Hydro-Climate Symposium

Oral

394493 - Equations of transient water flow and water flux in multi–dimensional fractional anisotropic soil media and fractional time

Wednesday, June 6
4:00 PM - 5:30 PM
Location: Lake Superior B

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 dimensionally-consistent continuity equation for soil water flow in multi-dimensional fractional soil space and fractional time is developed. For the equation of water flux in multi-dimensional 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 multi-dimensional 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 Brooks-Corey constitutive relationships for soil water into the fractional transient soil water flow equation, an explicit form of the equation is obtained in multi-dimensional fractional soil space and fractional time. The governing fractional equation is then specialized to the case of only vertical soil water flow in fractional time-space. 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.

M Levent Kavvas, California

Distinguished Professor
University of California, Davis

Presentation(s):

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Ali Ercan, California

Asst. Professional Researcher
UC Davis

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394493 - Equations of transient water flow and water flux in multi–dimensional fractional anisotropic soil media and fractional time



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