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1.
A quasi three-dimensional (QUASI 3-D) model is presented for simulating the subsurface water flow and solute transport in the unsaturated and in the saturated zones of soil. The model is based on the assumptions of vertical flow in the unsaturated zone and essentially horizontal groundwater flow. The 1-D Richards equation for the unsaturated zone is coupled at the phreatic surface with the 2-D flow equation for the saturated zone. The latter was obtained by averaging 3-D flow equation in the saturated zone over the aquifer thickness. Unlike the Boussinesq equation for a leaky-phreatic aquifer, the developed model does not contain a storage term with specific yield and a source term for natural replenishment. Instead it includes a water flux term at the phreatic surface through which the Richards equation is linked with the groundwater flow equation. The vertical water flux in the saturated zone is evaluated on the basis of the fluid mass balance equation while the horizontal fluxes, in that equation, are prescribed by Darcy law. A 3-D transport equation is used to simulate the solute migration. A numerical algorithm to solve the problem for the general quasi 3-D case was developed. The developed methodology was exemplified for the quasi 2-D cross-sectional case (QUASI2D). Simulations for three synthetic problems demonstrate good agreement between the results obtained by QUASI2D and two fully 2-D flow and transport codes (SUTRA and 2DSOIL). Yet, simulations with the QUASI2D code were several times faster than those by the SUTRA and the 2DSOIL codes. 相似文献
2.
An Explicit Finite Difference Model for Unconfined Aquifers 总被引：2，自引：0，他引：2
Most of the current simulation models for unconfined aquifers are based on the assumption that the free surface variation is small so that it can be combined with permeability to reduce the nonlinear Boussinesq equation to a linear partial differential equation (PDE). One of the most obvious reasons for using the linearization assumption is for the ease of numerical solution. This work presents a simpler alternative which permits an easy direct solution of the Boussinesq equation. A forward in time, central in space (FTCS) explicit finite difference method is used in the simulation model. The model was first validated by comparing its results with known analytical solution. It was then applied to an actual situation in which the short-term responses (from pumping) of an unconfined aquifer were simulated. The study shows that the stability of the model can be easily controlled, and because of the simple algorithm used, the code can be expeditiously developed and economically run on smaller machines. Due to the uncertainties in the calibration results, it is recommended here that more data be collected to improve the calibration before the model is used as a real-time simulation tool. 相似文献
3.
Abstract This paper develops a new analytical solution for the aquifer system, which comprises an unconfined aquifer on the top, a semi-confined aquifer at the bottom and an aquitard between them. This new solution is derived from the Boussinesq equation for the unconfined aquifer and one-dimensional leaky confined flow equation for the lower aquifer using the perturbation method, considering the water table over-height at the remote boundary. The head fluctuation predicted from this solution is generally greater than the one solved from the linearized Boussinesq equation when the ratio of the tidal amplitude to the thickness of unconfined aquifer is large. It is found that both submarine groundwater discharges from upper and lower aquifers increase with tidal amplitude–aquifer thickness ratio and may be underestimated if the discharge is calculated based on the average head fluctuation. The effects of the aquifer parameters and linearization of the Boussinesq equation on the normalized head fluctuation are also investigated. Editor D. Koutsoyiannis; Associate editor J. Simunek Citation Chuang, M.-H., Mahdi, A.-A. and Yeh, H.-D., 2012. A perturbation solution for head fluctuations in a coastal leaky aquifer system considering water table over-height. Hydrological Sciences Journal, 57 (1), 162–172. 相似文献
4.
Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection–diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring–neap tides (a bichromatic tidal system with the fundamental frequencies ω1andω2) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency ω1−ω2, i.e., the spring–neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations. 相似文献
5.
6.
This paper presents a new perturbation solution of the non-linear Boussinesq equation for one-dimensional tidal groundwater flow in a coastal unconfined aquifer. Built upon the work of Parlange et al. [Parlange, J.-Y., Stagnitti, F., Starr, J.L., Braddock, R.D., 1984. Free-surface flow in porous media and periodic solution of the shallow-flow approximation, J. Hydrol., 70, 251–263], the solution adopts a new perturbation parameter that is by definition less than unit, and thus is applicable to a wider range of physical conditions within the constraint of the Boussinesq approximation. This approach avoids a secular term in the third-order perturbation equation of Parlange et al. (1984), enabling the derivation of the third- and higher-order solutions. In comparison with a numerical (“exact”) solution, the new perturbation solution is shown to be slightly more accurate than that of Parlange et al. (1984) with the second-order approximation. The obtained third-order solution exhibits considerable improvement in accuracy. In relatively simple analytical forms, the present perturbation solution will help to understand better the non-linear characteristics of tidal water table fluctuations in as modeled by the non-linear Boussinesq equation coastal unconfined aquifers. 相似文献
7.
