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1.
The traditional Richards’ equation implies that the wetting front in unsaturated soil follows Boltzmann scaling, with travel distance growing as the square root of time. This study proposes a fractal Richards’ equation (FRE), replacing the integer-order time derivative of water content by a fractal derivative, using a power law ruler in time. FRE solutions exhibit anomalous non-Boltzmann scaling, attributed to the fractal nature of heterogeneous media. Several applications are presented, fitting the FRE to water content curves from previous literature. 相似文献
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《Advances in water resources》1999,23(3):217-228
The performance of in situ bioremediation to remove organic contaminants from contaminated aquifers depends on the physical and biochemical parameters. We characterize the performance by the contaminant removal rate and the region where biodegradation occurs, the biologically active zone (BAZ). The numerical fronts obtained by one-dimensional in situ bioremediation modeling reveal a traveling wave behavior: fronts of microbial mass, organic contaminant and electron acceptor move with a constant velocity and constant front shape through the domain. Hence, only one front shape and a linear relation between the front position and time is found for each of the three compounds. We derive analytical approximations for the traveling wave front shape and front position that agree perfectly with the traveling wave behavior resulting from the bioremediation model. Using these analytical approximations, we determine the contaminant removal rate and the BAZ. Furthermore, we assess the influence of the physical and biochemical parameters on the performance of the in situ bioremediation technique. 相似文献
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M. H. G. AMIN R. J. CHORLEY K. S. RICHARDS L. D. HALL T. A. CARPENTER MELENA CISLEROVA THOMAS VOGEL 《水文研究》1997,11(5):471-483
In this paper, the feasibility of using magnetic resonance imaging (MRI) to study water infiltration into a heterogeneous soil is examined, together with its difficulties and limitations. MRI studies of ponded water infiltration into an undisturbed soil core show that the combination of one- and two-dimensional imaging techniques provides a visual and non-destructive means of monitoring the temporal changes of soil water content and the moisture profile, and the movement of the wetting front. Two-dimensional images show air entrapment in repetitive ponded infiltration experiments. During the early stages of infiltration, one-dimensional images of soil moisture profiles clearly indicate preferential flow phenomena. The observed advance of wetting fronts can be described by a linear relationship between the square root of infiltration time (√t) and the distance of the wetting front from the soil surface. Similarly, the cumulative infiltration is also directly proportional to √t. Furthermore, from the MRI infiltration moisture profiles, it is possible to estimate the parameters that feature in infiltration equations. © 1997 by John Wiley & Sons, Ltd. 相似文献
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《Advances in water resources》2005,28(10):1021-1027
In uniform soils that are susceptible to unstable preferential flow, the water saturation exhibits a nonmonotonic profile upon continuous infiltration. This overshoot cannot be described by the conventional Richards equation. Here, solutions to the infiltrations using a popular nonequilibrium extension to the Richards equation are obtained using the traveling wave nature of the saturation profile. Quantitative comparisons are made to recent measurements of saturation overshoot. The nonequilibrium solutions can be made to fit the flux range of the overshoot, but the fit to the tip saturations is fair to poor at best. Also, small changes in porous media size and roughness require large changes in the magnitude of the nonequilibrium term to match the flux range. The results suggest that the nonequilibrium capillary pressure does not include the correct physics that controls the overshoot. 相似文献
6.
