论文标题
量化细胞流的耗散增强
Quantifying the dissipation enhancement of cellular flows
论文作者
论文摘要
我们研究细胞流的耗散增强。 Iyer，Xu和Zlatoš的先前工作产生了一系列细胞流，可以通过任意大量增加耗散。我们通过根据流量幅度，细胞大小和扩散率提供耗散增强的定量界限来改善这一结果。明确地表明，当流动振幅足够大时，混合时间是由一个单元格的退出时间以及当流量振幅较小时的有效扩散率的倒数。这与最佳启发式方法一致。我们还证明了将不可压缩流的耗散时间与混合时间有关的一般结果。证明背后的主要思想是概率研究动力学并构建成功的耦合。
We study the dissipation enhancement by cellular flows. Previous work by Iyer, Xu, and Zlatoš produces a family of cellular flows that can enhance dissipation by an arbitrarily large amount. We improve this result by providing quantitative bounds on the dissipation enhancement in terms of the flow amplitude, cell size and diffusivity. Explicitly we show that the mixing time is bounded by the exit time from one cell when the flow amplitude is large enough, and by the reciprocal of the effective diffusivity when the flow amplitude is small. This agrees with the optimal heuristics. We also prove a general result relating the dissipation time of incompressible flows to the mixing time. The main idea behind the proof is to study the dynamics probabilistically and construct a successful coupling.
