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1.
An exact, closed‐form analytical solution is derived for one‐dimensional (1D), coupled, steady‐state advection‐dispersion equations with sequential first‐order degradation of three dissolved species in groundwater. Dimensionless and mathematical analyses are used to examine the sensitivity of longitudinal dispersivity in the parent and daughter analytical solutions. The results indicate that the relative error decreases to less than 15% for the 1D advection‐dominated and advection‐dispersion analytical solutions of the parent and daughter when the Damköhler number of the parent decreases to less than 1 (slow degradation rate) and the Peclet number increases to greater than 6 (advection‐dominated). To estimate first‐order daughter product rate constants in advection‐dominated zones, 1D, two‐dimensional (2D), and three‐dimensional (3D) steady‐state analytical solutions with zero longitudinal dispersivity are also derived for three first‐order sequentially degrading compounds. The closed form of these exact analytical solutions has the advantage of having (1) no numerical integration or evaluation of complex‐valued error function arguments, (2) computational efficiency compared to problems with long times to reach steady state, and (3) minimal effort for incorporation into spreadsheets. These multispecies analytical solutions indicate that BIOCHLOR produces accurate results for 1D steady‐state, applications with longitudinal dispersion. Although BIOCHLOR is inaccurate in multidimensional applications with longitudinal dispersion, these multidimensional multispecies analytical solutions indicate that BIOCHLOR produces accurate steady‐state results when the longitudinal dispersion is zero. As an application, the 1D advection‐dominated analytical solution is applied to estimate field‐scale rate constants of 0.81, 0.74, and 0.69/year for trichloroethene, cis‐1,2‐dichloroethene, and vinyl chloride, respectively, at the Harris Palm Bay, FL, CERCLA site. 相似文献
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在岩石物理实验的基础上，综合运用水岩相互作用、表面物理、电化学等方面的理论，研究水型及矿化度变化对阿尔奇模型中的m、n值以及Waxman-Smits模型中B参数的影响及作用机理.结果表明，水型及矿化度的变化不仅对m、n、B值产生影响，由于在不同的浓度范围内，地层水矿化度对岩石颗粒表面偶电层厚度及平衡离子活动性的影响不同，还导致Archie公式中的m、n值以及Waxman-Smits模型中的B参数在不同矿化度范围内表现出不同的特征：低矿化度情况下，m、n、B值随着矿化度的降低而迅速减小；而当矿化度升高到一定程度以后，m、n、B值趋于稳定，此时的岩电参数是偶电层中扩散层消失后岩石电学特征的反映. 相似文献
4.
Dieter M. Imboden 《Earth and Planetary Science Letters》1975,27(2):221-228
A general one-dimensional equation for interstitial transport in accumulating and compacting sediments under non-steady state conditions is derived. As a consequence of compaction the metric along the path of a given horizon, i.e. the spatial distance between neighbouring particles, changes continually. Special emphasis is put on the treatment of advection caused by compaction. The resulting partial differential equation for the interstitial concentration of a given solute contains terms which can be evaluated based on data from a single sediment core. In addition, an integral over the time-derivative of porosity appears which would make it necessary to compare cores from the same site but at different times. Under quite general assumptions this last term may, however, be transformed into a form for which evaluation from a single core becomes possible. Several special solutions are treated such as total steady state, steady state at the surface, non-constant sedimentation rate with steady state compaction, and non-steady state with steady state compaction. The last case applies, e.g., to diffusion under the influence of changing boundary conditions at the water/sediment interface while the accumulation process remains in steady state. 相似文献
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We provide an approximate analytical solution for the substrate-microbial dynamics of the organic carbon cycle in natural soils under hydro-climatic variable forcing conditions. The model involves mass balance in two carbon pools: substrate and biomass. The analytical solution is based on a perturbative solution of concentrations, and can properly reproduce the numerical solutions for the full non-linear problem in a system evolving towards a steady state regime governed by the amount of labile carbon supplied to the system. The substrate and the biomass pools exhibit two distinct behaviors depending on whether the amount of carbon supplied is below or above a given threshold. In the latter case, the concentration versus time curves are always monotonic. Contrarily, in the former case the C-pool concentrations present oscillations, allowing the reproduction of non-monotonic small-scale biomass concentration data in a natural soil, observed so far only in short-term experiments in the rhizosphere. Our results illustrate the theoretical dependence of oscillations from soil moisture and temperature and how they may be masked at intermediate scales due to the superposition of solutions with spatially variable parameters. 相似文献
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J. S. Frederiksen 《地球物理与天体物理流体动力学》2013,107(1-4):85-97
Abstract A new nonlinear stability criterion is derived for baroclinic flows over topography in spherical geometry. The stability of a wide class of exact three-dimensional nonlinear steady state solutions subject to arbitrary disturbances is established. The resonance condition, at the highest total wavenumber, for the steady state solutions and the stability criteria for baroclinic flow in the absence of topography provide the boundaries of the regions of stability in the presence of topography. The analogous results for flow on periodic or infinite beta planes incorporating non-orthogonal function large scale flows are also discussed. 相似文献
