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Turbulence in protoplanetary disks, when present, plays a critical role intransporting dust particles embedded in the gaseous disk component. When usinga field description of dust dynamics, a diffusion approach is traditionallyused to model this turbulent dust transport. However, it has been shown thatclassical turbulent diffusion models are not fully self-consistent. Severalshortcomings exist, including the ambiguous nature of the diffused quantity andthe nonconservation of angular momentum. Orbital effects are also neglectedwithout an explicit prescription. In response to these inconsistencies, wepresent a novel Eulerian turbulent dust transport model for isotropic andhomogeneous turbulence on the basis of a mean-field theory. Our model is basedon density-weighted averaging applied to the pressureless fluid equations anduses appropriate turbulence closures. Our model yields novel dynamic equationsfor the turbulent dust mass flux and recovers existing turbulent transportmodels in special limiting cases, thus providing a more general andself-consistent description of turbulent particle transport. Importantly, ourmodel ensures the conservation of global angular and linear momentumunconditionally and implicitly accounts for the effects of orbital dynamics inprotoplanetary disks. Furthermore, our model correctly describes the verticalsettling-diffusion equilibrium solutions for both small and large particles.Hence, this work presents a generalized Eulerian turbulent dust transportmodel, establishing a comprehensive framework for more detailed studies ofturbulent dust transport in protoplanetary disks.

Beyond Diffusion: A Generalized Mean-Field Theory of Turbulent Dust Transport in Protoplanetary Disks