This paper presents a 3D model in sigma coordinates. Although the principles it is based on have been established for some time, some original aspects for this type of 3D mode splitting model are presented here. The model was designed to simulate flows in various coastal areas from the regional scale down to the inshore scale of small bays or estuaries where circulation is generally driven by a mix of processes. The processes to be modeled enable simplifications of the Navier–Stokes equations on the classic Boussinesq and hydrostatic hypotheses. These equations are transformed within a sigma framework to make free surface processing easier. The main point of our demonstration focuses on the original aspect of the coupling between barotropic and baroclinic modes especially designed for ADI. It explains how full consistency of the transport calculated within the 2D and 3D equation sets was obtained. Lastly, we describe the physical processes simulated on a realistic configuration at a regional scale in the Bay of Biscay. 相似文献
8.
A simple and accurate cubic approximation to the solution of the Boussinesq equation is given in case of power-law flux boundary condition being imposed at the inlet of an initially dry aquifer. The new approximation overcomes the numerical intensity of the earlier cubic approximation of Telyakovskiy and Allen [Telyakovskiy AS, Allen MB. Polynomial approximate solutions to the Boussinesq equation. Adv Water Resour 2006;29(12):1767–79], while producing comparably accurate results. 相似文献
9.
Achim Wirth 《Ocean Dynamics》2009,59(4):551-563
Results from numerical simulations of idealised, 2.5-dimensional Boussinesq, gravity currents on an inclined plane in a rotating
frame are used to determine the qualitative and quantitative characteristics of such currents. The current is initially geostrophically
adjusted. The Richardson number is varied between different experiments. The results demonstrate that the gravity current
has a two-part structure consisting of: (1) the vein, the thick part that is governed by geostrophic dynamics with an Ekman
layer at its bottom, and (2) a thin friction layer at the downslope side of the vein, the thin part of the gravity current.
Water from the vein detrains into the friction layer via the bottom Ekman layer. A self consistent picture of the dynamics
of a gravity current is obtained and some of the large-scale characteristics of a gravity current can be analytically calculated,
for small Reynolds number flow, using linear Ekman layer theory. The evolution of the gravity current is shown to be governed
by bottom friction. A minimal model for the vein dynamics, based on the heat equation, is derived and compares very well to
the solutions of the 2.5-dimensional Boussinesq simulations. The heat equation is linear for a linear (Rayleigh) friction
law and non-linear for a quadratic drag law. I demonstrate that the thickness of a gravity current cannot be modelled by a
local parameterisation when bottom friction is relevant. The difference between the vein and the gravity current is of paramount
importance as simplified (streamtube) models should model the dynamics of the vein rather than the dynamics of the total gravity
current. In basin-wide numerical models of the ocean dynamics the friction layer has to be resolved to correctly represent
gravity currents and, thus, the ocean dynamics. 相似文献
10.
11.
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
12.
《Advances in water resources》2005,28(10):1076-1082
Applications of the axisymmetric Boussinesq equation to groundwater hydrology and reservoir engineering have long been recognised. An archetypal example is invasion by drilling fluid into a permeable bed where there is initially no such fluid present, a circumstance of some importance in the oil industry. It is well known that the governing Boussinesq model can be reduced to a nonlinear ordinary differential equation using a similarity variable, a transformation that is valid for a certain time-dependent flux at the origin. Here, a new analytical approximation is obtained for this case. The new solution,, which has a simple form, is demonstrated to be highly accurate. 相似文献
13.
《Advances in water resources》2005,28(10):1032-1039
An existing capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-investigated. Existing solutions, based on the shallow flow expansion, have considered only the zeroth-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal aquifer adjacent to a sloping beach is derived. A new definition of the capillarity correction is proposed for small capillary fringes, and a simplified solution is derived. Comparisons of the two models show that the simplified model can be used in most cases. The significant effects of higher-order capillarity corrections on tidal fluctuations in a sloping beach are also demonstrated. 相似文献
14.
Qianqian Liu Gulimire Hanati Sulitan Danierhan Yin Zhang Zhiping Zhang 《Ground water》2019,57(6):969-979
As a component of arid ecosystems, groundwater plays an important role in plant growth; therefore, it is essential to use deterministic models to reconstruct the process of groundwater level change. Typically, the linearized solution of the one-dimensional (1-D) Boussinesq equation yields acceptable performance in simulating transient conditions over short recharge periods in ephemeral stream systems, but the ability of this solution to simulate multiyear changes in groundwater levels is limited. In this study, an improved groundwater hydraulics (GH-D2) model is built based on the groundwater hydraulics (GH) solution of the 1-D Boussinesq equation to simulate multiyear changes in the groundwater level in ephemeral stream systems. The model is validated in the lower reaches of the Tarim River to simulate groundwater level fluctuations within the scope of influence of the river (300, 500, 750, 1050 m) over a 16-year period (2000 to 2015). To evaluate the performance of the models, the bias, mean absolute error, root mean squared error, Nash-Sutcliffe efficiency (NSE), and coefficient of determination (R2) are calculated. The results show that the improved GH-D2 model, which considers ephemeral streamflow, unsteady flow theory and the delayed response effect of groundwater level changes, performs well in simulating multiyear changes in the groundwater level in the ephemeral stream system. The observed and simulated values of the groundwater level at different river distances are consistent, and the model provides a new basis for multiyear simulations of groundwater level fluctuations in ephemeral stream systems. 相似文献
15.
