The physical reason for a constant δv (St, l) at small l (for a given St) is that the relative velocity between nearby particles is dominated by their memory of the flow velocity difference they "saw" within a friction timescale in the past (Pan & Padoan 2010).…”

Section: Particles With St >mentioning

confidence: 99%

Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

Pan

Padoan

Scalo

et al. 2011

ApJ

Self Cite

120

109

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We study the clustering of inertial particles in turbulent flows and discuss its applications to dust particles in protoplanetary disks. Using numerical simulations, we compute the radial distribution function (RDF), which measures the probability of finding particle pairs at given distances, and the probability density function of the particle concentration. The clustering statistics depend on the Stokes number, St, defined as the ratio of the particle friction timescale, τ p , to the Kolmogorov timescale in the flow. In agreement with previous studies, we find that, in the dissipation range, the clustering intensity strongly peaks at St 1, and the RDF for St ∼ 1 shows a fast power-law increase toward small scales, suggesting that turbulent clustering may considerably enhance the particle collision rate. Clustering at inertial-range scales is of particular interest to the problem of planetesimal formation. At these large scales, the strongest clustering is from particles with τ p in the inertial range. Clustering of these particles occurs primarily around a scale where the eddy turnover time is ∼τ p . We find that particles of different sizes tend to cluster at different locations, leading to flat RDFs between different particles at small scales. In the presence of multiple particle sizes, the overall clustering strength decreases as the particle size distribution broadens. We discuss particle clustering in two recent models for planetesimal formation. We argue that, in the model based on turbulent clustering of chondrule-size particles, the probability of finding strong clusters that can seed planetesimals may have been significantly overestimated. We discuss various clustering mechanisms in simulations of planetesimal formation by gravitational collapse of dense clumps of meter-size particles, in particular the contribution from turbulent clustering due to the limited numerical resolution.

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Relative velocity of inertial particles in turbulent flows

Cited by 80 publications

References 49 publications

Dust Evolution in Protoplanetary Disks

Dust Evolution in Protoplanetary Disks

Scale dependence of multiplier distributions for particle concentration, enstrophy, and dissipation in the inertial range of homogeneous turbulence

Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

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