STRONGLY ANNOMALOUS SOLUTE TRANSPORT IN ANISOTROPIC FRACTAL FIELDS

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 2-D “operator-scaling” fractional Brownian motion (fBm) 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 osfBm 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 Mercado's [1967] purely stratified aquifer growth rate of plume apparent dispersivity proportional to mean distance. Apparent super-stratified growth must be the result of other demonstrable factors, such as initial plume size.