Analysis of hydrodynamic conditions in adjacent free and heterogeneous porous flow domains

The existence of a free‐flow domain (e.g. a liquid layer) adjacent to a porous medium is a common occurrence in many environmental and petroleum engineering problems. The porous media may often contain various forms of heterogeneity, e.g. layers, fractures, micro‐scale lenses, etc. These heterogeneities affect the pressure distribution within the porous domain. This may influence the hydrodynamic conditions at the free–porous domain interface and, hence, the combined flow behaviour. Under steady‐state conditions, the heterogeneities are known to have negligible effects on the coupled flow behaviour. However, the significance of the heterogeneity effects on coupled free and porous flow under transient conditions is not certain. In this study, numerical simulations have been carried out to investigate the effects of heterogeneous (layered) porous media on the hydrodynamics conditions in determining the behaviour of combined free and porous regimes. Heterogeneity in the porous media is introduced by defining a domain composed of two layers of porous media with different values of intrinsic permeability. The coupling of the governing equations of motion in free and porous domains has been achieved through the well‐known Beavers and Joseph interfacial condition. Of special interest in this work are porous domains with flow‐through ends. They represent the general class of problems where large physical domains are truncated to smaller sections for ease of mathematical analysis. However, this causes a practical difficulty in modelling such systems. This is because the information on flow behaviour, i.e. boundary conditions at the truncated sections, is usually not available. Use of artificial boundary conditions to solve these problems effectively implies the imposition of conditions that do not necessarily match with the solutions required for the interior of the domain. This difficulty is resolved in this study by employing ‘stress‐free boundary conditions’ at the open ends of the domains, which have been shown to provide accurate results by a number of previous workers. Copyright © 2005 John Wiley & Sons, Ltd.     

Accuracy of deflections of vertical determined from discrete solution of the geodetic boundary value problem

Summary The general problem of determining the figure of the earth leads to the solution of the geodetic boundary value problem. By its discrete approximation we obtain the discrete disturbing potential that maintains all properties of the original problem. Thus, the discrete approximation of the disturbing potential can be used in studying the behaviour of the earth's gravity field outside the disturbing masses. The deflections of the vertical are one of the quantities describing the behaviour of the earth's gravity field. A method for their computation from the discrete solution of the geodetic boundary value problem is put forth and estimates for its accuracy are given.     

Internal dissipative boundary layers in the cross-equatorial flow of a grounded deep western boundary current

It is known that dissipative adjustment must occur in the cross-equatorial dynamics of a deep western boundary current (DWBC) that is in planetary-geostrophic balance away from the equator. Theoretical modelling and numerical simulations suggest that the dissipative zones correspond to “small” isolated zonally-elongated regions within the trough and crest of a nonlinear stationary equatorial planetary wave that is formed as the DWBC flows eastward along the equator. An internal frictional boundary layer theory is advanced to describe the leading order structure of the DWBC in the dissipative regions, which asymptotically matches with the large scale inviscid flow characteristics in the equatorial region.     

Integrated surface–groundwater flow modeling: A free-surface overland flow boundary condition in a parallel groundwater flow model

Interactions between surface and groundwater are a key component of the hydrologic budget on the watershed scale. Models that honor these interactions are commonly based on the conductance concept that presumes a distinct interface at the land surface, separating the surface from the subsurface domain. These types of models link the subsurface and surface domains via an exchange flux that depends upon the magnitude and direction of the hydraulic gradient across the interface and a proportionality constant (a measure of the hydraulic connectivity). Because experimental evidence of such a distinct interface is often lacking in field systems, there is a need for a more general coupled modeling approach.     

Similarity solutions to the second boundary value problem of unsaturated flow through porous media

Similarity solutions to the second boundary value problem of unsaturated flow are studied in one-dimensional, semi-infinite porous media with the soil-water diffusivity proportional to some power of the water content. The existence and uniqueness of two types of similarity solutions to the problem are investigated and the properties of these solutions are presented. It is shown that these two types of similarity solutions exist and that they may not be unique for every parameter range studied. The use of the similarity solutions is discussed for the experimental determination of soil-water diffusivity.     

