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arXiv 1106.3945physics.flu-dyncond-mat.softnlin.CD
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移动壁加速混合

Moving walls accelerate mixing

Jean-Luc Thiffeault, Emmanuelle Gouillart, Olivier Dauchot

摘要:

在粘性流体中混合是具有挑战性的,但混沌平流原则上允许有效的混合。在最好的情况下,被动标量的浓度分布的衰减率应该是时间上的指数。在实践中,几位作者发现,容器壁处的无滑移边界条件可以大大减缓混合,将指数衰减变为幂律。这种减速影响整个混合区,而不仅仅是壁附近。这是因为当混沌混合区延伸到壁面时,有一分界线与之相连,沿分界线到壁面的距离在时间上是多项式的,并且控制了长时间的衰减。然而,如果壁被移动或旋转,封闭的轨道出现,从中心混合区分开的双曲固定点与同宿轨道。到达不动点的长时间方法是指数的,因此恢复了总体指数衰减,尽管在壁附近有一个薄的未混合区域。

英文摘要:

Mixing in viscous fluids is challenging, but chaotic advection in principle allows efficient mixing. In the best possible scenario,the decay rate of the concentration profile of a passive scalar should be exponential in time. In practice, several authors have found that the no-slip boundary condition at the walls of a vessel can slow down mixing considerably, turning an exponential decay into a power law. This slowdown affects the whole mixing region, and not just the vicinity of the wall. The reason is that when the chaotic mixing region extends to the wall, a separatrix connects to it. The approach to the wall along that separatrix is polynomial in time and dominates the long-time decay. However, if the walls are moved or rotated, closed orbits appear, separated from the central mixing region by a hyperbolic fixed point with a homoclinic orbit. The long-time approach to the fixed point is exponential, so an overall exponential decay is recovered, albeit with a thin unmixed region near the wall.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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