Patterned ground formation and penetrative convection in porous media

Abstract

A theoretical explanation is advanced consisting of a five stage process for the formation of polygonal ground which consists of stone borders forming regular hexagons and soil centres. One of these stages, namely the onset of convection in a porous soil between temperatures of 0°C and approximately 4-6°C, is studied analytically. Darcy's law is employed but variable permeability is allowed for and a parabolic density dependence on temperature is assumed. It is found that the theoretical predictions of the aspect ratio agree very well with field studies when a constant upper surface heat flux condition is imposed and an upwardly stratified permeability is chosen. Field study data, which agree very well with the theory, are reported in detail.     

The beneficial role of rubble mound coastal structures on seawater oxygenation

The beneficial role of rubble mound coastal structures on oxygenation under the effect of waves is discussed, based on analytical considerations and experimental data from laboratory experiments with permeable and impermeable structures. Significant oxygenation of the wave-protected area was observed as a result of horizontal transport through the permeable structure. A two-cell model describing the transport of dissolved oxygen (DO) near a rubble mound breakwater structure was developed and used for the determination of the oxygen transfer coefficients from the experimental data. Oxygen transfer through the air-water interface is considered a source term in the transport equation and the oxygen flux through the structure is taken into account. The mass transport equations for both sides of the structure are solved analytically in terms of time evolution of DO concentration. The behaviour of the solution is illustrated for three different characteristic cases of initial conditions. The oxygen transfer through the air-water interface in the wave-influenced area increases the DO content in the area; the resulting oxygen flux through the structure is discussed. The analytical results depend on the initial conditions, the oxygen transfer coefficient and the exchange flow rate through the structure. Experiments with impermeable structures show that air water oxygen transfer in the harbour area is negligible in the absence of waves. In addition the ratio of the horizontal DO flux to the vertical flux into the seaward side tends towards a constant value, independent of the initial conditions.     

Evaluating overland flow sediment transport capacity

An equation for evaluating the sediment transport capacity of overland flow is a necessary part of a physically based soil erosion model describing sediment detachment and transport as distributed processes. At first, for the hydraulic conditions of small-scale and large-scale roughness, the sediment transport capacity relationship used in the WEPP model is calibrated by Yalin and Govers' equation. The analysis shows that the transport coefficient K_t depends on the Shields parameter, Y, according to a semi-logarithmic (Yalin) or a linear (Govers) equation. The reliability of the semi-logarithmic equation is verified by Smart's, and Aziz and Scott's experimental data. Then the Low's formula, whose applicability is also proved by Smart's, and Aziz and Scott's data, is transformed as a stream power equation in which a stream power coefficient, K_SP, depending on Shields parameter, slope, sediment and water-specific weight, appears. A relationship between transport capacity and effective stream power is also proposed. Finally, the influence of rainfall on sediment transport capacity and the prediction of critical shear stress corresponding to overland flow are examined. © 1998 John Wiley & Sons, Ltd.     

Modelling the process of soil detachment by rill flow on steep loessial hillslopes

Soil detachment by rill flow is a key process of rill erosion, modelling this process can help in understanding rill erosion mechanisms. However, many soil detachment models are established on conceptual assumptions rather than experimental data. The objectives of this study were to establish a model of soil detachment by rill flow based on flume experimental data and to quantitatively verify the model. We simulated the process of soil detachment by rill flow in flume experiments with a soil-feeding hopper using loessial soil on steep slopes. Seven flow discharges, six slopes and five sediment loads were combined. Soil detachment capacity, sediment transport capacity, and soil detachment rate by rill flow under different sediment loads were measured. The process of soil detachment by rill flow can be modelled by a dual power function based on soil detachment capacity and transport capacity deficit as variables. The established model exhibited high credibility (NSE=0.97; R²=0.97). The contributions of soil detachment capacity and transport capacity deficit to soil detachment rate by rill flow reached 60% and 36%, respectively. Soil detachment capacity exerted more influence on soil detachment rate than did transport capacity deficit. The performance of the WEPP rill erosion equation is also favourable (NSE=0.95; R²=0.97). The two power exponents in the model we established strengthen the role of soil detachment capacity in soil detachment rate and weaken that for transport capacity deficit. Soil detachment capacity and transport capacity deficit played important roles in the determination of soil detachment rate by rill flow. The results can be applied to implement the numerical modeling and prediction of rill erosion processes on steep loessial hillslopes. © 2019 John Wiley & Sons, Ltd.     