Interplay between capillary, gravity and viscous forces in unsaturated porous media gives rise to a range of complex flow phenomena affecting morphology, stability and dynamics of wetting and drainage fronts. Similar average phase contents may result in significantly different fluid distribution and patterns affecting macroscopic transport properties of the unsaturated medium. The formulation of general force balance within simplified pore spaces yields scaling relationships for motion of liquid elements in which gravitational force in excess of capillary pinning force scales linearly with viscous force. Displacement fluid front morphology is described using dimensionless force ratios expressed as Bond and Capillary numbers. The concise representations of a wide range of flow regimes with scaling relations, and predictive capabilities of front morphology based on dimensionless numbers lend support to certain generalizations. Considering available experimental data, we are able to define conditions for onset of unstable and intermittent flows leading to enhanced liquid and gas entrapment. These results provide a basis for delineation of a tentative value of Bo ∼ 0.05 as an upper limit of applicability of the Richards equation (at pore to sample scales) and related continuum-based flow models. 相似文献
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We provide closed-form approximate solutions to models of horizontal infiltration described by the Boussinesq equation in a semi-infinite aquifer that is initially dry. The approximations preserve such important qualitative properties as scaling and wetting fronts. They are applicable to four types of boundary conditions, two on head and two on flux, enumerated in the paper. All the considered problems admit self-similar variables that allow reduction to boundary value problems for a nonlinear ordinary differential equation. This work extends recent results by Lockington et al. [Lockington DA, Parlange J-Y, Parlange MB, Selker J. Similarity solution of the Boussinesq equation. Adv Water Resour 2000;23(7):725–9] and Telyakovskiy et al. [Telyakovskiy AS, Braga GA, Furtado F. Approximate similarity solutions to the Boussinesq equation. Adv Water Resour 2002;25(2):191–4], with new approximations developed for two of the four cases and a new extension of a previously existing method for a third case. Numerical results extending the work of Shampine [Shampine LF. Some singular concentration dependent diffusion problems. ZAMM 1973;53:421–2] provide a basis for assessing the accuracy of the new methods. 相似文献
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The analysis of infiltration of 2D trickle irrigation under multiple‐line sources, governed by the celebrated Richards equation, is performed, aiming at determining the efficiency of trickle irrigation so as to reduce the water demand. A closed‐form solution is explicitly obtained by utilizing the Fourier integral transformation, and this serves as a means to compute the distribution of volumetric water content during trickle irrigation. Results for the infiltration of 2D trickle irrigation under single line and multiple‐line sources are presented, which illustrate the distribution of infiltration water that diffuses into the soil, and make it possible to calculate the period of time required for trickle irrigation for different plants. The results can be applied to verify complicated solutions from other numerical models. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Yoshisuke Nakano 《Advances in water resources》1983,6(2):71-78
The asymptotic behavior of solutions to the problem of wetting fronts is studied in one-dimensional, horizontal and infinite porous media with the soil-water diffusivity proportional to some power of the water content. The uniqueness of the similarity solution for the problem is studied and the properties of this solution are presented. It is shown that the similarity solution is an asymptotic solution of a wide class of initial value problems of wetting fronts in the media. The use of the similarity solution is discussed for the experimental determination of the soil-water diffusivity. 相似文献
10.
《水文科学杂志》2013,58(2):349-362
Abstract A methodology of time-step estimation for numerically solving the Richards equation is discussed. Its importance in simulating water movement in unsaturated—saturated soils is shown for infiltration into a soil profile by applying various time-step estimations and boundary conditions for different soils. In order to test the results of the computations, infiltration theory was applied. According to infiltration theory, the pressure head in the initially unsaturated part will not take positive values as long as the moisture front has not reached the phreatic level, or, in the case of a profile with a free-draining lower boundary, it is not saturated at the base. In other cases, the appearance of positive values of the pressure head produces incorrect values for the inflow rate q. 相似文献
11.
Analytical solutions for the water flow and solute transport equations in the unsaturated zone are presented. We use the Broadbridge and White nonlinear model to solve the Richards’ equation for vertical flow under a constant infiltration rate. Then we extend the water flow solution and develop an exact parametric solution for the advection-dispersion equation. The method of characteristics is adopted to determine the location of a solute front in the unsaturated zone. The dispersion component is incorporated into the final solution using a singular perturbation method. The formulation of the analytical solutions is simple, and a complete solution is generated without resorting to computationally demanding numerical schemes. Indeed, the simple analytical solutions can be used as tools to verify the accuracy of numerical models of water flow and solute transport. Comparison with a finite-element numerical solution indicates that a good match for the predicted water content is achieved when the mesh grid is one-fourth the capillary length scale of the porous medium. However, when numerically solving the solute transport equation at this level of discretization, numerical dispersion and spatial oscillations were significant. 相似文献