一个大气边界层非线性三维数值模式及其在太湖流域的应用

本模式用以K半经验理论为基础的闭合方程组求解,引进了地形作用、动量、热量和水汽的侧向扩散和垂直湍流交换以及凝结加热等物理过程,其中湍流交换系数K是地表粗糙度、几何高度、大气稳定度及风速切变等因子的函数。本模式还考虑了山地、平原和水面在地形高度、地表粗糙度、辐射、蒸发及热交换等方面的差异,在下垫面上建立热平衡方程与边界层内控制方程耦合。将模式应用于太湖流域,计算得到的该流域边界层内温、压、湿、风的分布特征与实际情况相似,模式具有一定的实用性。     

The nonlinear stabilization of a zonal shear flow instability

Abstract

The development of initially small perturbations in a weakly supercritical zonal shear flow on a β-plane is studied. Two different scenarios of evolution are possible. If the supercriticality is sufficiently small, the growth of a perturbation is stopped in the viscous critical layer regime; for this case the evolution equation (corrected by the inclusion of a quintic nonlinearity) is derived. At greater supercriticality the nonlinearity cannot stop the growth of the perturbation in a linear (viscous or unsteady) critical layer regime, and the evolution is more complicated. Transition to a nonlinear critical layer regime leads to a reduction in the growth rate and to a slowing (but not a stopping) of the increase in amplitude, A. These are connected to the formation of a plateau (S=constant) of width L=O(A ^½) in the profile of absolute vorticity, S. Careful analysis reveals that the growth in amplitude ceases only when the whole instability domain (where the slope of unperturbed S-profile is positive) becomes covered again by the plateau.     

The nonlinear development of disturbances in a zonal shear flow

Abstract

A study is made of the nonlinear stability of a weakly supercritical zonal shear flow in the β-plane approximation. The dynamics of initially small disturbances are examined. The main nonlinear effects are associated with the rearrangement of the critical layer. It is shown that as the wave grows in amplitude, linear regimes of the critical layer (viscous and nonstationary) change over to a nonlinear regime while the exponential law of disturbance growth becomes a power-law.     

基于非线性模型的TLD参数优化

高柔结构在强风或地震等环境荷载作用下，往往会产生较大的变形和位移。采用调谐液体阻尼器对结构进行控制时，需要选择合适的水箱尺寸和水深，以期获得最好的减振效果。以往的调谐液体阻尼器参数优化往往基于等效线性模型或在小幅值激励下有较好精度的非线性浅水波动模型。采用了一种具有非线性阻尼和非线性刚度的等效调谐质量阻尼器模型对影响调谐液体阻尼器减振效率的主要参数进行了优化，该模型不再受小幅值激励的限制。优化结果表明，激励幅值对TLD的最优参数和减振效果有明显影响，同时水箱长度对TLD减振效果也有明显影响，这是基于线性模型TLD优化不能得到的结论。     

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.     

A BME solution of the inverse problem for saturated groundwater flow

In most real-world hydrogeologic situations, natural heterogeneity and measurement errors introduce major sources of uncertainty in the solution of the inverse problem. The Bayesian Maximum Entropy (BME) method of modern geostatistics offers an efficient solution to the inverse problem by first assimilating various physical knowledge bases (hydrologic laws, water table elevation data, uncertain hydraulic resistivity measurements, etc.) and then producing robust estimates of the subsurface variables across space. We present specific methods for implementing the BME conceptual framework to solve an inverse problem involving Darcys law for subsurface flow. We illustrate one of these methods in the case of a synthetic one-dimensional case study concerned with the estimation of hydraulic resistivity conditioned on soft data and hydraulic head measurements. The BME framework processes the physical knowledge contained in Darcys law and generates accurate estimates of hydraulic resistivity across space. The optimal distribution of hard and soft data needed to minimize the associated estimation error at a specified sampling cost is determined. This work was supported by grants from the National Institute of Environmental Health Sciences (Grant no. 5 P42 ES05948 and P30ES10126), the National Aeronautics and Space Administration (Grant no. 60-00RFQ041), the Army Research Office (Grant no. DAAG55-98-1-0289), and the National Science Foundation under Agreement No. DMS-0112069.     

