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

Persistent Link:
http://hdl.handle.net/10150/185039
Title:
A quasilinear theory of time-dependent nonlocal dispersion in geologic media.
Author:
Zhang, You-Kuan.
Issue Date:
1990
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
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 violated because it deals with the above nonlinearity without formally limiting σᵧ². The theory predicts a significant drop in dimensionless longitudinal dispersivity when σᵧ² is large as compared to the case where σᵧ² is small. As a consequence of this drop the real asymptotic longitudinal dispersivity, which varies in proportion to σᵧ² when σᵧ² is small, is predicted to vary as σᵧ when σᵧ² is large. The dimensionless transverse dispersivity also drops significantly at early dimensionless time when σᵧ² is large. At late time this dispersivity attains a maximum near σᵧ² = 1, varies asymptotically at a rate proportional to σᵧ² when σᵧ² is small, and appears inversely proportional to σᵧ when σᵧ² is large. The actual asymptotic transverse dispersivity varies in proportion to σᵧ⁴ when σᵧ² is small and appears proportional to σᵧ when σᵧ² is large. One of the most interesting findings is that when the mean seepage velocity vector μ is at an angle to the principal axes of statistical anisotropy, the orientation of longitudinal spread is generally offset from μ toward the direction of largest log hydraulic conductivity correlation scale. When local dispersion is active, a plume starts elongating parallel to μ. With time the long axis of the plume rotates toward the direction of largest correlation scale, then rotates back toward μ, and finally stabilizes asymptotically at a relatively small angle of deflection. Application of the theory to depth-averaged concentration data from the recent tracer experiment at Borden, Ontario, yields a consistent and improved fit without any need for parameter adjustment.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Groundwater flow -- Mathematical models; Porous materials -- Mathematical models; Quasilinearization; Stochastic analysis.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Hydrology and Water Resources; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Neuman, Shlomo P.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleA quasilinear theory of time-dependent nonlocal dispersion in geologic media.en_US
dc.creatorZhang, You-Kuan.en_US
dc.contributor.authorZhang, You-Kuan.en_US
dc.date.issued1990en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractA 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 violated because it deals with the above nonlinearity without formally limiting σᵧ². The theory predicts a significant drop in dimensionless longitudinal dispersivity when σᵧ² is large as compared to the case where σᵧ² is small. As a consequence of this drop the real asymptotic longitudinal dispersivity, which varies in proportion to σᵧ² when σᵧ² is small, is predicted to vary as σᵧ when σᵧ² is large. The dimensionless transverse dispersivity also drops significantly at early dimensionless time when σᵧ² is large. At late time this dispersivity attains a maximum near σᵧ² = 1, varies asymptotically at a rate proportional to σᵧ² when σᵧ² is small, and appears inversely proportional to σᵧ when σᵧ² is large. The actual asymptotic transverse dispersivity varies in proportion to σᵧ⁴ when σᵧ² is small and appears proportional to σᵧ when σᵧ² is large. One of the most interesting findings is that when the mean seepage velocity vector μ is at an angle to the principal axes of statistical anisotropy, the orientation of longitudinal spread is generally offset from μ toward the direction of largest log hydraulic conductivity correlation scale. When local dispersion is active, a plume starts elongating parallel to μ. With time the long axis of the plume rotates toward the direction of largest correlation scale, then rotates back toward μ, and finally stabilizes asymptotically at a relatively small angle of deflection. Application of the theory to depth-averaged concentration data from the recent tracer experiment at Borden, Ontario, yields a consistent and improved fit without any need for parameter adjustment.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectGroundwater flow -- Mathematical modelsen_US
dc.subjectPorous materials -- Mathematical modelsen_US
dc.subjectQuasilinearizationen_US
dc.subjectStochastic analysis.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineHydrology and Water Resourcesen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorNeuman, Shlomo P.en_US
dc.contributor.committeememberMaddock, Thomas, IIIen_US
dc.contributor.committeememberWright, A. Larryen_US
dc.contributor.committeememberYeh, Jim T.-C.en_US
dc.identifier.proquest9024658en_US
dc.identifier.oclc704364841en_US
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