Non-linear evolution of the unstratified polydisperse dust settling instability

Faculty of Aerospace Engineering, Delft University of Technology, Kluyverweg 1, 2629 HS Delft, The Netherlands

^★ Corresponding author: hossam.saed@gmail.com

Received: 7 March 2025
Accepted: 14 July 2025

Abstract

Context. The dust settling instability (DSI) is a member of the resonant drag instability family, and is thus related to the streaming instability (SI). Linear calculations found that the unstratified monodisperse DSI has growth rates much higher than the SI even with lower initial dust-to-gas ratios. However, recent non-linear investigation found no evidence of strong dust clumping at the saturation level.

Aims. We seek to investigate the non-linear saturation of the mono- and polydisperse DSI. We examine the convergence behaviour with regard to both the numerical resolution as well as the number of species. By characterising the morphology of the dust evolution triggered by the DSI, we can shed more light on its role in planetesimal formation.

Methods. We performed a suite of 2D shearing box hydrodynamic simulations with the code IDEFIX, both in the mono- and polydisperse regimes. We focussed on the time evolution of the maximum dust density, noting the time at which the instability is triggered, and analysed the morphology of the resultant structure.

Results. In our monodisperse DSI simulations, the maximum dust density increases and the instability saturates earlier with a higher spatial resolution, with no signs of convergence yet. The polydisperse simulations do seem to converge with the number of species and produce maximum dust densities that are comparable to, albeit lower than, the monodisperse simulations. Different dust species tend to form adjacent but separate dust filaments, which may have implications on dust growth and further clumping.

Conclusions. The monodisperse DSI produces dust structure at densities high enough to likely lead to clumping. The polydisperse DSI produces lower but comparable dust densities at the same spatial resolution. Our idealised treatment suggests that the DSI is important for planetesimal formation, as it is less affected by the inclusion of a dust size distribution than the SI.