The streaming instability (SI) has been extensively studied in the linear and non-linear regimes as a mechanism to concentrate solids and trigger planetesimal formation in the midplane of protoplanetary discs. A related dust settling instability (DSI) applies to particles while settling towards the midplane. The DSI has previously been studied in the linear regime, with predictions that it could trigger particle clumping away from the midplane. This work presents a range of linear calculations and non-linear simulations, performed with FARGO3D, to assess conditions for DSI growth. We expand on previous linear analyses by including particle size distributions and performing a detailed study of the amount of background turbulence needed to stabilize the DSI. When including binned size distributions, the DSI often produces converged growth rates with fewer bins than the standard SI. With background turbulence, we find that the most favorable conditions for DSI growth are weak turbulence, characterized by $\alpha \lesssim 10^{-6}$ with intermediate-sized grains that settle from one gas scale-height. These conditions could arise during a sudden decrease in disc turbulence following an accretion outburst. Ignoring background turbulence, we performed a parameter survey of local 2D DSI simulations. Particle clumping was either weak or occurred slower than particles settle. Clumping was reduced by a factor of two in a comparison 3D simulation. Overall, our results strongly disfavor the hypothesis that the DSI significantly promotes planetesimal formation. Non-linear simulations of the DSI with different numerical methods could support or challenge these findings.

中文翻译：

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原行星盘中的尘埃沉降不稳定性

流动不稳定性 (SI) 已在线性和非线性区域中被广泛研究，作为一种在原行星盘的中平面中浓缩固体并触发微星形成的机制。相关的粉尘沉降不稳定性 (DSI) 适用于向中平面沉降的颗粒。DSI 之前曾在线性区域中进行过研究，并预测它可能会触发粒子从中平面聚集。这项工作提供了一系列使用 FARGO3D 执行的线性计算和非线性模拟，以评估 DSI 增长的条件。我们通过包括粒度分布并详细研究稳定 DSI 所需的背景湍流量来扩展先前的线性分析。当包括分箱尺寸分布时，DSI 通常会以比标准 SI 更少的 bin 产生收敛增长率。对于背景湍流，我们发现 DSI 增长的最有利条件是弱湍流，其特征是 $\alpha \lesssim 10^{-6}$ 具有从一个气体标度高度沉降的中等尺寸的晶粒。在吸积爆发后盘湍流突然减少期间，可能会出现这些情况。忽略背景湍流，我们对局部二维 DSI 模拟进行了参数调查。颗粒结块较弱或发生得比颗粒沉降慢。在比较 3D 模拟中，结块减少了两倍。总的来说，我们的结果强烈反对 DSI 显着促进微星形成的假设。