标题： 粘性超不稳定性、非线性波列以及致密行星环的细结构 显示英文标题

标题： The viscous overstability, nonlinear wavetrains, and finescale structure in dense planetary rings

摘要： 本文探讨了土星A环和B环中表现出的细尺度轴对称结构。我们旨在解释由卡西尼号UVIS和RSS仪器揭示的150-220米范围内的周期性微观结构，以及由卡西尼号ISS报告的1-10公里范围内的亮度不规则变化。我们认为前者结构对应于在粘性过稳定盘中自然形成的非线性波列的峰和谷。后者在更长尺度上的变化可能对应于波列振幅和波长的调制和缺陷。我们使用一个简单的流体动力学模型来探索这些想法，该模型捕捉了非弹性碰撞粒子盘的正确定性行为，同时使我们能够利用分析和半分析技术取得进展。具体而言，我们计算了一族行进的非线性密度波并确定了它们的稳定性特性。确认我们基本结果的详细数值模拟将出现在后续论文中。 显示英文摘要

摘要： This paper addresses the fine-scale axisymmetric structure exhibited in Saturn's A and B-rings. We aim to explain both the periodic microstructure on 150-220m, revealed by the Cassini UVIS and RSS instruments, and the irregular variations in brightness on 1-10km, reported by the Cassini ISS. We propose that the former structures correspond to the peaks and troughs of the nonlinear wavetrains that form naturally in a viscously overstable disk. The latter variations on longer scales may correspond to modulations and defects in the wavetrains' amplitudes and wavelength. We explore these ideas using a simple hydrodynamical model which captures the correct qualitative behaviour of a disk of inelastically colliding particles, while also permitting us to make progress with analytic and semi-analytic techniques. Specifically, we calculate a family of travelling nonlinear density waves and determine their stability properties. Detailed numerical simulations that confirm our basic results will appear in a following paper.