Flow structure over a wavy bed with vegetation cover

On the basis of experiments carried out in flume with a wavy bed with vegetation cover, flow velocity, turbulence intensities and Reynolds stress distributions are investigated. The wavy bed was similar to dune in this study. The fixed artificial dunes were constructed over the bed and artificial vegetation put over them in a laboratory flume. An Acoustic Doppler Velocimeter and spatially-averaged method were applied to determine turbulent flow components and shear velocity. Results were compared with a gravel bedform. It was observed that vegetation cover influences considerably the flow structure and displays clearly the flow separation and reattachment point. The law of the wall was not valid within the vegetation cover, but it was fitted well to the zone above the vegetation cover within the inner layer. For a wavy bed having the same dimensions, shear velocity and friction factor over vegetation cover are 1.7 and 2.6 times of those for the gravel bedform, respectively. The results of laboratory study were compared with those of river study.     

Analytical solutions for flow to a well through a fault

We present explicit analytical solutions to problems of steady groundwater flow to a pumping well in an aquifer divided by an infinite, linear fault. The transmissivity of the aquifer is allowed to jump from one side of the fault to the other to model the juxtaposition of host rocks with different hydrologic properties caused by faulting. The fault itself is represented as a thin anisotropic inhomogeneity; this allows the fault to act as a combined conduit–barrier to groundwater flow, as is commonly described in the literature. We show that the properties of the fault may be represented exactly by two lumped parameters—fault resistance and fault conductance—and that the effects of the fault on flow in the adjacent aquifer is independent of the fault width. We consider the limiting cases of a purely leaky and a purely conductive fault where the fault domain may be replaced exactly by internal boundary conditions, and we investigate the effects of fault properties on the flow behavior in the adjacent aquifers. We demonstrate that inferring fault properties based on field observations of head in the aquifer is inherently difficult, even when the fault may be described by one of the two limiting cases. In particular, the effects of a leaky fault and a conductive fault on heads and discharges in the aquifer opposite the fault from the well, are shown to be identical in some cases.     

Sheet flow hydrodynamics over a non-uniform sand bed channel

The current study experimentally investigates the flow characteristics and temporal variations in the sheet flow profile of a non-uniform sand bed channel. Experiments were done to explore turbulent structures in the presence of a sheet flow layer with and without seepage. The turbulent events, such as stream wise velocity, Reynolds shear stresses, and turbulence intensities were found to be increasing and vertical velocity was found decreasing with a sheet layer. The presence of a sheet layer also effects the turbulent energy production and energy dissipation. All the turbulence parameters with and without a sheet layer have also been influenced by the presence of downward seepage. The rate of sheet flow movement is increased with seepage, owing to increased turbulence with seepage. The current study used wavelet analysis on temporally lagged spatial bed elevation profiles obtained from a set of laboratory experiments and synchronized the wavelet coefficients with bed elevation fluctuation at different spatial scales. A spatial cross correlation analysis at multiple scales, based on the wavelet coefficients, has been done on these bed elevation datasets to observe the effect of downward seepage on the dynamic behavior of sheet flow at different length scales. It is found that seepage increases average bed celerity and also increases the celerity of sheet flow of similar length scales. This increase in the celerity has been hypothesized as the increase of sheet flow movement as well as the increase in turbulent parameters with seepage, which destabilizes the bed particles resulting in a disruption in the continuous propagation pattern of the sheet flow. The increase of sheet flow celerity with seepage is confirmed from the saturation level of the wavelet power spectra of the bed elevation series. The presence of seepage also affects the non-uniformity of collective sheet material.     

Analytical and numerical analysis of pressure drawdown in a poroelastic reservoir with complete overburden effect considered

Starting from an analytical reservoir model that incorporates full interaction with an elastic overburden, a new hybrid mathematical approach is developed by combining two numerical discretization methods. A tabular reservoir (petroleum reservoir or an aquifer) in an infinite or semi-infinite domain is viewed as a macroscopic displacement discontinuity, allowing use of the efficient displacement discontinuity mathematical method to calculate stresses and displacements that arise because of pressure changes. A 3-D finite element method using a poroelastic formulation is used to discretize the reservoir itself. By coupling the displacement discontinuity and finite element methods, a 3-D large-scale poroelastic reservoir can be simulated within an infinite or semi-infinite domain. The numerical model has been verified through comparison to known solutions, and some time-dependent pressure drawdown problems are analyzed. Results indicate that including the complete overburden (reservoir surroundings) response has a significant effect on pressure drawdown in a poroelastic reservoir during pumping, and should be incorporated in appropriate applications such as well test equations and subsidence analyses.     

