Anomalous diffusion due to long‐range velocity fluctuations in the absence of a mean flow
作者:
Donald L. Koch,
John F. Brady,
期刊:
Physics of Fluids A
(AIP Available online 1989)
卷期:
Volume 1,
issue 1
页码: 47-51
ISSN:0899-8213
年代: 1989
DOI:10.1063/1.857522
出版商: AIP
数据来源: AIP
摘要:
The dispersion of a tracer in a heterogeneous medium in which the tracer’s velocity has zero mean and a covariance that decays asx−&ggr;with distancexis studied using nonlocal advection–diffusion theory. If the velocity covariance decays slowly, &ggr;≤2, the tracer’s dispersive motion is non‐Fickian even at long times after its release. Under these circumstances, it is not possible to predict the dispersion by assuming that the tracer samples the velocity fluctuations primarily by molecular diffusion, even if the fluctuations are weak. Instead, we develop a self‐consistent theory in which the tracer samples each velocity fluctuation by the motion resulting from the other fluctuations. It is shown that in cases of anomalous diffusion, the tracer’s mean‐square displacement grows faster than linearly with time—ast4/(2+&ggr;)for 0<&ggr;<2 and ast(ln t)1/2for &ggr;≡2 ast→∞.
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