A quasi‐linear theory of non‐Fickian and Fickian subsurface dispersion: 1. Theoretical analysis with application to isotropic media

摘要: A theory is presented which accounts for 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 log hydraulic conductivities. Existing linear theories predict that, absence local dispersion, transverse dispersivities tend asymptotically to zero as Fickian conditions are reached. According our new quasi-linear these ascend peak values and then diminish gradually toward nonzero asymptotes proportional σY4 when conductivity variance σY2 much less than 1. All existing agree that isotropic asymptotic longitudinal dispersivity < 1, all nominally restricted mildly heterogeneous this inequality satisfied. However, appears be prone error extended strongly because it deals with above without formally limiting σY2. It predicts σY ≫ 1 media, both monotonically σY.