Analytical solutions of a routing problem for storm water in a detention basin

Abstract

Analytical solutions of a routing problem for storm water flowing through a linear reservoir are presented for the assumption of trapezoidal-shaped inflow hydrograph. The maximum ponded (water) depth in the detention basin is chosen as a main design criterion. Calculations are carried out for a given rain recurrence interval but for various rain durations and sand filter surface areas to reach the maximum permitted ponded depth. A design example is also provided.     

Sap flow and plant water sources for typical vegetation in a subtropical humid karst area of southwest China

Plant water use plays a crucial part in the soil–plant-atmosphere continuum. However, in karst regions, plants frequently suffer from water shortages due to low soil water storage capacity. Therefore, it is necessary to understand plant water consumption (as determined by sap flow) and seasonal variation of water sources to improve water management in karst catchments. In this study, thermal dissipation probes (TDP), calibrated using empirical equations, were used to measure the sap flow of three typical woody vegetations, including Coriaria nepalensis (sparse-shrub), Toona sinensis (secondary forest) and Populus adenopoda (shrub-grass). Oxygen and hydrogen stable isotopes were used to analyze seasonal variation of plant water sources. The results showed that: (1) T. Sinensis (3.89 ± 3.87 L·day⁻¹) had significantly higher daily sap flow than C. nepalensis (0.33 ± 0.37 L·day⁻¹) and P. adenopoda (0.09 ± 0.12 L·day⁻¹); (2) daily sap flow was closely correlated to photosynthetically active radiation (PAR) and vapour pressure deficit (VPD); (3) over the entire study period, plants mainly used water from the surface soil horizons; and (4) a greater proportion of epikarst water was used for C. nepalensis than by T. sinensis and P. adenopoda over the whole growth stage, and more epikarst water was used in early and mid-growth stages compared to the late stage for the three species. This study contributes to a deeper understanding of the plant water use strategies in karst regions, and is helpful for ecosystem management.     

Analytical solutions for 2D topography-driven flow in stratified and syncline aquifers

Two analytical solution methods are presented for regional steady-state groundwater flow in a two-dimensional stratified aquifer cross section where the water table is approximated by the topographic surface. For the first solution, the surficial aquifer is represented as a set of dipping parallel layers with different, but piecewise constant, anisotropic hydraulic conductivities, where the anisotropy is aligned with the dip of the layered formation. The model may be viewed as a generalization of the solutions developed by [Tóth JA. A theoretical analysis of groundwater flows in small drainage basins. J Geophys Res 1963;68(16):4795–812; Freeze R, Witherspoon P. Theoretical analysis of regional groundwater flow 1) analytical and numerical solution to the mathematical model, water resources research. Water Resour Res 1966;2(4):641–56; Selim HM. Water flow through multilayered stratified hillside. Water Resour Res 1975;11:949–57] to an multi-layer aquifer with general anisotropy, layer orientation, and a topographic surface that may intersect multiple layers. The second solution presumes curved (syncline) layer stratification with layer-dependent anisotropy aligned with the polar coordinate system. Both solutions are exact everywhere in the domain except at the topographic surface, where a Dirichlet condition is met in a least-squared sense at a set of control points; the governing equation and no-flow/continuity conditions are met exactly. The solutions are derived and demonstrated on multiple test cases. The error incurred at the location where the layer boundaries intersect the surface is assessed.     

Estimating snow distribution over a large area and its application for water resources

The spatial and temporal distribution of the snow water equivalent (SWE), snow density and snow depth were estimated by a method combining remote sensing technology and degree‐day techniques over a study area of 370 000 km². The advantages of this simulation model are its simplicity and the availability of degree‐day parameters, which can be successively evaluated by referring to snow area maps created from satellite images. This simulation worked very well for estimating SWE and helped to separate the areas of thin snow cover from heavier snowfall. However, shallow snow in warm regions led to some misjudgments in the snow area maps because of the time lag between when the satellite image was acquired and the simulation itself. Vulnerable areas, where a large variation in the amount of snow affects people's life, could be identified from the differences between heavy and light snow years. This vulnerability stems from a predicted lack of irrigation water for rice production caused by future climate change. The model developed in this study has the potential to contribute to water management activities and decision‐making processes when considering necessary adaptations to future climate change. Copyright © 2007 John Wiley & Sons, Ltd.     