Solute transport and water content measurements in clay soils using time domain reflectometry

Abstract

Clayey and saline soils have been shown to be problematic for time domain reflectometry (TDR) measurements. This study presents some of these problems and discusses solutions to them. Thirteen solute transport experiments were carried out in three undisturbed soil columns of swelling clay soil from Tunisia, labelled S1, S2, and S3 respectively. The columns were collected at three different physiographical regions within a catchment. Water fluxes ranged from 1.2 to 7.2 cm day^?1. The large solute transport heterogeneity and large tailing indicated that preferential flow was most pronounced in S1. The preferential flow took place in voids between structural elements and in wormholes. In S3, preferential flow was also evident, but not to the same extent as in S1. In S2, the solute transport was more uniform with little preferential flow. The heterogeneity of the solute transport increased with the water flux in S1 and to a smaller extent in S3, whereas it remained constant in S2. In a previous dye experiment in the field, preferential flow in cracks was observed at those sites where S1 and S3 were collected. In the column experiments, preferential flow in these cracks was less due to the higher initial water content compared to the dye experiments, indicating that the desiccation cracks were closed by the swelling clay.     

Multi-functional heat pulse probe measurements of coupled vadose zone flow and transport

Simultaneous measurement of coupled water, heat, and solute transport in unsaturated porous media is made possible with the multi-functional heat pulse probe (MFHPP). The probe combines a heat pulse technique for estimating soil heat properties, water flux, and water content with a Wenner array measurement of bulk soil electrical conductivity (EC_bulk). To evaluate the MFHPP, we conducted controlled steady-state flow experiments in a sand column for a wide range of water saturations, flow velocities, and solute concentrations. Flow and transport processes were monitored continuously using the MFHPP. Experimental data were analyzed by inverse modeling of simultaneous water, heat, and solute transport using an adapted HYDRUS-2D model. Various optimization scenarios yielded simultaneous estimation of thermal, solute, and hydraulic parameters and variables, including thermal conductivity, volumetric water content, water flux, and thermal and solute dispersivities. We conclude that the MFHPP holds great promise as an excellent instrument for the continuous monitoring and characterization of the vadose zone.     

Two-phase hydrodynamic and sediment transport modeling of wave-generated sheet flow

This numerical investigation was carried out to advance mechanistic understanding of sediment transport under sheet flow conditions. An Euler–Euler coupled two-phase flow model was developed to simulate fluid–sediment oscillatory sheet flow. Since the concentration of sediment particles is high in such flows, the kinematics of the fluid and sediment phases are strongly coupled. This model includes interaction forces, intergranular stresses and turbulent stress closure. Each phase was modeled via the Reynolds-Averaged Navier–Stokes equations, with interphase momentum conservation accounting for the interaction between the phases. The generation and transformation of turbulence was modeled using the two-equation k–ε$k''–''\epsilon$ turbulence model. Concentration and sediment flux profiles were compared with experimental data for sheet flow conditions considering both symmetric and asymmetric oscillatory flows. Sediment and fluid velocity variations, concentration profiles, sediment flux and turbulence parameters of wave-generated sheet flow were studied numerically with a focus on sediment transport characteristics. In all applications, the model predictions compared well with the experimental data. Unlike previous investigations in which the flow is driven by a horizontal pressure gradient, the present model solves the Navier–Stokes equations under propagating waves. The model’s ability to predict sediment transport under oscillatory sheet flow conditions underscores its potential for understanding the evolution of beach morphology.     

Non-isothermal soil water transport and evaporation

A detailed model was formulated to describe the non-isothermal transport of water in the unsaturated soil zone. The model consists of the coupled equations of mass conservation for the liquid phase, gas phase and water vapor and the energy conservation equation. The water transport mechanisms considered are convection in the liquid phase, and convection, diffusion and dispersion of vapor in the gas phase. The boundary conditions at the soil–atmosphere interface include dynamical mass flux and energy flux that accounts for radiation transport. Comparison of numerical simulations results with published experimental data demonstrated that the present model is able to describe water and energy transport dynamics, including situations of low and moderate soil moisture contents. Analysis of field studies on soil drying suggests that that dispersion flux of the water vapor near the soil surface, which is seldom considered in soil drying models, can make a significant contribution to the total water flux.     

