A quasilinear theory of time-dependent nonlocal dispersion in geologic media.

TL;DRAbstract

A theory is presented which accounts for a particular aspect of nonlinearity caused by the deviation of plume "particles" from their mean trajectory in three-dimensional, statistically homogeneous but anisotropic porous media under an exponential covariance of log hydraulic conductivities. Quasilinear expressions for the time-dependent nonlocal dispersivity and spatial covariance tensors of ensemble mean concentration are derived, as a function of time, variance σᵧ² of log hydraulic conductivity, degree of anisotropy, and flow direction. One important difference between existing linear theories and the new quasilinear theory is that in the former transverse nonlocal dispersivities tend asymptotically to zero whereas in the latter they tend to nonzero Fickian asymptotes. Another important difference is that while all existing theories are nominally limited to situations where σᵧ² is less than 1, the quasilinear theory is expected to be less prone to error when this restriction is violat

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