Semi-active model predictive control for 3rd generation benchmark problem using smart dampers

A semi-active strategy for model predictive control (MPC), in which magneto-rheological dampers are used as an actuator, is presented for use in reducing the nonlinear seismic response of high-rise buildings. A multi-step predictive model is developed to estimate the seismic performance of high-rise buildings, taking into account of the effects of nonlinearity, time-variability, model mismatching, and disturbances and uncertainty of controlled system parameters by the predicted error feedback in the multi-step predictive model. Based on the predictive model, a Kalman-Bucy observer suitable for semi-active strategy is proposed to estimate the state vector from the acceleration and semi-active control force feedback. The main advantage of the proposed strategy is its inherent stability, simplicity, on-line real-time operation, and the ability to handle nonlinearity, uncertainty, and time-variability properties of structures. Numerical simulation of the nonlinear seismic responses of a controlled 20-story benchmark building is carried out, and the simulation results are compared to those of other control systems. The results show that the developed semi-active strategy can efficiently reduce the nonlinear seismic response of high-rise buildings.     

A new solution and data analysis for gas flow to a barometric pumping well

When an open well is installed in an unsaturated zone, gas will flow to/from the well depending on the pressure difference between the well and the surrounding media. This process is called barometric pumping and the well is called a barometric pumping well (BPW). Understanding subsurface gas pressure distribution and gas flow rate to/from a BPW is indispensable to optimize passive soil vapor extraction. This study presents a 2-D semi-analytical solution to calculate the subsurface gas pressure and gas flow rate to/from a BPW with and without a check valve. The problem is conceptualized as a mixed-type boundary value problem. The solution for pumping without a check valve is used to analyze the behavior of the radius of influence (ROI). Results show that ROI is time-dependent. It increases with radial gas permeability and decreases with vertical gas permeability. Field application of the solution without a check valve demonstrates the high accuracy of the developed solution.     

暗支撑剪力墙非线性分析模型

建立了适合于带暗支撑剪力墙非线性分析的宏观单元模型,分别用带斜杆的多垂直杆单元模型和模拟框架单元模型对2个带暗支撑剪力墙进行了静力弹塑性分析,给出了模拟框架单元模型的刚度矩阵和杆件非线性力-变形关系,对两种不同单元模型的计算结果进行了对比,结果表明该两种模型能够较好反映带暗支撑剪力墙的弹性和塑性阶段的受力特点。     

Development of a new semi-analytical model for cross-borehole flow experiments in fractured media

Analysis of borehole flow logs is a valuable technique for identifying the presence of fractures in the subsurface and estimating properties such as fracture connectivity, transmissivity and storativity. However, such estimation requires the development of analytical and/or numerical modeling tools that are well adapted to the complexity of the problem. In this paper, we present a new semi-analytical formulation for cross-borehole flow in fractured media that links transient vertical-flow velocities measured in one or a series of observation wells during hydraulic forcing to the transmissivity and storativity of the fractures intersected by these wells. In comparison with existing models, our approach presents major improvements in terms of computational expense and potential adaptation to a variety of fracture and experimental configurations. After derivation of the formulation, we demonstrate its application in the context of sensitivity analysis for a relatively simple two-fracture synthetic problem, as well as for field-data analysis to investigate fracture connectivity and estimate fracture hydraulic properties. These applications provide important insights regarding (i) the strong sensitivity of fracture property estimates to the overall connectivity of the system; and (ii) the non-uniqueness of the corresponding inverse problem for realistic fracture configurations.     

