论文标题
多分散流的不稳定性I.紧密耦合的颗粒和终端速度近似
Polydisperse Streaming Instability I. Tightly coupled particles and the terminal velocity approximation
论文作者
论文摘要
我们介绍了流媒体不稳定性的多分散版本，其中尘埃成分被视为尺寸的连续体。我们表明，其行为与单分散流不稳定性有很大不同。我们专注于末端速度近似中紧密耦合的颗粒，并表明在动态时间尺度上成倍增长的不稳定模式。但是，对于灰尘与气体比的比统一小得多，它们仅限于径向波数，而径向波数$ \ sim 1/\叠加线{\ rm st} $远比单分散流式流动不稳定性增长率峰值大。这里$ \ Overline {\ rm st} \ ll 1 $是灰尘尺寸分布的合适的平均stokes数字。对于大于统一的灰尘与气体比率，也发现了在动态时间尺度上生长的多分散模式，与单分散流的不稳定性和类似的大波浪数相似。在较小的波数下，经典的单分散流不稳定性显示了世俗的生长，在末端速度近似下未发现生长的多分散模式。在终端速度近似的有效性区域之外，我们发现了在$ \ sim 10^4 $动力学时间尺度上生长的不稳定的环环模式。
We introduce a polydisperse version of the streaming instability, where the dust component is treated as a continuum of sizes. We show that its behaviour is remarkably different from the monodisperse streaming instability. We focus on tightly coupled particles in the terminal velocity approximation and show that unstable modes that grow exponentially on a dynamical time scale exist. However, for dust to gas ratios much smaller than unity they are confined to radial wave numbers that are a factor $\sim 1/\overline{\rm St}$ larger than where the monodisperse streaming instability growth rates peak. Here $\overline{\rm St} \ll 1$ is a suitable average Stokes number for the dust size distribution. For dust to gas ratios larger than unity, polydisperse modes that grow on a dynamical time scale are found as well, similar as for the monodisperse streaming instability and at similarly large wave numbers. At smaller wave numbers, where the classical monodisperse streaming instability shows secular growth, no growing polydisperse modes are found under the terminal velocity approximation. Outside the region of validity for the terminal velocity approximation, we have found unstable epicyclic modes that grow on $\sim 10^4$ dynamical time scales.
