Title: Mass crystals and cage effect in vorticity crystals Show Chinese title

Title: 质量晶体和旋度晶体中的笼效应

Abstract: We study the motion of tiny heavy inertial particles advected by a two dimensional inviscid fluid flow composed of $N$ identical point vortices regularly placed on a ring, and forming a crystal. In the limit of weak particle inertia, we show asymptotically that, in the reference frame of the crystal, inertial particles have $N$ asymptotically stable equilibrium positions located outside the crystal, in agreement with numerical observations by Ravichandran et al. (Sadhana 42, 2017). In addition to these "satellite" attracting points, we observe that for $N \ge 3$ the center of the ring, though degenerate, is a stable equilibrium position for inertial particles. This creates a kind of cage effect, where inclusions slowly drift towards the center under the effect of the surrounding vortices. This cage effect is observed to persist even at larger Stokes numbers, in contrast with the satellite attracting points that vanish when the Stokes number is above some critical value. Show Chinese abstract

Abstract: 我们研究由$N$个在环上规则放置的相同点涡组成的二维无粘流场中，微小重惯性粒子的运动，这些点涡形成一个晶体。在粒子惯性较弱的极限情况下，我们通过渐近分析表明，在晶体参考系中，惯性粒子具有$N$个渐近稳定的平衡位置，位于晶体之外，这与 Ravichandran 等人的数值观察结果一致（Sadhana 42, 2017）。除了这些“卫星”吸引点外，我们还观察到对于$N \ge 3$，环的中心虽然是退化的，但仍然是惯性粒子的稳定平衡位置。这产生了一种笼效应，包含物在周围涡旋的作用下缓慢地向中心漂移。这种笼效应即使在较大的斯托克斯数下也持续存在，与当斯托克斯数超过某个临界值时消失的卫星吸引点形成对比。