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We studied the problem of local‐ and field‐scale infiltration over a particular class of heterogeneous soils. At the local scale, the soils are described as being vertically non‐uniform, with the saturated hydraulic conductivity continuously decreasing with depth according to a power law function. Analogous to the Green–Ampt model, analytical expressions are first developed for local‐scale infiltration using a sharp front approximation, and model results are compared with numerical solutions of the Richards equation. These results show that saturation does not occur from below in soils with such vertical non‐uniformity, thereby allowing for the use of a sharp front approximation. Because of vertical non‐uniformity, ponding conditions are achieved locally even for rainfall rates less than the surface saturated hydraulic conductivity. Furthermore, infiltration rates asymptotically approach zero at long times. To determine field‐scale infiltration properties, the spatial variability in the surface saturated hydraulic conductivity is represented by a log‐normal random field. Using cumulative infiltration as the independent variable, expressions are developed for the ensemble mean of field‐scale infiltration and the expected time for a given depth of water to infiltrate over the field. Surface horizontal heterogeneity is found to control field‐scale infiltration at small times, whereas local vertical non‐uniformity exerts a strong control at long times. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
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《Advances in water resources》1998,22(2):103-116
We consider a one-dimensional model biodegradation system consisting of two reaction–advection equations for nutrient and pollutant concentrations and a rate equation for biomass. The hydrodynamic dispersion is ignored. Under an explicit condition on the decay and growth rates of biomass, the system can be approximated by two component models by setting biomass kinetics to equilibrium. We derive closed form solutions for constant speed traveling fronts for the reduced two component models and compare their profiles in homogeneous media. For a spatially random velocity field, we introduce travel time and study statistics of degradation fronts via representations in terms of the travel time probability density function (pdf) and the traveling front profiles. The travel time pdf does not vary with the nutrient and pollutant concentrations and only depends on the random water velocity. The traveling front profiles are expressed analytically or semi-analytically as functions of the travel time. The problem of nonlinear transport by a random velocity reduces to two subproblems: one being nonlinear transport by a known (unit) velocity, and the other being linear (advective) transport by a random velocity. The approach is illustrated through some examples where the randomness in velocity stems from the spatial variability of porosity. 相似文献
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Spatial distribution of soil macroporosity was determined for a forest podzol from tension infiltrometer measurements at the soil surface. Surface‐derived macroporosity values were compared with point infiltration characteristics obtained from soil water content and soil water chemistry measurements during an experimental irrigation, and with parameters of a kinematic wave model applied to soil water content data. Macroporosity estimated by the tension infiltrometer ranged from 0·00087 to 0·0219% of soil volume, and infiltration at these two sites was dominated by propagation of a well‐defined wetting front through the soil profile and bypass flow via soil macropores, respectively. Infiltration at sites with intermediate macroporosities reflected a combination of these two processes, although results were inconclusive at one site owing to lateral flow at the base of the soil profile. There was no agreement between macroporosities estimated by the tension infiltrometer and the kinematic wave model. The maximum soil conductance parameter within the profile at a site, however, was related directly to the surface‐derived macroporosity. The partial agreement between surface‐derived macroporosity estimates and point infiltration characteristics shown here supports the use of tension infiltrometry as a rapid, non‐destructive method of assessing spatial variations in the relative contribution of macropore flow to the infiltration process. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
15.
《Advances in water resources》1998,21(4):315-324
The paper deals with numerical solutions to the Richards equation to simulate one-dimensional flow processes in the unsaturated zone of layered soil profiles. The equation is expressed in the pressure-based form and a finite-difference algorithm is developed for accurately estimating the values of the hydraulic conductivity between two neighboring nodes positioned in different soil layers, often referred to as the interlayer hydraulic conductivity. The algorithm is based upon flux conservation and continuity of pressure potential at the interface between two consecutive layers, and does not add significantly to simulation run time. The validity of the model is established for a number of test problems by comparing numerical results with the analytical solutions developed by Srivastava and Yeh29 which hold for vertical infiltration towards the water table in a two-layer soil profile. The results show a significant reduction in relative mass balance errors when using the proposed model. Some specific insights into its numerical performance are also gained by comparisons with a numerical model in which the more common geometric averaging operator acts on the interlayer conductivities. 相似文献
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Nathan Paldor 《地球物理与天体物理流体动力学》2013,107(3):171-191
Abstract It is shown that the inclusion of the nonlinear terms in the equations of motion of a coupled density front of zero potential vorticity results in wave solutions which merely propagate with time. The linear theory, on the other hand, predicts an exponential temporal growth. The nonlinear equation admits steady solutions representing standing waves whereas if the nonlinear terms are omitted no steady solutions exist. The general initial value problem is difficult to solve numerically since the linear problem is ill posed. In addition we prove that the general similarity solution of the nonlinear equation tends to zero for large times, at any point in space, regardless of the initial condition. 相似文献
17.
