### Abstract

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 of log hydraulic conductivities. Existing linear theories predict that, in the absence of local dispersion, transverse dispersivities tend asymptotically to zero as Fickian conditions are reached. According to our new quasi‐linear theory these dispersivities ascend to peak values and then diminish gradually toward nonzero Fickian asymptotes which are proportional to σ_{Y}
^{4} when the log hydraulic conductivity variance σ_{Y}
^{2} is much less than 1. All existing theories agree that in isotropic media the asymptotic longitudinal dispersivity is proportional to σ_{Y}
^{2} when σ_{Y}
^{2} <1, and all are nominally restricted to mildly heterogeneous media in which this inequality is satisfied. However, the quasi‐linear theory appears to be less prone to error than linear theories when extended to strongly heterogeneous media because it deals with the above nonlinearity without formally limiting σ_{Y}
^{2}. It predicts that when σ_{Y} ≫ 1 in isotropic media, both the longitudinal and transverse dispersivities ascend monotonically toward Fickian asymptotes proportional to σ_{Y}.

Original language | English (US) |
---|---|

Pages (from-to) | 887-902 |

Number of pages | 16 |

Journal | Water Resources Research |

Volume | 26 |

Issue number | 5 |

DOIs | |

State | Published - 1990 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Water Science and Technology

### Cite this

**A quasi‐linear theory of non‐Fickian and Fickian subsurface dispersion : 1. Theoretical analysis with application to isotropic media.** / Neuman, Shlomo P; Zhang, You‐Kuan ‐K.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 26, no. 5, pp. 887-902. https://doi.org/10.1029/WR026i005p00887

}

TY - JOUR

T1 - A quasi‐linear theory of non‐Fickian and Fickian subsurface dispersion

T2 - 1. Theoretical analysis with application to isotropic media

AU - Neuman, Shlomo P

AU - Zhang, You‐Kuan ‐K

PY - 1990

Y1 - 1990

N2 - 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 of log hydraulic conductivities. Existing linear theories predict that, in the absence of local dispersion, transverse dispersivities tend asymptotically to zero as Fickian conditions are reached. According to our new quasi‐linear theory these dispersivities ascend to peak values and then diminish gradually toward nonzero Fickian asymptotes which are proportional to σY 4 when the log hydraulic conductivity variance σY 2 is much less than 1. All existing theories agree that in isotropic media the asymptotic longitudinal dispersivity is proportional to σY 2 when σY 2 <1, and all are nominally restricted to mildly heterogeneous media in which this inequality is satisfied. However, the quasi‐linear theory appears to be less prone to error than linear theories when extended to strongly heterogeneous media because it deals with the above nonlinearity without formally limiting σY 2. It predicts that when σY ≫ 1 in isotropic media, both the longitudinal and transverse dispersivities ascend monotonically toward Fickian asymptotes proportional to σY.

AB - 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 of log hydraulic conductivities. Existing linear theories predict that, in the absence of local dispersion, transverse dispersivities tend asymptotically to zero as Fickian conditions are reached. According to our new quasi‐linear theory these dispersivities ascend to peak values and then diminish gradually toward nonzero Fickian asymptotes which are proportional to σY 4 when the log hydraulic conductivity variance σY 2 is much less than 1. All existing theories agree that in isotropic media the asymptotic longitudinal dispersivity is proportional to σY 2 when σY 2 <1, and all are nominally restricted to mildly heterogeneous media in which this inequality is satisfied. However, the quasi‐linear theory appears to be less prone to error than linear theories when extended to strongly heterogeneous media because it deals with the above nonlinearity without formally limiting σY 2. It predicts that when σY ≫ 1 in isotropic media, both the longitudinal and transverse dispersivities ascend monotonically toward Fickian asymptotes proportional to σY.

UR - http://www.scopus.com/inward/record.url?scp=84945098599&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84945098599&partnerID=8YFLogxK

U2 - 10.1029/WR026i005p00887

DO - 10.1029/WR026i005p00887

M3 - Article

AN - SCOPUS:84945098599

VL - 26

SP - 887

EP - 902

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 5

ER -