稠密行星环中的粘性超稳定性、非线性波列和精细尺度结构
The viscous overstability, nonlinear wavetrains, and finescale structure in dense planetary rings
摘要：
本文讨论了土星A环和B环的细尺度轴对称结构。我们的目标是解释卡西尼UVIS和RSS仪器揭示的150- 220米的周期性微观结构，以及卡西尼国际空间站报告的1- 10公里亮度的不规则变化。我们建议，前者的结构对应的波峰和波谷的非线性波列，自然形成的粘性过稳定盘。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。我们探索这些想法使用一个简单的流体动力学模型，捕捉正确的定性行为的磁盘的非弹性碰撞粒子，同时也使我们能够取得进展的分析和半分析技术。具体来说，我们计算了一个家庭的旅行非线性密度波，并确定其稳定性。详细的数值模拟，证实我们的基本结果将出现在下面的文件。
英文摘要：
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.
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