具有变化相互作用范围的二维流动中的剧烈松弛
Violent relaxation in two-dimensional flows with varying interaction range
摘要：
理解系统向平衡态的弛豫是统计力学中一个长期存在的问题。在这里，我们通过考虑一类二维或地球物理流动来解决长程相互作用在这一过程中的作用，其中流体粒子之间的相互作用随距离变化为$\sim$ r^（$α$ --2）与$α$ \textgreater{} 0。以前的研究在欧拉情况下$α$ = 2已表明收敛到各种准定态通过改变初始状态。出乎意料的是，通过用规定的初始状态改变$α$来恢复所有这些状态。对于小的$α$，粗化过程导致形成一个尖锐的界面之间的两个区域的均匀化$α$ -涡;对于大的$α$，流被吸引到一个稳定的偶极结构通过一个双极性过程。
英文摘要：
Understanding the relaxation of a system towards equilibrium is a longstanding problem in statistical mechanics. Here we address the role of long-range interactions in this process by considering a class of two-dimensional or geophysical flows where the interaction between fluid particles varies with the distance as $\sim$ r^($α$--2) with $α$ \textgreater{} 0. Previous studies in the Euler case $α$ = 2 had shown convergence towards a variety of quasi-stationary states by changing the initial state. Unexpectedly, all those regimes are recovered by changing $α$ with a prescribed initial state. For small $α$, a coarsening process leads to the formation of a sharp interface between two regions of homogenized $α$-vorticity; for large $α$, the flow is attracted to a stable dipolar structure through a filamentation process.
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