HR: 0800h
AN: H51F-0439    [Abstracts]
TI: Lagrangian framework of super-Fickian dispersion
AU: * Benson, D A
EM: dbenson@mines.edu
AF: Department of Geology and Geological Engineering, Colorado School of Mines, 1516 Illinois St, Golden, CO 80401 United States
AU: Zhang, Y
EM: yong.zhang@dri.edu
AF: Division of Hydrologic Sciences, Desert Research Institute, 2215 Raggio Parkway, Reno, NV 89512 United States
AU: Meerschaert, M M
EM: mcubed@maths.otago.ac.nz
AF: Department of Mathematics and Statistics, University of Otago, Dunedin, PO Box 56 New Zealand
AU: Scheffler, H
EM: pscheff@unr.edu
AF: Department of Mathematics, University of Nevada, 1664 North Virginia Street, Reno, NV 89557 United States
AB: The super-Fickian dispersion of solutes in fractal media can be simulated by a spatially fractional advection-dispersion equation (fADE). We build Lagrangian (random walk) particle-tracking solutions of the fADE to emulate the dynamics of solute particles undergoing super-Fickian dispersion. The motions of these random-walking particles reflect the influence of the large-scale physical heterogeneity of the porous medium. In the case where the plume spreads with a unique rate in different (not necessarily orthogonal) directions, the particles move along each preferential direction with the pdf of displacements satisfying the density of a Lévy noise (as opposed to a Gaussian noise). The directional structure of plumes is captured by the mixture of motions in different directions described by the spectral measure. For an irregular groundwater flux field, the particles disperse according to projections along adjacent velocity streamlines where the absolute directions and magnitude of the spectral measure changes locally. When the dispersion coefficient varies smoothly along the transport distance, the Lagrangian description of particle motion contains an additional Lévy noise scaled by the dispersion gradient. For all cases containing a space-dependent dispersion coefficient, whether the dispersion flux is Markovian will influence significantly the dynamics of particles.
DE: 1719 Hydrology
DE: 1829 Groundwater hydrology
DE: 1831 Groundwater quality
SC: Hydrology [H]
MN: Fall Meeting 2005