M Levent Kavvas, California
Distinguished Professor
University of California, Davis
Presentation(s):

Wednesday, June 6
4:00 PM – 5:30 PM
HydroClimate Symposium
Oral
M Levent Kavvas, California
Distinguished Professor
University of California, Davis
Ali Ercan, California
Asst. Professional Researcher
UC Davis
In this study governing equations for transient soil water flow and soil water flux in fractional time and in fractional multidimensional anisotropic soil media are developed. Toward the development of the fractional governing equations, first a dimensionallyconsistent continuity equation for soil water flow in multidimensional fractional soil space and fractional time is developed. For the equation of water flux in multidimensional fractional soil space and fractional time, a dimensionally consistent equation is also developed. It is shown that this fractional water flux equation approaches the conventional Darcy's equation as the fractional derivative powers approach integer values. From the combination of the fractional continuity and water flux equations, the governing equation of transient soil water flow in multidimensional fractional soil space and fractional time is obtained. It is shown that this equation approaches the conventional Richards equation as the fractional derivative powers approach integer values. Then by the introduction of the BrooksCorey constitutive relationships for soil water into the fractional transient soil water flow equation, an explicit form of the equation is obtained in multidimensional fractional soil space and fractional time. The governing fractional equation is then specialized to the case of only vertical soil water flow in fractional timespace. It is shown that the developed governing equations, in their fractional time but integer space forms, show behavior consistent with the previous experimental observations concerning the diffusive behavior of soil water flow.
Distinguished Professor
University of California, Davis
Wednesday, June 6
4:00 PM – 5:30 PM
Asst. Professional Researcher
UC Davis
Wednesday, June 6
4:00 PM – 5:30 PM
394715  Numerical Application to One Dimensional Fractional Soil Water Flow
Wednesday, June 6
4:00 PM – 5:30 PM
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