Transient anomalous diffusion in Poiseuille flow
Transient anomalous diffusion in Poiseuille flow
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DOI：
10.1017/s0022112001004906
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发表时间：
2001-08
影响因子：
3.7
通讯作者：
M. Latini;A. Bernoff
中科院分区：
文献类型：
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作者：
M. Latini;A. Bernoff
我们重新审视了层流管泊肃叶流中示踪剂点排放弥散的经典问题。对于管道中心的放电，我们表明在小的无量纲扩散 D 的限制下，示踪剂扩散可以分为三个状态。对于小时间 (t [Lt ] D−1/3)，扩散主导平流，产生球对称高斯色散云。在较大时间 (t [Gt ] D−1) 下，流动处于经典泰勒流态，示踪剂在管道中横向均匀化，并以高斯分布纵向扩散。然而，在中间状态（D−1/3 [Gt ] t [Gt ] D−1）中，纵向扩散是异常的，其宽度与 t [Lt ] Dt2 成比例，并且纵向分布明显不对称。我们提出了一种在这种情况下有效的新解决方案，并用数值验证了我们的结果。对于偏心释放也给出了类似的结果；这里，异常状态下的分布宽度为 D1/2t3/2。这些结果表明，反常扩散是早于泰勒体系的点放电剪切分散的标志。
We revisit the classical problem of dispersion of a point discharge of tracer in laminar pipe Poiseuille flow. For a discharge at the centre of the pipe we show that in the limit of small non-dimensional diffusion, D, tracer dispersion can be divided into three regimes. For small times (t [Lt ] D−1/3), diffusion dominates advection yielding a spherically symmetric Gaussian dispersion cloud. At large times (t [Gt ] D−1), the flow is in the classical Taylor regime, for which the tracer is homogenized transversely across the pipe and diffuses with a Gaussian distribution longitudinally. However, in an intermediate regime (D−1/3 [Gt ] t [Gt ] D−1), the longitudinal diffusion is anomalous with a width proportional to t [Lt ] Dt2 and a distinctly asymmetric longitudinal distribution. We present a new solution valid in this regime and verify our results numerically. Analogous results are presented for an off-centre release; here the distribution width scales as D1/2t3/2 in the anomalous regime. These results suggest that anomalous diffusion is a hallmark of the shear dispersion of point discharges at times earlier than the Taylor regime.