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Ensemble solute transport in two‐dimensional operator‐scaling random fields
Author(s) -
Monnig Nathan D.,
Benson David A.,
Meerschaert Mark M.
Publication year - 2008
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/2007wr005998
Subject(s) - scaling , plume , isotropy , brownian motion , random field , anisotropy , statistical physics , mathematics , mechanics , physics , geometry , statistics , meteorology , quantum mechanics
Motivated by field measurements of aquifer hydraulic conductivity ( K ), recent techniques were developed to construct anisotropic fractal random fields in which the scaling, or self‐similarity parameter, varies with direction and is defined by a matrix. Ensemble numerical results are analyzed for solute transport through these two‐dimensional “operator‐scaling” fractional Brownian motion ln( K ) fields. Both the longitudinal and transverse Hurst coefficients, as well as the “radius of isotropy” are important to both plume growth rates and the timing and duration of breakthrough. It is possible to create operator‐scaling fractional Brownian motion fields that have more “continuity” or stratification in the direction of transport. The effects on a conservative solute plume are continually faster‐than‐Fickian growth rates, highly non‐Gaussian shapes, and a heavier tail early in the breakthrough curve. Contrary to some analytic stochastic theories for monofractal K fields, the plume growth rates never exceed A. Mercado's (1967) purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent superstratified growth must be the result of other demonstrable factors, such as initial plume size.