In this paper, a simple stochastic and physically justified procedure for modeling turbulent diffusion in a Lagrangian form was presented to determine the trajectories of individual particles in a gaseous turbulent protoplanetary disk.
Abstract:
In order to understand how the chemical and isotopic compositions of dust grains in a gaseous turbulent protoplanetary disk are altered during their journey in the disk, it is important to determine their individual trajectories. We study here the dust-diffusive transport using lagrangian numerical simulations using the the popular "turbulent diffusion" formalism. However it is naturally expressed in an Eulerian form, which does not allow the trajectories of individual particles to be studied. We present a simple stochastic and physically justified procedure for modeling turbulent diffusion in a Lagrangian form that overcomes these difficulties. We show that a net diffusive flux F of the dust appears and that it is proportional to the gas density ({\rho}) gradient and the dust diffusion coefficient Dd: (F=Dd/{\rho}\timesgrad({\rho})). It induces an inward transport of dust in the disk's midplane, while favoring outward transport in the disk's upper layers. We present tests and applications comparing dust diffusion in the midplane and upper layers as well as sample trajectories of particles with different sizes. We also discuss potential applications for cosmochemistry and SPH codes.
TL;DR: In this paper, the authors evaluate the extent to which the net transport of solids can be diagnostic of the existence of meridional circulation and find that their net, vertically integrated radial flux is actually quite insensitive to the flow structure for a given vertical average of the turbulence parameter, which they explain.
Q1. What are the contributions mentioned in the paper "Three-dimensional lagrangian turbulent diffusion of dust grains in a protoplanetary disk: method and first applications" ?
The authors study here the dust-diffusive transport using Lagrangian numerical simulations using the popular “ turbulent diffusion ” formalism. However, it is naturally expressed in an Eulerian form, which does not allow the trajectories of individual particles to be studied. The authors present a simple stochastic and physically justified procedure for modeling turbulent diffusion in a Lagrangian form that overcomes these difficulties. The authors show that a net diffusive flux F of the dust appears and that it is proportional to the gas density ( ρ ) gradient and the dust diffusion coefficient Dd: ( F = Dd/ρ × grad ( ρ ) ). The authors present tests and applications comparing dust diffusion in the midplane and upper layers as well as sample trajectories of particles with different sizes. The authors also discuss potential applications for cosmochemistry and smoothed particle hydrodynamic codes.
Q2. What have the authors stated for future works in "Three-dimensional lagrangian turbulent diffusion of dust grains in a protoplanetary disk: method and first applications" ?
In this paper, the authors have presented a numerical tool ( LIDT3D ) for simulating 3D transport of dust in a turbulent gaseous protoplanetary disk using an implicit Lagrangian approach, in order to allow tracking of individual particles in gas. In the first example, the authors show that diffusive transport in the upper layers of the disk is more efficient than in the disk ’ s midplane and may significantly increase the radial transport of dust. In particular, the authors show that the density of particles diffusing in the disk ’ s midplane only is about 5–10 times less than for the 3D case, in which particles are allowed to move vertically in the disk ( Figure 8 ). The authors then plan to use this to compute the equilibrium distribution of dust in observed protoplanetary disks and couple the results with a radiative transfer code to compare them to observations.