Hypermixing in linear shear flow
Hypermixing in linear shear flow
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DOI：
10.1029/2011wr010737
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发表时间：
2011-09-10
影响因子：
5.4
通讯作者：
Le Borgne, Tanguy
中科院分区：
文献类型：
--
作者：
Bolster, Diogo;Dentz, Marco;Le Borgne, Tanguy
在本技术说明中，我们研究二维线性剪切流中的混合。我们推导了无界二维剪切流中任意初始条件的浓度场的解析表达式。我们专注于点初始条件的解，并研究 (1) 第二中心矩作为羽流分散的度量，(2) 稀释指数作为混合状态的度量，以及 (3) 标量耗散率作为混合速率的度量。先前已经表明，溶质扩散随着时间的立方而增长，因此是超分散的。在此，我们证明稀释指数随时间呈二次方增加，而均匀介质则呈线性增加。类似地，标量耗散率在 t(-3) 时衰减，而对于均匀介质，它在 t(-2) 时衰减得更慢。混合比均匀介质中的混合要强得多，因此我们将观察到的行为称为超混合。
In this technical note we study mixing in a two-dimensional linear shear flow. We derive analytical expressions for the concentration field for an arbitrary initial condition in an unbounded two-dimensional shear flow. We focus on the solution for a point initial condition and study the evolution of (1) the second centered moments as a measure for the plume dispersion, (2) the dilution index as a measure of the mixing state, and (3) the scalar dissipation rate as a measure for the rate of mixing. It has previously been shown that the solute spreading grows with the cube of time and thus is hyperdispersive. Herein we demonstrate that the dilution index increases quadratically with time in contrast to a homogeneous medium, for which it increases linearly. Similarly, the scalar dissipation rate decays as t(-3), while for a homogeneous medium it decreases more slowly as t(-2). Mixing is much stronger than in a homogeneous medium, and therefore we term the observed behavior hypermixing.