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

2017 ◽  
Vol 21 (3) ◽  
pp. 1547-1557 ◽  
Author(s):  
M. Levent Kavvas ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Fractional Derivative ◽  
Soil Water ◽  
Water Flow ◽  
Continuity Equation ◽  
Water Flux ◽  
Anisotropic Media ◽  
Governing Equations ◽  
Soil Matrix ◽  
Soil Water Flow ◽  
Soil Water Flux

Abstract. 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.

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

2016 ◽  
Author(s):  
M. Levent Kavvas ◽  
Ali Ercan ◽  
James Polsinelli
Keyword(s):  
Fractional Derivative ◽  
Soil Water ◽  
Water Flow ◽  
Continuity Equation ◽  
Water Flux ◽  
Anisotropic Media ◽  
Governing Equations ◽  
Soil Matrix ◽  
Soil Water Flow ◽  
Soil Water Flux

Abstract. 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's 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.

scholarly journals Numerical Evaluation of Fractional Vertical Soil Water Flow Equations

Water ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 511
Author(s):  
Ali Ercan ◽  
M. Levent Kavvas
Keyword(s):  
Porous Media ◽  
Soil Water ◽  
Water Flow ◽  
Water Movement ◽  
Least Square ◽  
Flow In Porous Media ◽  
Fickian Diffusion ◽  
Richards Equation ◽  
Governing Equations ◽  
Soil Water Flow

Significant deviations from standard Boltzmann scaling, which corresponds to normal or Fickian diffusion, have been observed in the literature for water movement in porous media. However, as demonstrated by various researchers, the widely used conventional Richards equation cannot mimic anomalous diffusion and ignores the features of natural soils which are heterogeneous. Within this framework, governing equations of transient water flow in porous media in fractional time and multi-dimensional fractional soil space in anisotropic media were recently introduced by the authors by coupling Brooks–Corey constitutive relationships with the fractional continuity and motion equations. In this study, instead of utilizing Brooks–Corey relationships, empirical expressions, obtained by least square fits through hydraulic measurements, were utilized to show the suitability of the proposed fractional approach with other constitutive hydraulic relations in the literature. Next, a finite difference numerical method was proposed to solve the fractional governing equations. The applicability of the proposed fractional governing equations was investigated numerically in comparison to their conventional counterparts. In practice, cumulative infiltration values are observed to deviate from conventional infiltration approximation, or the wetting front through time may not be consistent with the traditional estimates of Richards equation. In such cases, fractional governing equations may be a better alternative for mimicking the physical process as they can capture sub-, super-, and normal-diffusive soil water flow processes during infiltration.

scholarly journals Simulating preferential soil water flow and tracer transport using the Lagrangian Soil Water and Solute Transport Model

2019 ◽  
Author(s):  
Alexander Sternagel ◽  
Ralf Loritz ◽  
Wolfgang Wilcke ◽  
Erwin Zehe
Keyword(s):  
Solute Transport ◽  
Soil Water ◽  
Water Flow ◽  
Field Experiments ◽  
Preferential Flow ◽  
Sensitivity Analyses ◽  
Tracer Transport ◽  
Soil Matrix ◽  
Soil Water Flow ◽  
Water And Solute Transport

Abstract. We propose an alternative model to overcome these weaknesses of the Darcy-Richards approach and to simulate preferential soil water flow and tracer transport in macroporous soils. Our LAST-Model (Lagrangian Soil Water and Solute Transport) relies on a Lagrangian perspective on the movement of water particles carrying a solute mass through the soil matrix and macropores. We advance the model of Zehe and Jackisch (2016) by two main extensions: a) a new routine for solute transport within the soil matrix and b) the implementation of an additional 1-D preferential flow domain which simulates flow and transport in a population of macropores. Infiltration into the matrix and the macropores depends on their moisture state and subsequently macropores are gradually filled. Macropores and matrix interact through diffusive mixing of water and solutes between the two domains which depends on their water content and matric potential at the considered depths. The LAST-Model is then evaluated with sensitivity analyses and tested against tracer field experiments at three different sites. The results show the internal and physical validity of the model and the robustness of our solute transport and the linear mixing approach. Further, the model is able to simulate preferential flow through macropores and to depict well the observed 1-D solute mass profile of a tracer experiment with a high computational efficiency and short simulation times.

scholarly journals Capillary rise affecting crop yields under different environmental conditions

2016 ◽  
Author(s):  
Joop Kroes ◽  
Iwan Supit ◽  
Martin Mulder ◽  
Jos Van Dam ◽  
Paul Van Walsum
Keyword(s):  
Soil Water ◽  
Water Flow ◽  
Crop Yields ◽  
Capillary Rise ◽  
Water Flux ◽  
Flow Regimes ◽  
Crop Growth ◽  
Groundwater Levels ◽  
Soil Water Flow ◽  
The Impact

Abstract. This paper describes analyses of different soil water flow regimes on growth and yields of grass, maize and potato crops in the Dutch delta, with a focus on the role of capillary rise. Different flow regimes are characterised by differences in soil composition and structure are derived from a national soil database. Capillary rise and its influence on crop growth and resulting yields is simulated using Swap-Wofost with different boundary conditions. Case studies and model experiments are used to illustrate the impact of capillary rise. This impact is clearly present in situations where a groundwater level is present (85 % of NL) but also in other situations the impact of capillary rise on crop growth and production is considerable. When one compares situations with average groundwater levels with free drainage conditions without capillary rise yield-reductions of grassland, maize and potatoes are respectively 25, 4 and 15 % or respectively about 3.2, 0.5 and 1.6 ton dry Matter per ha. Neglecting capillary rise also has impact on the downward leaching water flux, the groundwater recharge. Impact can be considerable; for grassland and potatoes the reduction is 17 and 46 % or 64 and 34 mm. Modelling of soil water flow should consider capillary rise of soil water which will results in improved yield and downward leaching simulations.

scholarly journals Soil water flow due to surface topography in research drainage plots

age ◽  
2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Sally Logsdon ◽  
Cindy Cambardella
Keyword(s):  
Surface Topography ◽  
Soil Water ◽  
Water Flow ◽  
Soil Water Flow
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