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A turnstile mechanism for fronts propagating in fluid flows

机译:用于前沿在流体流中传播的旋转机构

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摘要

We consider the propagation of fronts in a periodically driven flowingmedium. It is shown that the progress of fronts in these systems may bemediated by a turnstile mechanism akin to that found in chaotic advection. Wefirst define the modified ("active") turnstile lobes according to the evolutionof point sources across a transport boundary. We then show that the lobeboundaries may be constructed from stable and unstable \emph{burning invariantmanifolds}---one-way barriers to front propagation analogous to traditionalinvariant manifolds for passive advection. Because the burning invariantmanifolds (BIMs) are one-dimensional curves in a three-dimensional ($xy\theta$)phase space, their projection into $xy$-space exhibits several key differencesfrom their advective counterparts: (lobe) areas are not preserved, BIMs mayself-intersect, and an intersection between stable and unstable BIMs does notmap to another such intersection. These differences must be accommodated in thecorrect construction of the new turnstile. As an application, we consider alobe-based treatment protocol for protecting an ocean bay from an invadingalgae bloom.
机译:我们考虑在周期性驱动的流动介质中前沿的传播。结果表明,这些系统中锋线的进展可能是由类似于混沌平流中发现的旋转门机制所介导的。我们首先根据跨传输边界的点源的演变定义修改后的(“活动”)旋转栅瓣。然后我们表明,叶边界可能是由稳定和不稳定的\ emph {燃烧不变流形}构成的,这是类似于传统不变流形的被动对流的单向障碍物,用于前方传播。由于燃烧不变流形(BIM)是三维($ xy \ theta $)相空间中的一维曲线,因此它们投影到$ xy $空间中与对流对应物有几个关键区别:(波瓣)区域未保留,BIM可能会自相交,并且稳定BIM和不稳定BIM之间的交集不会映射到另一个此类交集。这些差异必须适应新旋转栅门的正确构造。作为一种应用,我们考虑了基于Alobe的处理协议来保护海洋海湾免受藻类水华的侵袭。

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  • 年度 2013
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