Non - Classical Transport in Fractal Media as Applied to Radioactive Waste Problem : Anisotropic Random Advection Model - 11147

Advection flow is a dominating physical mechanism of contaminant transport over geologic fractured media. Natural fractures often combine into percolation cluster, having fractal properties. As a result long-ranged correlations arise in the fluctuating velocity field of infiltration flux. The presence of preferred direction due to the gravity force leads to the strong anisotropy of the advection velocity field. Two basic dimensionless parameters and determine power exponents in the flux correlation spatial decay and anisotropy property, respectively. The values of these parameters are the key factors determining transport regimes. In the parameter domain expressed by inequalities and 0 h > 1 β > ( ) 1 2 h β + < 1 2 < β < , anisotropic super-diffusion regime is realized. When the inequalities , 1 h < ( ) 1 h 2 β + > are valid, a compromise arises between two various transport regimes that is super-diffusion along the vertical direction and classical diffusion in horizontal plane. Concentration decay at long distances (in concentration tails) is of exponential type. Horizontal size of concentration signal undergoes to contraction at asymptotically large distances. Anomalous transport modes are realized at times when the contaminant plume sizes are much less than the correlation length, which is an upper bound of the fractality interval. At the later times contaminant transport occurs in a classical anisotropic diffusion-advection regime. The change of transport regimes in time results in a two-stage structure of concentration tails at later times. The nearest stage of the tail has classical Gaussian form and the remote one is of super-diffusive type.