Analytical solutions for benchmarking cold regions subsurface water flow and energy transport models: One-dimensional soil thaw with conduction and advection

Numerous cold regions water flow and energy transport models have emerged in recent years. Dissimilarities often exist in their mathematical formulations and/or numerical solution techniques, but few analytical solutions exist for benchmarking flow and energy transport models that include pore water phase change. This paper presents a detailed derivation of the Lunardini solution, an approximate analytical solution for predicting soil thawing subject to conduction, advection, and phase change. Fifteen thawing scenarios are examined by considering differences in porosity, surface temperature, Darcy velocity, and initial temperature. The accuracy of the Lunardini solution is shown to be proportional to the Stefan number. The analytical solution results obtained for soil thawing scenarios with water flow and advection are compared to those obtained from the finite element model SUTRA. Three problems, two involving the Lunardini solution and one involving the classic Neumann solution, are recommended as standard benchmarks for future model development and testing.     

A two-grid method for coupled free flow with porous media flow

This paper presents a two-grid method for solving systems of partial differential equations modelling incompressible free flow coupled with porous media flow. This work considers both the coupled Stokes and Darcy as well as the coupled Navier-Stokes and Darcy problems. The numerical schemes proposed are based on combinations of the continuous finite element method and the discontinuous Galerkin method. Numerical errors and convergence rates for solutions obtained from the two-grid method are presented. CPU times for the two-grid algorithm are shown to be significantly less than those obtained by solving the fully coupled problem.     

Use of Large-Eddy Simulation for the bed shear stress estimation over a dune

Environmental flows are generally characterized by complex bed morphology and high current speeds. Such configurations favor the formation of vortex structures that strongly affect hydrody-namics and sediment transport. Large-Eddy Simulation (LES) enables investigation of the dynam-ics of the largest turbulence scales and, thanks to enhanced calculation resources, has now become applicable for simulating environmental flows. In this paper, a LES approach is developed in a CFD code (TELEMAC-3D), which was originally developed to simulate free surface flows using RANS methods. The present developments involve implementing subgrid models, boundary con-ditions and numerical schemes suitable for LES. The LES version of TELEMAC-3D was validated by comparing results on the model with experimental data for flow past a cylinder. Then, the model was applied to a test case representing flow over dunes. After validating the hydrodynamics, the model was used to assess the bottom shear stress, using both a RANS and a LES approach. Com-parison highlighted the potential contribution of LES to investigating the hydrodynamic forces acting on the bottom.     

Bayesian seismic inversion for estimating fluid content and fracture parameters in a gas-saturated fractured porous reservoir

Understanding the effects of in situ fluid content and fracture parameters on seismic characteristics is important for the subsurface exploration and production of fractured porous rocks. The ratio of normal-to-shear fracture compliance is typically utilized as a fluid indicator to evaluate anisotropy and identify fluids filling the fractures, but it represents an underdetermined problem because this fluid indicator varies as a function of both fracture geometry and fluid content. On the bases of anisotropic Gassmann's equation and linear-slip model, we suggest an anisotropic poroelasticity model for fractured porous reservoirs. By combining a perturbed stiffness matrix and asymptotic ray theory, we then construct a direct relationship between the PP-wave reflection coefficients and characteristic parameters of fluids(P-and S-wave moduli) and fractures(fracture quasi-weaknesses), thereby decoupling the effects of fluid and fracture properties on seismic reflection characterization.By incorporating fracture quasi-weakness parameters, we propose a novel parameterization method for elastic impedance variation with offset and azimuth(EIVOA). By incorporating wide-azimuth observable seismic reflection data with regularization constraints, we utilize Bayesian seismic inversion to estimate the fluid content and fracture parameters of fractured porous rocks. Tests on synthetic and real data demonstrate that fluid and fracture properties can be reasonably estimated directly from azimuthal seismic data and the proposed approach provides a reliable method for fluid identification and fracture characterization in a gas-saturated fractured porous reservoir.     

Analytical solutions of the advection‐dispersion equation for transient groundwater flow. A numerical validation

An analytical transport‐model was developed to simulate the propagation of a contaminant in one‐ and two‐dimensional transient flow in groundwater. It is proved that the distribution of concentration at a given time and for a given discharge is identical to that obtained for a different discharge if the volumetric flux of water is the same in the two cases. The results of simulations have been compared with results obtained using the MT3DMS numerical model. There is good agreement when the calculated concentrations are flux‐weighted concentrations. On the other hand, there is a notable divergence when the resident mode is considered. Resident mode concentrations express the mass per unit volume whereas flux mode concentrations express the ratio of mass flux to fluid flux. The solutions presented in this paper can thus be a useful alternative to code MT3DMS when the objective is to simulate concentrations in transient flow according to a resident mode. Copyright © 2008 John Wiley & Sons, Ltd.     