Preferred infiltration is mainly perceived as vertically down whereas subsurface storm flow is thought to occur parallel to slopes. The transition from vertical to lateral flow in a layered hillslope soil is the focus of the contribution. Transient flow is assumed to move as a wetting front. Three time‐domain reflectometry (TDR) wave‐guides, each 0·15 m long, were mounted in the shape of a truncated tetrahedron with its peak pointing down. Each wave‐guide focuses the front velocity along its axis. The three front‐velocity vectors are decomposed into their x, y and z components, which are then assembled to the resultant velocity vector. The volume density flux of preferred flow is the product of the front velocity and the mobile water content. The latter is the amplitude of transient soil moisture measured with each wave‐guide. The resultant vector of the volume flux density is computed similarly to the velocity vector. The experimental approach allows for the rapid assessment of transient flows without relying on the variation of water potentials. The experiments indicate that the directions of the resultant vectors of velocity and volume flux density can be estimated if the moisture variations of the three TDR wave‐guides are strongly correlated during the passing of the wetting front. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
18.
V. P. Singh 《水文研究》1995,9(7):783-796
Error equations for the kinematic wave and diffusion wave approximations with lateral inflow neglected in the momentum equation are derived under simplified conditions for space-independent flows. These equations specify error as a function of time in the flow hydrograph. The kinematic wave, diffusion wave and dynamic wave solutions are parameterized through a dimensionless parameter γ which is dependent on the initial conditions. This parameter reflects the effect of initial flow depth, channel-bed slope, lateral inflow, infiltration and channel roughness when the initial condition is non-vanishing; it reflects the effect of bed slope, channel roughness and acceleration due to gravity when the initial condition is vanishing. The error equations are found to be the Riccati equation. The structure of the error equations in the case when the momentum equation neglects lateral inflow is different from that when the lateral inflow is included. 相似文献
19.
Infiltration experiments have been performed at three sites along a well-known catena under virgin tropical rain forest using a portable sprinkling infiltrometer. Experimentally determined infiltration curves are presented. Infiltration curves are also simulated on the basis of the Mein-Larson equation. The parameters for this model have been obtained from the infiltration curves (saturated conductivity) and simple soil moisture determinations (fillable porosity). The agreement between experimentally determined and modelled infiltration is reasonable, provided (a) saturated conductivity as derived from the experimental data is corrected, (b) a storage parameter, also derived from the experimental data, is added to the Mein-Larson model, and (c) the decline in soil porosity with depth is either small or occurs abruptly at shallow depth. Comparison of observed infiltration rates with rainfall intensity shows that Horton Overland Flow has to occur naturally at least on the middle and lower section of the catena. Despite the fact that most parameters can be estimated in principle from basic soil data, it remains advisable to obtain sprinkling infiltrometer field measurements, because of soil variability due to dynamic surface conditions, macroporosity, air entrapment, and irregularity of the wetting front. 相似文献
20.
Hysteresis is a common feature exhibited in hydraulic properties of an unsaturated soil. The movement of wetting front and the hysteresis effect are important factors which impact the shear strength of the unsaturated soil and the mechanics of shallow landslides. These failures are mainly triggered by the deepening of the wetting front accompanied by a decrease in matric suction induced by infiltration. This research establishes a method for determining a stability analysis of unsaturated infinite soil slopes, integrating the influence of infiltration and the water retention curve hysteresis. Furthermore, the present stability analysis method including the infiltration model and the advanced Mohr–Coulomb failure criterion calculates the variations of the safety factor (FS) in accordance with different slope angle, depth and hydrological processes. The experimentally measured data on the effect of hysteresis are also carried out for comparison. Numerical analyses, employing both wetting and drying hydraulic behaviour of unsaturated soil, are performed to study the difference in soil‐water content as observed in the experiments. The simulating approximations also fully responded to the experimental data of sand box. The results suggest that the hysteresis behaviour affect the distribution of soil‐water content within the slope indeed. The hysteresis made the FS values a remarkable recovery during the period of non‐rainfall in a rainfall event. The appropriate hydraulic properties of soil (i.e. wetting or drying) should be used in accordance with the processes that unsaturated soil actually experience. This method will enable us to acquire more accurate matric suction head and the unsaturated soil‐shear strength as it changes with the hysteretic flow, in order to calculate into the stability analysis of shallow landslides. An advanced understanding of the process mechanism afforded by this method is critical to realizing a reliable and appropriate design for slope stabilization. It also offers some immediate reference information to the disaster reduction department of the government. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献