A Correction on Coastal Heads for Groundwater Flow Models

We introduce a simple correction to coastal heads for constant‐density groundwater flow models that contain a coastal boundary, based on previous analytical solutions for interface flow. The results demonstrate that accurate discharge to the sea in confined aquifers can be obtained by direct application of Darcy's law (for constant‐density flow) if the coastal heads are corrected to ((α + 1)/α)h_s ? B/2α, in which h_s is the mean sea level above the aquifer base, B is the aquifer thickness, and α is the density factor. For unconfined aquifers, the coastal head should be assigned the value . The accuracy of using these corrections is demonstrated by consistency between constant‐density Darcy's solution and variable‐density flow numerical simulations. The errors introduced by adopting two previous approaches (i.e., no correction and using the equivalent fresh water head at the middle position of the aquifer to represent the hydraulic head at the coastal boundary) are evaluated. Sensitivity analysis shows that errors in discharge to the sea could be larger than 100% for typical coastal aquifer parameter ranges. The location of observation wells relative to the toe is a key factor controlling the estimation error, as it determines the relative aquifer length of constant‐density flow relative to variable‐density flow. The coastal head correction method introduced in this study facilitates the rapid and accurate estimation of the fresh water flux from a given hydraulic head measurement and allows for an improved representation of the coastal boundary condition in regional constant‐density groundwater flow models.     

Modelling soil solute release and transport in run‐off on a loessial slope with and without surface stones

Stone covers on loessial slopes can increase the time of infiltration by slowing the velocity of the overland flow, which reduces the transport of solutes, but few mechanistic models have been tested under water‐scouring conditions. We carried out field experiments to test a previously proposed, physically based model of water and solute transport. The area of soil infiltration was calculated from the uncovered surface area, and Richards' equation and the kinematic wave equation were used to describe water infiltration and flow along slopes with stone covers. The transport of chemicals into the run‐off from the surface soil, presumably by diffusion, and their movement in the soil profile could be described by the convection–diffusion equations of the model. The simulated and measured data correlated well. The stones on the soil surface reduced the area available for infiltration but increased the Manning coefficient, eventually leading to increased water infiltration and decreased solute loss with run‐off. Our results indicated that the traditional model of water movement and solute migration could be used to simulate water transport and solute migration for stone‐covered soil on loessial slopes.     

Pressure Oscillation Effects on the Saffman-Taylor Instability

— We studied experimentally the stability of the front between two immiscible fluids in a Hele-Shaw cell, which consists of two parallel glass plates separated by a narrow spacing. The fluid flow in a Hele-Shaw cell is governed by the Laplace's equation (pressure field) and Darcy's law (fluid transport), which makes of this experimental setup a two-dimensional analog of a porous medium (FABER, 1997). SAFFMAN and TAYLOR (1958) demonstrated that when the injected fluid is less viscous than the displaced one, the front between the fluids can be unstable and fingers may develop along the interface. We investigated the possibility of influencing the development of the Saffman-Taylor instability by modulating the injection pressure with weak periodic oscillations of low frequency (5 to 15 Hz). A series of experiments were performed, in which the evolution of the interface between the injected air and the displaced silicon oil was recorded with the help of a numerical photo camera. We observed that the oscillations of the injection pressure inhibit the development of fingers. We quantified the observed stabilization effect by performing a harmonic analysis of the shape of the front, and suggested an interpretation in terms of “stiffening” of the interface.     

Water flux and sediment transport within a forested landscape: the role of connectivity,subsurface flow,and slope length scale on transport mechanism

The connectivity and upscaling of overland runoff and sediment transport are important issues in hillslope hydrology to identify water flux and sediment transport within landscape. These processes are highly variable in time and space with regard to their interactions with vegetation and soil surface conditions. The generation of overland runoff and its spatial connectivity were examined along a slope to determine the variations in the transport mechanism of runoff and soil particles by rain splash and overland runoff. Field experiments were conducted by erosion plots on a steep hillslope at lengths of 5, 10, and 15 m. The overland runoff connectivity and flow transport distance decreased with the slope length, while spatial variability of infiltration increased significantly with the slope length. Observation of subsurface flow revealed that surface soil and litter layer could have important role in water transport. However, the surface soil water content and water flux transport along the slope was highly variable for different storm events; the variability was related to the complexity of the system, mainly by way of the initial wetness conditions and infiltration characteristics. Only net rain‐splashed soil was measurable, but examination of the water flux, overland runoff and sediment transport connectivity, characteristics of sheetwash, and the variability in spatial infiltration indicated an increase in the contribution of the rain splash transport mechanism along the slope. Copyright © 2013 John Wiley & Sons, Ltd.     