Synthetic tidal parameters for gravity over China and its neighbor area

The synthetic tidal parameters with high spatial resolution for gravity over China and its neighbor area are con- structed with Earth’s tidal model and ocean tide loading calculated using TPXO7 global ocean tide model as well as tidal data over China seas. The comparison between synthetic parameters and ones observed by spring gravime- ters at some seismic network stations and Hong Kong station and one observed by super-conducting gravimeter at Wuhan station shows that the average differences in amplitude factors and phases are smaller than 0.005 and 0.5° respectively; and that the discrepancies between observational and synthetic parameters are dependent on gravim- etric technique in that the synthetic parameters are in well agreement with the superconducting gravimetric obser- vations. This also indicates that the synthetic result is a good estimation for tidal gravity, and the numerical results in the present paper not only can provide ground and space gravimetry such as absolute gravimetry with correction model of tidal gravity, but also provide effective tidal parameters over areas where no observation is carried out.     

Analytical solution for two-phase flow in a wellbore using the drift-flux model

This paper presents analytical solutions for steady-state, compressible two-phase flow through a wellbore under isothermal conditions using the drift flux conceptual model. Although only applicable to highly idealized systems, the analytical solutions are useful for verifying numerical simulation capabilities that can handle much more complicated systems, and can be used in their own right for gaining insight about two-phase flow processes in wells. The analytical solutions are obtained by solving the mixture momentum equation of steady-state, two-phase flow with an assumption that the two phases are immiscible. These analytical solutions describe the steady-state behavior of two-phase flow in the wellbore, including profiles of phase saturation, phase velocities, and pressure gradients, as affected by the total mass flow rate, phase mass fraction, and drift velocity (i.e., the slip between two phases). Close matching between the analytical solutions and numerical solutions for a hypothetical CO₂ leakage problem as well as to field data from a CO₂ production well indicates that the analytical solution is capable of capturing the major features of steady-state two-phase flow through an open wellbore, and that the related assumptions and simplifications are justified for many actual systems. In addition, we demonstrate the utility of the analytical solution to evaluate how the bottomhole pressure in a well in which CO₂ is leaking upward responds to the mass flow rate of CO₂-water mixture.     

Dynamics of deformation and water flow in heterogeneous porous media and its impact on soil properties

The interaction of geomechanics and flow within a soil body induces deformation and pore pressure change. Deformation may change hydrogeological and elastic properties, which alters the mechanical behaviour and results in non‐linearity. To investigate this interaction effect in a heterogeneous porous medium, a stochastic poroelastic model is proposed. Monte Carlo simulations are performed to determine the mean and uncertainty of the parameter changes, displacement, and change in pore water pressure. Hydraulic conductivity is treated as the only random variable in the coupled geomechanics‐flow system due to its large variation compared to other mechanical and hydrogeological properties in natural environments. The three considered non‐linear models for the interaction between parameters and deformation are those that consider (1) porosity and hydraulic conductivity; (2) porosity and Young's modulus; and (3) a combined effect that includes porosity, hydraulic conductivity, and Young's modulus. Boundary effects on the coupled system are also explored. The relationships between changes of porosity, hydraulic conductivity, and Young's modulus are analytically shown to be non‐linear. Among the considered parameters, the deformation effect induces the largest reduction in hydraulic conductivity. The deformation‐induced change in hydraulic conductivity shows the most significant effect on the mean and variance of the change in pore water pressure and displacement, while changes in Young's modulus have the least effect. When the deformation effect is considered, the superposition relationship does not exist in the mean displacement and mean change in pore water pressure for the three scenarios considered; it exists for the case without deformation effects. Deformation also causes a reduction in the effective hydraulic conductivity for the whole domain. The scenario that considers both loading and discharge boundaries has larger changes in hydrogeological and geo‐mechanical parameters than those in scenarios that consider loading and discharge boundaries separately. The results indicate that the interaction between deformation and changes in parameters has a profound effect on the poroelastic system. The effect of deformation should thus be considered in modelling and practice. Copyright © 2009 John Wiley & Sons, Ltd.     