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.     

开边界海盆尺度环流模式模拟北太平洋CFCs分布

利用一个开边界北太平洋海盆尺度环流模式模拟了北太平洋CFCs的吸收和分布.模式计算了CFC_11海气界面通量及其在海洋中的输运和再分布,考察了开边界对模式模拟结果的影响以及开边界模式中不同沿等密度面扩散系数的影响.打开南边界可以很好地改善赤道以南海区的CFC_11模拟.增加沿等密度面扩散系数使得137°E和165°E断面模拟的高CFC_11水向南、向下输送的强度和影响范围都有明显增大,能很好地改善西北太平洋的模拟结果.西北太平洋是CFC_11的一个重要的汇区,此外在赤道东太平洋上升流区还存在一个小的汇区.     

完全匹配层吸收边界在孔隙介质弹性波模拟中的应用

模拟弹性波在孔隙介质中传播,需要稳定有效的吸收边界来消除或尽可能的减小由人工边界引起的虚假反射. 本文在前人工作基础上,首次建立了弹性孔隙介质情况下完全匹配层吸收边界的高阶速度-应力交错网格有限差分算法,并详细讨论了完全匹配层的构建及其有限差分算法实现. 首先,本文通过均匀孔隙模型的数值解与解析解的对比,验证所提出的数值方法的正确性;然后,本文考察了完全匹配层对不同入射角度入射波和自由表面上的瑞利波的吸收性能,将完全匹配层与廖氏和阻尼吸收边界进行了对比,研究了这三种吸收边界在不同吸收厚度情况下对弹性波吸收能力. 数值结果表明,在孔隙介质中,完全匹配层作为吸收边界能十分有效地吸收衰减外行波,无论对体波还是面波,是一种高效边界吸收算法.     

A new ellipsoidal gravimetric, satellite altimetry and astronomic boundary value problem, a case study: The geoid of Iran

A new gravimetric, satellite altimetry, astronomical ellipsoidal boundary value problem for geoid computations has been developed and successfully tested. This boundary value problem has been constructed for gravity observables of the type (i) gravity potential, (ii) gravity intensity (i.e. modulus of gravity acceleration), (iii) astronomical longitude, (iv) astronomical latitude and (v) satellite altimetry observations. The ellipsoidal coordinates of the observation points have been considered as known quantities in the set-up of the problem in the light of availability of GPS coordinates. The developed boundary value problem is ellipsoidal by nature and as such takes advantage of high precision GPS observations in the set-up. The algorithmic steps of the solution of the boundary value problem are as follows:

- Application of the ellipsoidal harmonic expansion complete up to degree and order 360 and of the ellipsoidal centrifugal field for the removal of the effect of global gravity and the isostasy field from the gravity intensity and the astronomical observations at the surface of the Earth.

- Application of the ellipsoidal Newton integral on the multi-cylindrical equal-area map projection surface for the removal from the gravity intensity and the astronomical observations at the surface of the Earth the effect of the residual masses at the radius of up to 55 km from the computational point.

- Application of the ellipsoidal harmonic expansion complete up to degree and order 360 and ellipsoidal centrifugal field for the removal from the geoidal undulations derived from satellite altimetry the effect of the global gravity and isostasy on the geoidal undulations.

- Application of the ellipsoidal Newton integral on the multi-cylindrical equal-area map projection surface for the removal from the geoidal undulations derived from satellite altimetry the effect of the water masses outside the reference ellipsoid within a radius of 55 km around the computational point.

- Least squares solution of the observation equations of the incremental quantities derived from aforementioned steps in order to obtain the incremental gravity potential at the surface of the reference ellipsoid.

- The removed effects at the application points are restored on the surface of reference ellipsoid.

- Application of the ellipsoidal Bruns’ formula for converting the potential values on the surface of the reference ellipsoid into the geoidal heights with respect to the reference ellipsoid.

- Computation of the geoid of Iran has successfully tested this new methodology.