标题： 原行星吸积盘中垂直剪切不稳定性的一个最小模型 显示英文标题

标题： A minimal model for vertical shear instability in protoplanetary accretion disks

摘要： 垂直剪切不稳定性是一种轴对称效应，被认为能够驱动原行星吸积盘中磁不活跃区域的湍流。 在这里，我们在三种包含均匀密度流体、分层大气和平流盘剪切盒部分的“最小模型”解析模型中研究了它的物理机制。 这些分析表明，垂直剪切不稳定性本质上与中纬度地球大气中的斜升对称不稳定性相似，在地转气流存在垂直切变以及墨西哥湾流顶层混合的情况下也是如此。 我们展示了为了获得不稳定性，流体质点的坡度应该超过盘径向-垂直平面上平均绝对动量的坡度。 我们从三个角度提供了详细且相互一致的物理解释：角动量守恒的角度、流体径向和方位角涡度分量之间动力学相互作用的角度，以及涉及广义Solberg-H{\o }岛瑞利条件的能量角度。 此外，我们解释了为什么无粘动力学产生振荡不稳定模式，并从不稳定性中分离出振荡机制。 显示英文摘要

摘要： The Vertical Shear Instability is an axisymmetric effect suggested to drive turbulence in the magnetically inactive zones of protoplanetary accretion disks. Here we examine its physical mechanism in analytically tractable ``minimal models" in three settings that include a uniform density fluid, a stratified atmosphere, and a shearing-box section of a protoplanetary disk. Each of these analyses show that the vertical shear instability's essence is similar to the slantwise convective symmetric instability in the mid-latitude Earth atmosphere, in the presence of vertical shear of the baroclinic jet stream, as well as mixing in the top layers of the Gulf Stream. We show that in order to obtain instability the fluid parcels' slope should exceed the slope of the mean absolute momentum in the disk radial-vertical plane. We provide a detailed and mutually self-consistent physical explanation from three perspectives: in terms of angular momentum conservation, as a dynamical interplay between a fluid's radial and azimuthal vorticity components, and from an energy perspective involving a generalized Solberg-H{\o}iland Rayleigh condition. Furthermore, we explain why anelastic dynamics yield oscillatory unstable modes and isolate the oscillation mechanism from the instability one.