Analysis of Enhanced Diffusion in Taylor Dispersion via a Model Problem
Analysis of Enhanced Diffusion in Taylor Dispersion via a Model Problem
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通过模型问题分析泰勒色散中的增强扩散
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
C. E. Wayne
中科院分区：
文献类型：
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作者：
M. Beck;Osman Chaudhary;C. E. Wayne
我们考虑了一个简单的示踪剂浓度演化模型，它受制于无限大流道中粘度为ν≪1的流体的背景剪切流动。泰勒在20世纪50年代观察到，在这种情况下，示踪剂以与1/ν成比例的速度扩散，而不是以与ν成比例的预期速度扩散。结合傅立叶分析和中心流形理论，我们给出了这种增强扩散的数学解释。更准确地说，我们证明了，当浓度的高模按指数衰减时，低模按代数方式衰减，但衰减的速度更快。此外，低模的行为由适当中心流形上的有限维动力学控制，这恰好对应于粘度与1/ν成比例的流体的扩散。
We consider a simple model of the evolution of the concentration of a tracer, subject to a background shear flow by a fluid with viscosity ν ≪ 1 in an infinite channel. Taylor observed in the 1950s that, in such a setting, the tracer diffuses at a rate proportional to 1∕ν, rather than the expected rate proportional to ν. We provide a mathematical explanation for this enhanced diffusion using a combination of Fourier analysis and center manifold theory. More precisely, we show that, while the high modes of the concentration decay exponentially, the low modes decay algebraically, but at an enhanced rate. Moreover, the behavior of the low modes is governed by finite-dimensional dynamics on an appropriate center manifold, which corresponds exactly to diffusion by a fluid with viscosity proportional to 1∕ν.