Fickian dispersion is anomalous
The thesis put forward here is that the occurrence of Fickian dispersion in geophysical settings is a rare event and consequently should be labeled as anomalous. What people classically call anomalous is really the norm. In a Lagrangian setting, a process with mean square displacement which is proportional to time is generally labeled as Fickian dispersion. With a number of counter examples we show why this definition is fraught with difficulty. In a related discussion, we show an infinite second moment does not necessarily imply the process is super dispersive. By employing a rigorous mathematical definition of Fickian dispersion we illustrate why it is so hard to find a Fickian process. We go on to employ a number of renormalization group approaches to classify nonFickian dispersive behavior. Scaling laws for the probability density function for a dispersive process, the distribution for the first passage times, the mean first passage time, and the finitesize Lyapunov exponent are presented for fixed points of both deterministic and stochastic renormalization group operators. The fixed points of the renormalization group operators are pselfsimilar processes. A generalized renormalization group operator is introduced whose fixed points form a set of generalized selfsimilar processes. Finally, powerlaw clocks aremore »
 Authors:

^{[1]};
^{[2]}
 Purdue Univ., West Lafayette, IN (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 OSTI Identifier:
 1236687
 Report Number(s):
 LAUR1520679
Journal ID: ISSN 00221694; PII: S0022169415004497
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Hydrology
 Additional Journal Information:
 Journal Volume: 531; Journal Issue: P1; Journal ID: ISSN 00221694
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 58 GEOSCIENCES nonFickian; anomalous; transport; scaling; renormalization
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