An analysis of infiltration with moisture content distribution in a two‐dimensional discretized water content domain

On the basis of unsaturated Darcy's law, the Talbot–Ogden method provides a fast unconditional mass conservative algorithm to simulate groundwater infiltration in various unsaturated soil textures. Unlike advanced reservoir modelling methods that compute unsaturated flow in space, it only discretizes the moisture content domain into a suitable number of bins so that the vertical water movement is estimated piecewise in each bin. The dimensionality of the moisture content domain is extended from one dimensional to two dimensional in this study, which allows us to distinguish pore shapes within the same moisture content range. The vertical movement of water in the extended model imitates the infiltration phase in the Talbot–Ogden method. However, the difference in this extension is the directional redistribution, which represents the horizontal inter‐bin flow and causes the water content distribution to have an effect on infiltration. Using this extension, we mathematically analyse the general relationship between infiltration and the moisture content distribution associated with wetting front depths in different bins. We show that a more negatively skewed moisture content distribution can produce a longer ponding time, whereas a higher overall flux cannot be guaranteed in this situation. It is proven on the basis of the water content probability distribution independent of soil textures. To illustrate this analysis, we also present numerical examples for both fine and coarse soil textures. Copyright © 2014 John Wiley & Sons, Ltd.     

Brine transport in porous media: self-similar solutions

In this paper we analyze a model for brine transport in porous media, which includes a mass balance for the fluid, a mass balance for salt, Darcy's law and an equation of state, which relates the fluid density to the salt mass fraction. This model incorporates the effect of local volume changes due to variations in the salt concentration. Density variations affect the compressibility of the fluid, which in turn cause additional fluid flow. Two specific situations are investigated that lead to self similarity. We study the relative importance of the compressibility effect in terms of the relative density difference. Semi-analytical solutions are obtained as well as asymptotic expressions in terms of the relative density difference. It is found that the volume changes have a small but noticeable effect on the mass transport only when the salt concentration gradients are large. Some results on the simultaneous transport of brine and dissolved (radioactive) tracers are presented.     

Measuring hydraulic permeability in a streambed using the packer test

Permeability of a streambed is an important factor regulating nutrient and oxygen availability for aquatic biota. In order to investigate the relationship, an accurate permeability should be measured. However, it is difficult to measure permeability in a coarse gravel bed using a conventional permeability test. Moreover, turbulent flow may occur in coarse bed material, and then deviations from Darcy's law do occur. Thus, permeability calculated following Darcy's law may be overestimated under turbulent flow conditions and should be corrected. The packer test can be used in highly permeable gravel beds. We developed a field method applicable to a gravel bed using the packer test and derived an equation adopting a law of turbulent flow to study the problems under any type of flow condition. The accuracy of the equation was examined using a laboratory flume with a gravel bed. The results suggested that permeability calculated from Hvorslev's equation is overestimated for turbulent flow. In contrast, our equation, developed here, could evaluate permeability accurately under any type of flow condition. Copyright © 2005 John Wiley & Sons, Ltd.     

Non-passive transport of volatile organic compounds in the unsaturated zone

A detailed model was formulated to describe the non-passive transport of water-soluble chemicals in the unsaturated zone and used to illustrate one-dimensional infiltration and redistribution of alcohol–water mixtures. The model includes the dependence of density, viscosity, surface tension, molecular diffusion coefficient in the liquid-phase, and gas–liquid partition coefficient on the aqueous mixture composition. It also takes into account the decrease in the gas–liquid partition coefficient at high capillary pressures, in accordance with Kelvin’s equation for multi-component mixtures. Simulation of butanol–water mixtures infiltration in sand was in agreement with the experimental data and simulations reported in the literature. Simulation of methanol infiltration and redistribution in two different soils showed that methanol concentration significantly affects volumetric liquid content and concentration profiles, as well as the normalized volatilization and evaporation fluxes. Dispersion in the liquid-phase was the predominant mechanism in the transport of methanol when dispersivity at saturation was set to 7.8 cm. Liquid flow was mainly due to capillary pressure gradients induced by changes in volumetric liquid content. However, for dispersivity at saturation set to 0.2 cm, changes in surface tension due to variation in composition induced important liquid flow and convection in the liquid-phase was the most active transport mechanism. When the Kelvin effect was ignored within the soil, the gas-phase diffusion was significantly lower, leading to lower evaporation flux of water and higher volumetric liquid contents near the soil surface.     

