Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time

<p>In this study, a dimensionally consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For...

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Main Authors: M. L. Kavvas, T. Tu, A. Ercan, J. Polsinelli
Format: Article
Language:English
Published: Copernicus Publications 2020-01-01
Series:Earth System Dynamics
Online Access:https://www.earth-syst-dynam.net/11/1/2020/esd-11-1-2020.pdf
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spelling doaj-ec2d6a2cd1724752b7cc2d29f7304e342020-11-25T03:22:51ZengCopernicus PublicationsEarth System Dynamics2190-49792190-49872020-01-011111210.5194/esd-11-1-2020Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional timeM. L. Kavvas0T. Tu1T. Tu2A. Ercan3J. Polsinelli4Hydrologic Research Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, USAJ. Amorocho Hydraulics Laboratory (JAHL), Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, USAnow at: Department of Environmental Science, Policy, and Management, University of California, Berkeley, CA 94720, USAJ. Amorocho Hydraulics Laboratory (JAHL), Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, USAHydrologic Research Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, USA<p>In this study, a dimensionally consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multidimensional unconfined aquifer, a previously developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, two numerical applications to unconfined aquifer groundwater flow are presented to show the skills of the proposed fractional governing equation. As shown in one of the numerical applications, the newly developed governing equation can produce heavy-tailed recession behavior in unconfined aquifer discharges.</p>https://www.earth-syst-dynam.net/11/1/2020/esd-11-1-2020.pdf
collection DOAJ
language English
format Article
sources DOAJ
author M. L. Kavvas
T. Tu
T. Tu
A. Ercan
J. Polsinelli
spellingShingle M. L. Kavvas
T. Tu
T. Tu
A. Ercan
J. Polsinelli
Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time
Earth System Dynamics
author_facet M. L. Kavvas
T. Tu
T. Tu
A. Ercan
J. Polsinelli
author_sort M. L. Kavvas
title Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time
title_short Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time
title_full Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time
title_fullStr Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time
title_full_unstemmed Fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time
title_sort fractional governing equations of transient groundwater flow in unconfined aquifers with multi-fractional dimensions in fractional time
publisher Copernicus Publications
series Earth System Dynamics
issn 2190-4979
2190-4987
publishDate 2020-01-01
description <p>In this study, a dimensionally consistent governing equation of transient unconfined groundwater flow in fractional time and multi-fractional space is developed. First, a fractional continuity equation for transient unconfined groundwater flow is developed in fractional time and space. For the equation of groundwater motion within a multi-fractional multidimensional unconfined aquifer, a previously developed dimensionally consistent equation for water flux in unsaturated/saturated porous media is combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. Combining the fractional continuity and groundwater motion equations, the fractional governing equation of transient unconfined aquifer flow is then obtained. Finally, two numerical applications to unconfined aquifer groundwater flow are presented to show the skills of the proposed fractional governing equation. As shown in one of the numerical applications, the newly developed governing equation can produce heavy-tailed recession behavior in unconfined aquifer discharges.</p>
url https://www.earth-syst-dynam.net/11/1/2020/esd-11-1-2020.pdf
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