Formation of one-dimensional waves for resonant flow in a channel

When a forcing moves in a shallow channel at a velocity near the phase velocity for linear long waves, energy cannot escape from the forcing at the linear group velocity and nonlinear effects become important in describing the resulting flow. This flow is termed resonant or transcritical. It has been found both experimentally and numerically that large amplitude upstream propagating waves are generated by the forcing. These waves are straight crested, even though the forcing is two-dimensional. It is shown that these upstream waves become straight crested due to geometrical effects aided by the presence of side walls. Using energy conservation, approximate values of the amplitude of the upstream waves are obtained which are compared with recent experimental and numerical results.     

A network theory approach for a better understanding of overland flow connectivity

Hydrological connectivity describes the physical coupling (linkages) of different elements within a landscape regarding (sub‐) surface flows. A firm understanding of hydrological connectivity is important for catchment management applications, for example, habitat and species protection, and for flood resistance and resilience improvement. Thinking about (geomorphological) systems as networks can lead to new insights, which has also been recognized within the scientific community, seeing the recent increase in the use of network (graph) theory within the geosciences. Network theory supports the analysis and understanding of complex systems by providing data structures for modelling objects and their linkages, and a versatile toolbox to quantitatively appraise network structure and properties. The objective of this study was to characterize and quantify overland flow connectivity dynamics on hillslopes in a humid sub‐Mediterranean environment by using a combination of high‐resolution digital‐terrain models, overland flow sensors and a network approach. Results showed that there are significant differences between overland flow connectivity on agricultural areas and semi‐natural shrubs areas. Significant positive correlations between connectivity and precipitation characteristics were found. Significant negative correlations between connectivity and soil moisture were found, most likely because of soil water repellency and/or soil surface crusting. The combination of structural networks and dynamic networks for determining potential connectivity and actual connectivity proved a powerful tool for analysing overland flow connectivity. Copyright © 2016 John Wiley & Sons, Ltd.     

A double-porosity model for a fractured aquifer with non-Darcian flow in fractures

Abstract

Non-Darcian flow in a finite fractured confined aquifer is studied. A stream bounds the aquifer at one side and an impervious stratum at the other. The aquifer consists of fractures capable of transmitting water rapidly, and porous blocks which mainly store water. Unsteady flow in the aquifer due to a sudden rise in the stream level is analysed by the double-porosity conceptual model. Governing equations for the flow in fractures and blocks are developed using the continuity equation. The fluid velocity in fractures is often too high for the linear Darcian flow so that the governing equation for fracture flow is modified by Forcheimer's equation, which incorporates a nonlinear term. Governing equations are coupled by an interaction term that controls the quasi-steady-state fracture—block interflow. Governing equations are solved numerically by the Crank-Nicolson implicit scheme. The numerical results are compared to the analytical results for the same problem which assumes Darcian flow in both fractures and blocks. Numerical and analytical solutions give the same results when the Reynolds number is less than 0.1. The effect of nonlinearity on the flow appears when the Reynolds number is greater than 0.1. The higher the rate of flow from the stream to the aquifer, the higher the degree of nonlinearity. The effect of aquifer parameters on the flow is also investigated. The proposed model and its numerical solution provide a useful application of nonlinear flow models to fractured aquifers. It is possible to extend the model to different types of aquifer, as well as boundary conditions at the stream side. Time-dependent flow rates in the analysis of recession hydrographs could also be evaluated by this model.     

Eddy correlations for water flow in a single fracture with abruptly changing aperture

Fluid flow in single fractures with non‐uniform apertures is an important research subject in many disciplines. The abruptly changing aperture is a special case of such non‐uniformity. This paper simulates water flow in a single fracture with abruptly changing aperture (SF‐ACA) using the Lattice Boltzmann Method (LBM) and the Finite Volume Method (FVM). The flow occurs with the Reynolds number (Re) ranging from 5 to 900 and a ratio of aperture change (E) of 3 (E = D/d, where D and d are the larger and smaller apertures, respectively). For Re values between 5 and 100, both LBM and FVM can successfully simulate the eddy development in the expansion regime of an SF‐ACA. Flow with high Re values (up to 900) is simulated by FVM, which appears to be numerically more stable than LBM for high‐Re flow problems studied here. The flow symmetry in the expansion regime breaks at the Re value between 400 and 500. Our simulation result shows a linear relationship between l₁/d and Re at low Re (5–100) or higher Re (110–900) values, where defined as the length from the location of abrupt expansion to the right edge of the first eddy along the flow direction. If considering the simulation results for the entire simulated range of Re (5–900), the l₁/d–Re relationship is better described by a non‐linear logarithmical function. The l₁/d approaches an asymptotic constant at large Re. Copyright © 2011 John Wiley & Sons, Ltd.