LISEM: A SINGLE-EVENT PHYSICALLY BASED HYDROLOGICAL AND SOIL EROSION MODEL FOR DRAINAGE BASINS. I: THEORY,INPUT AND OUTPUT

A new physically based hydrological and soil erosion model has been developed, which can be used for planning and conservation purposes: the LImburg Soil Erosion Model (LISEM). The LISEM model is one of the first examples of a physically based model that is completely incorporated in a raster Geographical Information System. This incorporation facilitates easy application in larger catchments, improves the user friendliness by avoiding conversion routines and allows remotely sensed data to be used. Processes incorporated in the model are rainfall, interception, surface storage in micro-depressions, infiltration and vertical movement of water in the soil, overland flow, channel flow, detachment by rainfall and throughfall, detachment by overland flow and transport capacity of the flow. Special attention has been given to the influence of tractor wheelings, small roads and surface sealing. Vertical movement of water in the soil is simulated using the Richard's equation. Optionally, the user can choose the Holtan or the Green–Ampt infiltration model. For the distribution flow routing, a four-point finite-difference solution of the kinematic wave is used together with Manning's equation.     

Transport in chemically and mechanically heterogeneous porous media. I: Theoretical development of region-averaged equations for slightly compressible single-phase flow

Transport processes in heterogeneous porous media are often treated in terms of one-equation models. Such treatment assumes that the velocity, pressure, temperature, and concentration can be represented in terms of a single large-scale averaged quantity in regions having significantly different mechanical, thermal, and chemical properties. In this paper we explore the process of single-phase flow in a two-region model of heterogeneous porous media. The region-averaged equations are developed for the case of a slightly compressible flow which is an accurate representation for a certain class of liquid-phase flows. The analysis leads to a pair of transport equations for the region averaged pressures that are coupled through a classic exchange term, in addition to being coupled by a diffusive cross effect. The domain of validity of the theory has been identified in terms of a series of length and timescale constraints.In Part II the theory is tested, in the absence of adjustable parameters, by comparison with numerical experiments for transient, slightly compressible flow in both stratified and nodular models of heterogeneous porous media. Good agreement between theory and experiment is obtained for nodular and stratified systems, and effective transport coefficients for a wide range of conditions are presented on the basis of solutions of the three closure problems that appear in the theory. Part III of this paper deals with the principle of large-scale mechanical equilibrium and the region-averaged form of Darcy's law. This form is necessary for the development and solution of the region-averaged solute transport equations that are presented in Part IV. Finally, in Part V we present results for the dispersion tensors and the exchange coefficient associated with the two-region model of solute transport with adsorption.     

Estimating finite difference block equivalent hydraulic conductivity for numerically solving the Richards' equation

A method is proposed for calculating the equivalent hydraulic conductivity (EHC) within a finite difference block (FDB). Application of the constant‐flux assumption of Darcy's Law, the EHC equals to the integration of effective hydraulic conductivity (K_w) as a function of pressure head (h_w) divided by the head difference at the ends of the FDB. Error analysis show that the constant‐flux (CF) EHC estimates are better than those computed by the commonly used arithmetic‐mean (AM), geometric‐mean (GM), and harmonic‐mean (HM) techniques. CF EHC results are even more superior at larger interblock head difference situations. Simulations of water infiltration experiments show that simulations using the CF EHC or AM or GM weighting technique have only slight difference while applying the Neumann type boundary condition at the ground surface. In case of the Dirichlet type boundary condition, however, the CF EHC is superior to the other two in correctly estimating the depth of infiltration while enlarging the grid size. Therefore, it is recommended to adopt the CF EHC with a larger grid size to the more stable and more efficient results. Copyright © 2007 John Wiley & Sons, Ltd.     

Soil erosion and pollutant transport during rainfall-runoff processes

The pollutant from land surface applied to agricultural chemicals is one of the major sources of contamination in water bodies. The pollutant transport within a watershed is profoundly influenced by the rainfall-runoff processes, especially the associated upland erosion and sediment transport processes because most of pollutant can be dissolved into water or attached to the soil particles. A set of soil experiments in laboratory was conducted in this paper to investigate the impacts of upland erosion and sediment transport on pollutant loads. The soil utilized for the experiments was the silty sand collected from Loess Plateau, China; and ammonium bicarbonate was applied on the soil surface as the pollutant source. Runoff discharge, soil loss, and ammonia- and nitrate-nitrogen concentrations were measured to establish the relationships which can help the numerical model to predict the pollutant losses coupled with upland soil erosion during the rain-fall-runoff processes. The experimental results indicate the ammonia-nitrogen concentration in runoff reaches the peak at the initial stage of the overland flow generation, and quickly decreases and approaches to the steady state. The ammonia-nitrogen transported by the soil loss also makes contributions to the nitrogen loss; and its amount mainly depends on the soil transport rate. The ammonia-nitrogen dissolved in overland flow is dominant due to the strong aqueous solution of ammonium bicarbonate during the first storm right after its application.