### Abstract

When the quasi‐linear theory developed in paper 1 is applied to anisotropic media it shows, in contrast to the isotropic case, that longitudinal and transverse dispersivities may become asymptotically proportional to σ_{Y} when the log hydraulic conductivity variance σ_{Y}
^{2} is much smaller than 1. It further implies, among other phenomena, that when the mean seepage velocity vector μ is at an angle to the principal axes of statistical anisotropy, the long axis of a plume is generally offset toward the direction of the largest log hydraulic conductivity correlation scale; when μ is at 45° to the bedding in strongly stratified media, the longitudinal axis is nearly parallel to the bedding under non‐Fickian conditions. As Fickian conditions are approached, the plume rotates toward μ and stabilizes asymptotically at a relatively small angle of deflection depending on σ_{Y}
^{2}. Application of the quasi‐linear theory to depth‐averaged concentration data from a tracer experiment at Borden, Ontario, yields a consistent and improved fit to a two‐dimensional model without any need for parameter adjustment. Three‐dimensional models are shown to be in fundamental conflict with observed behavior at Borden and in other stratified formations; we show that, in principle, this conflict is easy to resolve by accounting for local hydraulic anisotropy.

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

Pages (from-to) | 903-913 |

Number of pages | 11 |

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 : 2. Application to anisotropic media and the Borden site.** / Zhang, You‐Kuan ‐K; Neuman, Shlomo P.

Research output: Contribution to journal › Article

*Water Resources Research*, vol. 26, no. 5, pp. 903-913. https://doi.org/10.1029/WR026i005p00903

}

TY - JOUR

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

T2 - 2. Application to anisotropic media and the Borden site

AU - Zhang, You‐Kuan ‐K

AU - Neuman, Shlomo P

PY - 1990

Y1 - 1990

N2 - When the quasi‐linear theory developed in paper 1 is applied to anisotropic media it shows, in contrast to the isotropic case, that longitudinal and transverse dispersivities may become asymptotically proportional to σY when the log hydraulic conductivity variance σY 2 is much smaller than 1. It further implies, among other phenomena, that when the mean seepage velocity vector μ is at an angle to the principal axes of statistical anisotropy, the long axis of a plume is generally offset toward the direction of the largest log hydraulic conductivity correlation scale; when μ is at 45° to the bedding in strongly stratified media, the longitudinal axis is nearly parallel to the bedding under non‐Fickian conditions. As Fickian conditions are approached, the plume rotates toward μ and stabilizes asymptotically at a relatively small angle of deflection depending on σY 2. Application of the quasi‐linear theory to depth‐averaged concentration data from a tracer experiment at Borden, Ontario, yields a consistent and improved fit to a two‐dimensional model without any need for parameter adjustment. Three‐dimensional models are shown to be in fundamental conflict with observed behavior at Borden and in other stratified formations; we show that, in principle, this conflict is easy to resolve by accounting for local hydraulic anisotropy.

AB - When the quasi‐linear theory developed in paper 1 is applied to anisotropic media it shows, in contrast to the isotropic case, that longitudinal and transverse dispersivities may become asymptotically proportional to σY when the log hydraulic conductivity variance σY 2 is much smaller than 1. It further implies, among other phenomena, that when the mean seepage velocity vector μ is at an angle to the principal axes of statistical anisotropy, the long axis of a plume is generally offset toward the direction of the largest log hydraulic conductivity correlation scale; when μ is at 45° to the bedding in strongly stratified media, the longitudinal axis is nearly parallel to the bedding under non‐Fickian conditions. As Fickian conditions are approached, the plume rotates toward μ and stabilizes asymptotically at a relatively small angle of deflection depending on σY 2. Application of the quasi‐linear theory to depth‐averaged concentration data from a tracer experiment at Borden, Ontario, yields a consistent and improved fit to a two‐dimensional model without any need for parameter adjustment. Three‐dimensional models are shown to be in fundamental conflict with observed behavior at Borden and in other stratified formations; we show that, in principle, this conflict is easy to resolve by accounting for local hydraulic anisotropy.

UR - http://www.scopus.com/inward/record.url?scp=0000403189&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000403189&partnerID=8YFLogxK

U2 - 10.1029/WR026i005p00903

DO - 10.1029/WR026i005p00903

M3 - Article

VL - 26

SP - 903

EP - 913

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 5

ER -