Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

Abstract

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.

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

“…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:…”

Interactions between inertial particles and shocklets in compressible turbulent flow

“…25,26 The interaction between very heavy particles and compressible turbulence has been studied by using the same model as for the incompressible case, i.e., only the Stokes drag is considered. 27,28 The detailed model for particles in a compressible flow has been developed recently. [29][30][31] It has also been shown that for certain particle parameters, the point-particle model can still be used to study the particle-shock interaction.…”

Formation of (exo–)planets

“…This is indeed the case with small scale turbulent eddies (e.g. Pan et al 2011). But if a vortex rotates slowly enough it can be in a so-called "geostrophic balance", which means that its pressure gradients are compensated by Coriolis forces.…”

“…While this model is highly appealing, it should be understood that it is based on scaling relations to extrapolate results from numerical simulations, which inherently have limited spatial resolution, to the real world, where turbulence eddies span many orders of magnitude in size. As pointed out by Pan et al (2011) these scaling relations might be too optimistic in the above papers, meaning that in reality the probabilities of spontaneous planetesimal formation might be prohibitively low. It is clear, however, that the last word is not said on this topic, and it remains an exciting possibility.…”