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The concentration fluctuations resulting from hazardous releases in the subsurface are modeled through the concentration moments. The local solute exposure concentration, resulting from the heterogeneous velocity field and pore scale dispersion in the subsurface, is a random function characterized by its statistical moments. The approximate solution to the exact equation that describes the evolution of concentration standard moments in the aquifer transport is proposed in a recursive form. The expressions for concentration second, third and fourth central moments are derived and evaluated for various flow and transport conditions. The solutions are sought by starting from the exact upper bound solution with the zero pore scale dispersion and introducing the physically based approximation that allows the inclusion of the pore scale dispersion resulting in simple closed-form expressions for the concentration statistical moments. The concentration moments are also analyzed in the relative and absolute frame of reference indicating their combined importance in the practical cases of the subsurface contaminant plume migration. The influence of pore scale dispersion with different source sizes and orientations are analyzed and discussed with respect to common cases in the environmental risk assessment problems. The results are also compared with the concentration measurements of the conservative tracer collected in the field experiments at Cape Cod and Borden Site. 相似文献
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Harold Ritchie 《地球物理与天体物理流体动力学》2013,107(1-2):49-92
Abstract The behavior of Rossby waves on a shear flow in the presence of a nonlinear critical layer is studied, with particular emphasis on the role played by the critical layer in a Rossby wave resonance mechanism. Previous steady analyses are extended to the resonant case and it is found that the forced wave dominates the solution, provided the flow configuration is not resonant for the higher harmonics induced by the critical layer. Numerical simulations for the forced initial value problem show that the solution evolves towards the analysed steady state when conditions are resonant for the forced wave, and demonstrate some of the complications that arise when they are resonant for higher harmonics. In relating the initial value and steady problems, it is argued that the time dependent solution does not require the large mean flow distortion that Haberman (1972) found to be necessary outside the critical layer in the steady case. 相似文献
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A two-dimensional equation governing the steady state spatial concentration distribution of a reactive constituent within a heterogeneous advective–dispersive flow field is solved analytically. The solution which is developed for the case of a single point source can be generalized to represent analogous situations with any number of separate point sources. A limiting case of special interest has a line source of constant concentration spanning the domain’s upstream boundary. The work has relevance for improving understanding of reactive transport within various kinds of advection-dominated natural or engineered environments including rivers and streams, and bioreactors such as treatment wetlands. Simulations are used to examine quantitatively the impact that transverse dispersion (deviations from purely stochastic-convective flow) can have on mean concentration decline in the direction of flow. Results support the contention that transverse mixing serves to enhance the overall rate of reaction in such systems. 相似文献
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Walter K. Dodds 《Aquatic Sciences - Research Across Boundaries》1993,55(2):132-142
Dissolved inorganic nutrient pools are small relative to particulate pools, and dissolved pools turnover rapidly. It has been observed that pools change little from day to day on the sampling scales usually employed. A simple model is presented where uptake and regeneration rates balance to cause a local steady state concentration for dissolved inorganic nutrients. Enrichment and dilution perturbation experiments with lake water support the idea of steady state nutrient concentrations. Although inorganic nutrient concentrations are often controlled by biota, the absolute concentrations present tell little about the activity of that biota. 相似文献
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The problem of free vibration of non-linear structures is considered initially. It is shown that this problem can be represented as a non-linear eigenvalue problem. Variational principles for non-linear eigenvalue problems are defined. These variational principles are implemented with finite element models to define numerical approximations for the free vibration problem. The solution of these approximate equations provides a set of non-linear modal vectors and natural frequencies which vary with the amplitude of the solution. The non-linear eigenvalue parameters can be used in modal expansion approximations for the non-linear transient or steady state response of structural systems. To demonstrate the proposed techniques the free vibration and steady state vibration characteristics of a geometrically non-linear circular plate are determined. 相似文献
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The evolution of localised jets and periodic nonlinear waves in rotating shallow water magnetohydrodynamics (rotating SWMHD) and standard rotating shallow water model (RSW) is compared within the framework of translationally-invariant 1.5-dimensional configurations, which are traditionally used in geophysical fluid dynamics for studying geostrophic adjustment and frontogenesis. Such configurations also allow for exact nonlinear wave solutions in both models. A theory of the magneto-geostrophic adjustment, i.e. adjustment of an arbitrary initial configuration to a state of magneto-geostrophic equilibrium in RSWMHD, is developed and confirmed by numerical simulations with a finite-volume well-balanced code. The code is resolving all kinds of waves in the model and corresponding weak solutions equally well. It is benchmarked by reproducing exact solutions – steady essentially nonlinear Alfvèn and mixed magneto-inertia-gravity waves – and used to demonstrate robustness of these solutions with respect to localised along-wave perturbations. It is also shown how the results on adjustment can be extended to the fully 2-dimensional case. 相似文献
13.
