Precision Measurements of Stretching and Compression in Fluid Mixing
Precision Measurements of Stretching and Compression in Fluid Mixing
复制标题
流体混合中拉伸和压缩的精确测量
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. Gollub
中科院分区：
文献类型：
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作者：
G. Voth;G. Haller;J. Gollub
将杂质混合到流动流体中是许多科学领域的重要过程，包括地球物理过程、化学反应器和微流体装置。在某些情况下，例如周期流，非线性动力学的概念为理解混合 2, 3, 4, 5,... 提供了深刻的理论基础。不幸的是，该理论的组成部分，即相关庞加莱图的不动点和不变流形，仍然无法直接进行实验研究，从而限制了可以获得的见解。利用产生混沌混合的二维流体流中示踪粒子轨迹的精确测量，我们直接测量随时间变化的拉伸和压缩场。这些量以前只能在数值上获得，但沿着与稳定和不稳定流形一致的线达到局部最大值，从而揭示了控制混合的动态结构。发现无源杂质场的轮廓或水平集在每个时刻都与大压缩线（不稳定流形）平行排列。随着湍流的临近，这种联系似乎会持续存在。流体流动的速度场与其分散的杂质形成的图案之间的关系可能很复杂。即使是简单的二维时间周期流动也会产生混乱的混合和复杂的材料分布，其中附近的流体元素彼此强烈分离。基本过程涉及流体元素的重复拉伸和折叠以及小尺度扩散的组合。然而，为了了解材料的复杂分布实际上是如何产生的，重要的是确定连接不同时间流体元素位置的非线性图，并显示这些图如何分离附近的元素。这需要比以前更精确、更快速地测量流场。我们的工作依赖于高分辨率测量
The mixing of an impurity into a flowing fluid is an important process in many areas of science, including geophysical processes, chemical reactors, and microfluidic devices. In some cases, for example periodic flows, the concepts of nonlinear dynamics provide a deep theoretical basis for understanding mixing 2, 3, 4, 5, . Unfortunately, the building blocks of this theory, i.e. the fixed points and invariant manifolds of the associated Poincaré map, have remained inaccessible to direct experimental study, thus limiting the insight that could be obtained. Using precision measurements of tracer particle trajectories in a two-dimensional fluid flow producing chaotic mixing, we directly measure the time-dependent stretching and compression fields. These quantities, previously available only numerically, attain local maxima along lines coinciding with the stable and unstable manifolds, thus revealing the dynamical structures that control mixing. Contours or level sets of a passive impurity field are found to be aligned parallel to the lines of large compression (unstable manifolds) at each instant. This connection appears to persist as the onset of turbulence is approached. The relationship between the velocity field of a fluid flow and the pattern formed by an impurity that it disperses can be intricate. Even simple time-periodic flows in two dimensions can produce chaotic mixing and complex distributions of material, in which nearby fluid elements diverge strongly from each other . The fundamental processes involve a combination of repeated stretching and folding of fluid elements in combination with diffusion at small scales. However, to understand how the complex distributions of material actually arise, it is important to determine the nonlinear maps that connect the positions of fluid elements at different times, and to show how these maps separate nearby elements. This requires more precise and rapid measurement of flow fields than has been accomplished previously. Our work depends on high resolution measurements