DOI: 10.5194/hess-21-1547-2017
Scopus记录号: 2-s2.0-85015165958
论文题名: Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time
作者: Levent Kavvas M ; , Ercan A ; , Polsinelli J
刊名: Hydrology and Earth System Sciences
ISSN: 10275606
出版年: 2017
卷: 21, 期: 3 起始页码: 1547
结束页码: 1557
语种: 英语
Scopus关键词: Anisotropic media
; Anisotropy
; Equations of motion
; Flow of water
; Hydraulics
; Soil moisture
; Soils
; Constitutive relationships
; Continuity equations
; Diffusive behavior
; Fractional derivatives
; Fractional equation
; Governing equations
; Soil water fluxes
; Vertical direction
; Time and motion study
; anisotropic medium
; anisotropy
; equation
; flux measurement
; hydraulic conductivity
; Richards equation
; soil water
; vertical distribution
; water flow
英文摘要: In this study dimensionally consistent governing equations of continuity and motion for transient soil water flow and soil water flux in fractional time and in fractional multiple space dimensions in anisotropic media are developed. Due to the anisotropy in the hydraulic conductivities of natural soils, the soil medium within which the soil water flow occurs is essentially anisotropic. Accordingly, in this study the fractional dimensions in two horizontal and one vertical directions are considered to be different, resulting in multi-fractional multi-dimensional soil space within which the flow takes place. 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. It is shown that the fractional soil water flow continuity equation approaches the conventional integer form of the continuity equation as the fractional derivative powers approach integer values. For the motion equation of soil water flow, or the equation of water flux within the soil matrix in multi-dimensional fractional soil space and fractional time, a dimensionally consistent equation is also developed. Again, it is shown that this fractional water flux equation approaches the conventional Darcy equation as the fractional derivative powers approach integer values. From the combination of the fractional continuity and motion 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 and of only horizontal 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. © The Author(s) 2017. Citation statistics:
资源类型: 期刊论文
标识符: http://119.78.100.158/handle/2HF3EXSE/79224
Appears in Collections: 气候变化事实与影响
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作者单位: Hydrologic Research Laboratory, Department of Civil and Environmental Engineering, University of California, Davis, CA, United States
Recommended Citation:
Levent Kavvas M,, Ercan A,, Polsinelli J. Governing equations of transient soil water flow and soil water flux in multi-dimensional fractional anisotropic media and fractional time[J]. Hydrology and Earth System Sciences,2017-01-01,21(3)