Jacob Zaidel 《Ground water》2013,51(6):952-959
Known analytical solutions of groundwater flow equations are routinely used for verification of computer codes. However, these analytical solutions (e.g., the Dupuit solution for the steady‐state unconfined unidirectional flow in a uniform aquifer with a flat bottom) represent smooth and continuous water table configurations, simulating which does not pose any significant problems for the numerical groundwater flow models, like MODFLOW. One of the most challenging numerical cases for MODFLOW arises from drying‐rewetting problems often associated with abrupt changes in the elevations of impervious base of a thin unconfined aquifer. Numerical solutions of groundwater flow equations cannot be rigorously verified for such cases due to the lack of corresponding exact analytical solutions. Analytical solutions of the steady‐state Boussinesq equation, associated with the discontinuous water table configurations over a stairway impervious base, are presented in this article. Conditions resulting in such configurations are analyzed and discussed. These solutions appear to be well suited for testing and verification of computer codes. Numerical solutions, obtained by the latest versions of MODFLOW (MODFLOW‐2005 and MODFLOW‐NWT), are compared with the presented discontinuous analytical solutions. It is shown that standard MODFLOW‐2005 code (as well as MODFLOW‐2000 and older versions) has significant convergence problems simulating such cases. The problems manifest themselves either in a total convergence failure or erroneous results. Alternatively, MODFLOW‐NWT, providing a good match to the presented discontinuous analytical solutions, appears to be a more reliable and appropriate code for simulating abrupt changes in water table elevations. 相似文献
14.
Morten Jakobsen 《Studia Geophysica et Geodaetica》2012,56(1):1-20
Forward seismic modelling in the acoustic approximation, for variable velocity but constant density, is dealt with. The wave
equation and the boundary conditions are represented by a volume integral equation of the Lippmann-Schwinger (LS) or Fredholm
type. A T-matrix (or transition operator) approach from quantum mechanical potential scattering theory is used to derive a
family of linear and nonlinear approximations (cluster expansions), as well as an exact numerical solution of the LS equation.
For models of 4D anomalies involving small or moderate contrasts, the Born approximation gives identical numerical results
as the first-order t-matrix approximation, but the predictions of an exact T-matrix solution can be quite different (depending
on spatial extention of the perturbations). For models of fluid-saturated cavities involving large or huge contrasts, the
first-order t-matrix approximation is much more accurate than the Born approximation, although it does not lead to significantly
more time-consuming computations. If the spatial extention of the perturbations is not too large, it is practical to use the
exact T-matrix solution which allows for arbitrary contrasts and includes all the effects of multiple scattering. 相似文献
15.
P.W. France 《Journal of Hydrology》1974,21(4):381-398
A numerical method is presented for analysing either steady state or transient three-dimensional groundwater flow problems. The governing equation is formulated in terms of the finite element process using the Galerkin approach, and cubic isoparametric elements are used to simulate the flow domain as these permit accurate modelling of curved boundaries. Particular attention is paid to the time dependent movement of the phreatic surface where an iterative technique based on the replacement of the original transient problem by a discrete number of steady state problems is used to effect a solution. Furthermore, in tracing the movement of the surface use is made of the element formulation theory in order to compute the normal to the boundary.The validity of the technique is first established by analysing a radially symmetrical problem for which an alternative analytical solution is available. Finally, a general three-dimensional flow system is studied for which there is no known analytical solution. It is shown that relatively few elements are required to yield practical solutions. 相似文献
16.