One-dimensional transient groundwater flow from a divide to a river in an unconfined aquifer described by the Boussinesq equation was studied. We derived the analytical solution for the water table recession and drainage change process described with a linearized Boussinesq equation with a physically based initial condition. A method for determining the average water table in the solutions was proposed. It is shown that the solution derived in the form of infinite series can be well approximated with the simplified solution which contains only the leading term of the original solution. The solution and their simplification can be easily evaluated and used by others to study the groundwater flow problems, such as drainage and base flow estimation, in an unconfined aquifer. 相似文献
16.
This is the first of a two‐part paper exploring the coevolution of bedrock weathering and lateral flow in hillslopes using a simple low‐dimensional model based on hydraulic groundwater theory (also known as Dupuit or Boussinesq theory). Here, we examine the effect of lateral flow on the downward fluxes of water and solutes through perched groundwater at steady state. We derive analytical expressions describing the decline in the downward flux rate with depth. Using these, we obtain analytical expressions for water age in a number of cases. The results show that when the permeability field is homogeneous, the spatial structure of water age depends qualitatively on a single dimensionless number, Hi. This number captures the relative contributions to the lateral hydraulic potential gradient of the relief of the lower‐most impermeable boundary (which may be below the weathering front within permeable or incipiently weathered bedrock) and the water table. A “scaled lateral symmetry” exists when Hi is low: age varies primarily in the vertical dimension, and variations in the horizontal dimension x almost disappear when the vertical dimension z is expressed as a fraction z/H(x) of the laterally flowing system thickness H(x). Taking advantage of this symmetry, we show how the lateral dimension of the advection–diffusion‐reaction equation can be collapsed, yielding a 1‐D vertical equation in which the advective flux downward declines with depth. The equation holds even when the permeability field is not homogeneous, as long as the variations in permeability have the same scaled lateral symmetry structure. This new 1‐D approximation is used in the accompanying paper to extend chemical weathering models derived for 1‐D columns to hillslope domains. 相似文献
17.
An alternative Boussinesq equation considering the effect of hysteresis on coastal groundwater waves 
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下载免费PDF全文 This paper presents an alternative Boussinesq equation considering hysteresis effect via a third‐order derivative term. By introducing an improved moisture–pressure retention function, this equation describes, with reasonable precision, groundwater propagation in coastal aquifers subject to Dirichlet boundary condition of different oscillation frequencies. Test results confirmed that it is necessary to consider horizontal and vertical flows in unsaturated zone, because of their variable influences on hysteresis. Hysteresis in unsaturated zone can affect the water table wave number of groundwater wave motion, such as wave damping rate and phase lag. Oscillations with different periods exert different hysteresis effect on wave propagation. Truncation/shrinkage of unsaturated zones also affects the strength of hysteresis. These impacts can be reflected in the alternative Boussinesq equation by adjusting the parameter representing the variation rate of moisture associated with pressure change, as opposed to traditional computationally expensive hysteresis algorithms. The present Boussinesq equation is simple to use and can provide feasible basis for future coupling of groundwater and surface water models. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
18.
Benoit Cushman-Roisin 《地球物理与天体物理流体动力学》2013,107(1-2):35-59
Abstract A new model of convection and mixing is presented. The fluid is envisioned as being composed of two buoyant interacting fluids, called thermals and anti-thermals. In the context of the Boussinesq approximation, pairs of governing equations are derived for thermals and anti-thermals. Each pair meets an Invariance Principle as a consequence of the reciprocity in the roles played by thermals and anti-thermals. Each pair is transformed into an average equation for which interaction terms cancel and another very simple equation linking the two fluid properties. An important parameter of the model is the fraction, f, of area occupied by thermals to the total area. A dynamic saturation equilibrium between thermals and antithermals is assumed. This implies a constant values of f throughout the system. The set of equations is written in terms of mean values and root-mean-square fluctuations, in keeping with equations of turbulence theories. The final set consists of four coupled non-linear differential equations. The model neglects dissipation and can be applied to any convective situations where molecular viscosity and diffusivity may be neglected. Applications of the model to mixed-layer deepening and penetrative convection are presented in subsequent papers. 相似文献
19.
A mathematical model is presented to describe the variations of the water table in an unconfined aquifer due to time-varying recharge applied from four rectangular basins. The model is developed by solving the linearised Boussinesq equation using the extended finite Fourier cosine transform. The time-varying recharge rate is approximated by a number of piecewise linear elements of different lengths and slopes depending on the nature of the variation in recharge rate. Application of this model for the prediction of water table fluctuations and in the sensitivity analysis of various controlling parameters on the aquifer response is demonstrated in an example. 相似文献
20.
A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches 总被引：3，自引：0，他引：3
H. T. Teo D. S. Jeng B. R. Seymour D. A. Barry L. Li 《Advances in water resources》2003,26(12):1239-1247
The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, N=αcotβ (in which β is the beach slope, α is the amplitude parameter and is the shallow water parameter) and are limited to tan−1(α)βπ/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as and α increase, and reaches 7% of the linear solution. 相似文献