2:15 PM - 2:30 PM
[PPS07-13] Development of a subgrid model to handle the turbulent diffusion of dust grains in protoplanetary disks
Keywords:protoplanetary disk, computational fluid dynamics, dust, planet formation
When considering the distribution of dust in protoplanetary disks, it is essential to treat the diffusion processes due to gas turbulence correctly. Dust diffusion, in particular, determines the amount of dust supplied to the gas planet and the circumplanetary disk at the outer edge of the planetary gap. Dust diffusion is also closely related to the width and brightness of the dust ring formed by the planetary gap, which is intriguing in the link between planet formation theory and disk observations.
The two-fluid approximation, in which dust is treated as a pressureless fluid, is widely used when considering the dust dynamics in protoplanetary disks. In the two-fluid approximation, the turbulent diffusion of dust is incorporated by (1) introducing it as a mass diffusion term in the dust continuity equation (e.g., Weber et al., 2019) or (2) defining the flow velocity due to turbulent diffusion and including it in the dust equation of motion (e.g., Binkert et al., 2023). However, none of these methods ensure momentum conservation in the dust-gas system. Unphysical assumptions, such as treating the diffusion coefficient of the gas and of the dust as the same, are also widely used. These can be particularly problematic when the dust-to-gas mass ratio is high and the gas cannot be treated as a uniform, steady background, such as near planetary gaps.
This study investigates a new formulation for treating dust diffusion processes in isotropic turbulence. We apply a formalism of the Large Eddy Simulation (LES) used in turbulence simulations to the dust-gas system of a protoplanetary disk. We redefine the dust diffusion coefficient by modeling the dust motion in response to turbulent eddies on a subgrid scale assuming Kolmogorov turbulence. We also propose an algorithm to treat the exchange of conserved quantities between resolved-scale and subgrid-scale and between dust and gas in a self-consistent manner and also discuss its validity.
The two-fluid approximation, in which dust is treated as a pressureless fluid, is widely used when considering the dust dynamics in protoplanetary disks. In the two-fluid approximation, the turbulent diffusion of dust is incorporated by (1) introducing it as a mass diffusion term in the dust continuity equation (e.g., Weber et al., 2019) or (2) defining the flow velocity due to turbulent diffusion and including it in the dust equation of motion (e.g., Binkert et al., 2023). However, none of these methods ensure momentum conservation in the dust-gas system. Unphysical assumptions, such as treating the diffusion coefficient of the gas and of the dust as the same, are also widely used. These can be particularly problematic when the dust-to-gas mass ratio is high and the gas cannot be treated as a uniform, steady background, such as near planetary gaps.
This study investigates a new formulation for treating dust diffusion processes in isotropic turbulence. We apply a formalism of the Large Eddy Simulation (LES) used in turbulence simulations to the dust-gas system of a protoplanetary disk. We redefine the dust diffusion coefficient by modeling the dust motion in response to turbulent eddies on a subgrid scale assuming Kolmogorov turbulence. We also propose an algorithm to treat the exchange of conserved quantities between resolved-scale and subgrid-scale and between dust and gas in a self-consistent manner and also discuss its validity.