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| Titel |
When do diffusing particles forget their initial positions? |
| VerfasserIn |
N. Suciu, C. Vamoş, F. A. Radu, H. Vereecken, P. Knabner |
| Konferenz |
EGU General Assembly 2010
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 12 (2010) |
| Datensatznummer |
250032984
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| Zusammenfassung |
| The finding that the variance of the displacements can generally be decomposed as sum of
dispersion and memory terms shows that diffusing particles always remember their itinerary
in spatially inhomogeneous environments. The memory-free diffusive behavior linear in time
of the dispersion can only occur after the extinction of the memory terms produced by
correlations between velocity fluctuations and initial positions of the particles. For random
initial conditions outcome of the evolution of the process, as for instance solute plumes
observed after the beginning of contaminant events in natural aquifers, the memory terms
quantify the transitory or persistent anomalous behavior of the transport. In environments
with finite spatial correlation ranges, particles forget memory and normal diffusion occurs in
the long-time limit. In case of infinite correlation ranges, e.g. perfectly stratified
flows, indefinitely persistent memory can be observed and memory terms have the
same nonlinear scaling with the time as the anomalous diffusion. For deterministic
initial conditions independent of velocity statistics, like those designed for tracer
experiments, the memory terms quantify the strong dependence of the macroscopic
observables of the transport processes on the shape and dimension of the source.
Global Random Walk simulations of transport in heterogeneous aquifers show
that the standard deviation of the memory terms is a good measure of the large
sample-to-sample fluctuations of the variance caused by large asymmetric sources. The
simulations indicate that if the random velocity field has finite correlation range the
particles forget the deterministic initial positions in the long-time limit and the
variance is self-averaging, with clear tendency toward normal diffusion. If in addition,
the Lagrangian velocity field is statistically homogeneous, or equivalently if the
mean Green function of the transport problem is invariant to spatial translations,
then the ensemble averaged memory terms necessarily vanish. Consequently, the
spatial moments of the mean Green function, independent of deterministic initial
conditions, supply an “ergodic” description of the pre-asymptotic behavior of the mean
concentration. On the contrary, for random initial conditions, the mean memory terms are
non-vanishing whenever the velocity field has non-zero correlation lengths and the
translation-invariance of the mean Green function as well as the ergodic description break
down. |
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