HUANG Guanhua HUANG Quanzhong ZHAN Hongbin CHEN Jing XIONG Yunwu FENG Shaoyuan 《中国科学D辑(英文版)》2005,48(Z2)
The newly developed Fractional Advection-Dispersion Equation (FADE), which is FADE was extended and used in this paper for modelling adsorbing contaminant transport by adding an adsorbing term. A parameter estimation method and its corresponding FORTRAN based program named FADEMain were developed on the basis of Nonlinear Least Square Algorithm and the analytical solution for one-dimensional FADE under the conditions of step input and steady state flow. Data sets of adsorbing contaminants Cd and NH4+-N transport in short homogeneous soil columns and conservative solute NaCI transport in a long homogeneous soil column, respectively were used to estimate the transport parameters both by FADEMain and the advection-dispersion equation (ADE) based program CXTFIT2.1. Results indicated that the concentration simulated by FADE agreed well with the measured data. Compared to the ADE model, FADE can provide better simulation for the concentration in the initial lower concentration part and the late higher concentration part of the breakthrough curves for both adsorbing contaminants. The dispersion coefficients for ADE were from 0.13 to 7.06 cm2/min, while the dispersion coefficients for FADE ranged from 0.119 to 3.05 cm1.856/min for NaCI transport in the long homogeneous soil column. We found that the dispersion coefficient of FADE increased with the transport distance, and the relationship between them can be quantified with an exponential function. Less scale-dependent was also found for the dispersion coefficient of FADE with respect to ADE. 相似文献
17.
Real‐time pseudodynamic (PSD) testing is an experimental technique for evaluating the dynamic behaviour of a complex structure. During the test, when the targeted command displacements are not achieved by the test structure, or a delay in the measured restoring forces from the test structure exists, the reliability of the testing method is impaired. The stability and accuracy of real‐time PSD testing in the presence of amplitude error and a time delay in the restoring force is presented. Systems consisting of an elastic single degree of freedom (SDOF) structure with load‐rate independent and dependent restoring forces are considered. Bode plots are used to assess the effects of amplitude error and a time delay on the steady‐state accuracy of the system. A method called the pseudodelay technique is used to derive the exact solution to the delay differential equation for the critical time delay that causes instability of the system. The solution is expressed in terms of the test structure parameters (mass, damping, stiffness). An error in the restoring force amplitude is shown to degrade the accuracy of a real‐time PSD test but not destabilize the system, while a time delay can lead to instability. Example calculations are performed for determining the critical time delay, and numerical simulations with both a constant delay and variable delay in the restoring force are shown to agree well with the stability limit for the system based on the critical time delay solution. The simulation models are also used to investigate the effects of a time delay in the PSD test of an inelastic SDOF system. The effect of energy dissipation in an inelastic structure increases the limit for the critical time delay, due to the energy removed from the system by the energy dissipation. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
18.
The exponential decline in saturated hydraulic conductivity with depth: a novel method for exploring its effect on water flow paths and transit time distribution 
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下载免费PDF全文 The strong vertical gradient in soil and subsoil saturated hydraulic conductivity is characteristic feature of the hydrology of catchments. Despite the potential importance of these strong gradients, they have proven difficult to model using robust physically based schemes. This has hampered the testing of hypotheses about the implications of such vertical gradients for subsurface flow paths, residence times and transit time distribution. Here we present a general semi‐analytical solution for the simulation of 2D steady‐state saturated‐unsaturated flow in hillslopes with saturated hydraulic conductivity that declines exponentially with depth. The grid‐free solution satisfies mass balance exactly over the entire saturated and unsaturated zones. The new method provides continuous solutions for head, flow and velocity in both saturated and unsaturated zones without any interpolation process as is common in discrete numerical schemes. This solution efficiently generates flow pathlines and transit time distributions in hillslopes with the assumption of depth‐varying saturated hydraulic conductivity. The model outputs reveal the pronounced effect that changing the strength of the exponential decline in saturated hydraulic conductivity has on the flow pathlines, residence time and transit time distribution. This new steady‐state model may be useful to others for posing hypotheses about how different depth functions for hydraulic conductivity influence catchment hydrological response. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
19.
A new benchmark semi-analytical solution is proposed for the verification of density-driven flow codes. The problem deals with a synthetic square porous cavity subject to different salt concentrations at its vertical walls. A steady state semi-analytical solution is investigated using the Fourier–Galerkin method. Contrarily to the standard Henry problem, the cavity benchmark allows high truncation orders in the Fourier series and provides semi-analytical solutions for very small diffusion cases. The problem is also investigated numerically to validate the semi-analytical solution. The obtained results represent a set of new test case high quality data that can be effectively used for benchmarking density-driven flow codes. 相似文献
20.
Erol Varoḡlu 《Advances in water resources》1982,5(1):35-41
A method of solution for the diffusion-convection equation in one spatial dimension has been developed previously. The generalization of this method into two-spatial dimensions will be presented. The method employs space-time volume elements with edges joining the nodes at subsequent time levels oriented along the characteristics of the associated pure convection problem. The accuracy and utility of the method are demonstrated by solving several examples and results are compared with the exact solutions. 相似文献