Articles | Volume 21, issue 3
Hydrol. Earth Syst. Sci., 21, 1547–1557, 2017
https://doi.org/10.5194/hess-21-1547-2017

Special issue: Modeling hydrological processes and changes

Hydrol. Earth Syst. Sci., 21, 1547–1557, 2017
https://doi.org/10.5194/hess-21-1547-2017

Research article 13 Mar 2017

Research article | 13 Mar 2017

Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time

M. Levent Kavvas et al.

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Cited articles

Baumer, B. and Meerschaert, M. M.: Fractional diffusion with two time scales, Physica A, 373, 237–251, 2007.
Baumer, B., Benson, D., and Meerschaert, M. M.: Advection and dispersion in time and space, Physica A, 350, 245–262, 2005.
Bear, J.: Hydraulics of groundwater, McGraw-Hill Inc., New York, 1979.
Benson, D. A., Wheatcraft, S. W., and Meerschaert, M. M.: Application of a fractional advection-dispersion equation, Water Resour. Res., 36, 1403–1412, 2000a.
Benson, D. A., Wheatcraft, S. W., and Meerschaert, M. M.: The fractional-order governing equation of Levy motion, Water Resour. Res., 36, 1413–1423, 2000b.
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Short summary
In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. By the introduction of the Brooks–Corey constitutive relationships, an explicit form of the equations is obtained. The developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations.