Concentration Of Particles In Turbulence Research Articles

Cascade Model for Planetesimal Formation by Turbulent Clustering

Abstract We use a newly developed cascade model of turbulent concentration of particles in protoplanetary nebulae to calculate several properties of interest to the formation of primitive planetesimals and to the meteorite record. The model follows, and corrects, calculations of the primary initial mass function (IMF) of planetesimals by Cuzzi et al., in which an incorrect cascade model was used. Here we use the model of Hartlep et al., which has been validated against several published numerical simulations of particle concentration in turbulence. We find that, for a range of nebula and particle properties, planetesimals may be “born big,” formed as sandpiles with diameters in the range 10–100 km, directly from freely floating particles. The IMFs have a modal nature, with a well-defined peak rather than a power-law size dependence. Predictions for the inner and outer parts of the nebula behave similarly in this regard, and observations of primitive bodies in the inner and outer nebula support such modal IMFs. Also, we present predictions of local particle concentrations on several lengthscales in which particles “commonly” find themselves, which have significance for meteoritical observations of the redox state and isotopic fractionation in regions of chondrule formation. An important difference between these results and those of Cuzzi et al. is that particle growth by sticking must proceed to a radius range of at least one to a few centimeters for the IMF and meteoritical properties to be most plausibly satisfied. That is, as far as the inner nebula goes, the predominant “particles” must be aggregates of chondrules (or chondrule-size precursors) rather than individual chondrules themselves.

From boulders to planetary systems

In this chapter, we will give a brief overview on our current theoretical understanding how planets form from the solid material in circumstellar disks in the core accretion-gas capture model. This chapter will not be as concise and complete as a review on this matter, yet will serve as an introductory text to generate interest in the subject. Students are referred to comprehensive text books and some important reviews. This chapter will discuss “dusty storms”, e.g. the dust transport in turbulent protoplanetary disks, followed by the latest model of planetesimal formation, e.g. gravoturbulent planetesimal formation, which deals with particle concentration in turbulence and N-body simulations thereof. We also briefly describe the core accretion-gas capture process and talk about nascent planets, e.g. the observability of planet–disk interaction concluding with the migration of young planets and the final arrangement of planetary systems.

Heavy Particle Concentration in Turbulence at Dissipative and Inertial Scales

Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles form fractal clusters with properties independent of the Reynolds number. Clustering is there optimal when the particle response time is of the order of the Kolmogorov time scale tau(eta). In the inertial range, the particle distribution is no longer scale invariant. It is, however, shown that deviations from uniformity depend on a rescaled contraction rate, which is different from the local Stokes number given by dimensional analysis. Particle distribution is characterized by voids spanning all scales of the turbulent flow; their signature in the coarse-grained mass probability distribution is an algebraic behavior at small densities.