Beyond diffusion: a generalized mean-field theory of turbulent dust transport in protoplanetary discs

Abstract

ABSTRACT Turbulence in protoplanetary discs, when present, plays a critical role in transporting dust particles embedded in the gaseous disc component. When using a field description of dust dynamics, a diffusion approach is traditionally used to model this turbulent dust transport. However, it has been shown that classical turbulent diffusion models are not fully self-consistent. Several shortcomings exist, including the ambiguous nature of the diffused quantity and the non-conservation of angular momentum. Orbital effects are also neglected without an explicit prescription. In response to these inconsistencies, we present a novel Eulerian turbulent dust transport model for isotropic and homogeneous turbulence on the basis of a mean-field theory. Our model is based on density-weighted averaging applied to the pressureless fluid equations and uses appropriate turbulence closures. Our model yields novel dynamic equations for the turbulent dust mass flux and recovers existing turbulent transport models in special limiting cases, thus providing a more general and self-consistent description of turbulent particle transport. Importantly, our model ensures the conservation of global angular and linear momentum unconditionally and implicitly accounts for the effects of orbital dynamics in protoplanetary discs. Furthermore, our model correctly describes the vertical settling–diffusion equilibrium solutions for both small and large particles. Hence, this work presents a generalized Eulerian turbulent dust transport model, establishing a comprehensive framework for more detailed studies of turbulent dust transport in protoplanetary discs.