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Earth System Dynamics An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/esd-2019-37
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/esd-2019-37
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 29 Jul 2019

Submitted as: research article | 29 Jul 2019

Review status
This discussion paper is a preprint. A revision of this manuscript was accepted for the journal Earth System Dynamics (ESD) and is expected to appear here in due course.

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

M. Levent Kavvas1, Tongbi Tu2,a, Ali Ercan2, and James Polsinelli1 M. Levent Kavvas et al.
  • 1Hydrologic Research Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA 95616, USA
  • 2J. Amorocho Hydraulics Laboratory (JAHL), Department of Civil and Environmental Engineering, University of California - Davis, CA, 95616, USA
  • anow at: Department of Environmental Science, Policy and Management, University of California, Berkeley, CA 94720

Abstract. 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 multi-dimensional 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, a numerical application to an unconfined aquifer groundwater flow problem is presented to show the skills of the proposed fractional governing equation.

M. Levent Kavvas et al.
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Interactive discussion
Status: closed
Status: closed
AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment
Printer-friendly Version - Printer-friendly version Supplement - Supplement
M. Levent Kavvas et al.
M. Levent Kavvas et al.
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Short summary
After deriving a fractional continuity equation, a previously-developed equation for water flux in porous media was combined with the Dupuit approximation to obtain an equation for groundwater motion in multi-fractional space in unconfined aquifers. As demonstrated in the numerical application, the orders of the fractional space and time derivatives modulate the speed of groundwater table evolution, slowing the process with the decrease in the powers of the fractional derivatives from 1.
After deriving a fractional continuity equation, a previously-developed equation for water flux...
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