Turbulent transport of atmospheric aerosols and formation of large-scale structures

Turbulent transport of aerosols and droplets in a random velocity field with a finite correlation time is studied. We derived a mean-field equation and an equation for the second moment for a number density of aerosols. The finite correlation time of random velocity field results in the appearance of the high-order spatial derivatives in these equations. The finite correlation time and compressibility of the velocity field can cause a depletion of turbulent diffusion and a modification of an effective mean drift velocity. The coefficient of turbulent diffusion in the vertical direction can be depleted by 25 % due to the finite correlation time of a turbulent velocity field. The latter result is in compliance with the known anisotropy of the coefficient of turbulent diffusion in the atmosphere. The effective mean drift velocity is caused by a compressibility of particles velocity field and results in formation of large-scale inhomogeneities in spatial distribution of aerosols in the vicinity of the atmospheric temperature inversion. Results obtained by Saffman (1960) for the effect of molecular diffusivity in turbulent diffusion are generalized for the case of compressible and anisotropic random velocity field. A mechanism of formation of small-scale inhomogeneities in particles spatial distribution is also discussed. This mechanism is associated with an excitation of a small-scale instability of the second moment of number density of particles. The obtained results are important in the analysis of various atmospheric phenomena, e.g., atmospheric aerosols, droplets and smog formation.     

扩散波的时空反演与洪水实时预报技术

以扩散波方程描述天然河道中的洪水波运动规律。将数学物理反问题理论和离散反演算法与河道流量演算相结合提出了扩散波实时预报的方法。该法的特点是在求解流量场Ｑ（ｘ,ｔ）的同时反演计算扩散波波速Ｃ（ｘ,ｔ）和扩散系数Ｄ（ｘ,ｔ）,根据不断监测的新信息系列,直接利用原偏微分方程进行参数的实时校正和预报过程实时修正。     

One-dimensional unsteady solute transport along unsteady flow through inhomogeneous medium

The one-dimensional linear advection–diffusion equation is solved analytically by using the Laplace integral transform. The solute transport as well as the flow field is considered to be unsteady, both of independent patterns. The solute dispersion occurs through an inhomogeneous semi-infinite medium. Hence, velocity is considered to be an increasing function of the space variable, linearly interpolated in a finite domain in which solute dispersion behaviour is studied. Dispersion is considered to be proportional to the square of the spatial linear function. Thus, the coefficients of the advection–diffusion equation are functions of both the independent variables, but the expression for each coefficient is considered in degenerate form. These coefficients are reduced into constant coefficients with the help of a new space variable, introduced in our earlier works, and new time variables. The source of the solute is considered to be a stationary uniform point source of pulse type.     

The fast dynamo in interstellar turbulence

The α effect and coefficient of eddy diffusivity are calculated for the magnetic field in a random flow with recovery. Such a flow loses its memory abruptly at random times that form a Poisson flow of events. Interstellar turbulence sustained by supernova outbursts is one physical realization of such a flow. The growth rates and configurations of large-scale galactic magnetic fields for this situation are close to those predicted by simple galactic dynamo models. At the same time, the model of a flow with recovery makes it possible to trace the role of the effective “forgetting” of correlations. The presence of this forgetting distinguishes interstellar turbulence from other types of random flows.     

帷幕灌浆扩散半径及数值模拟的研究

从连续性方程出发,考虑浆液压力对土体孔隙率的影响,分析推导了浆液在多孔介质中的渗流规律,并给出了扩散半径的简单近似计算公式;然后将二相流理论应用到注浆研究中,假设孔隙由水和浆液完全充填,且二者不相混溶,建立了浆液驱水的非稳定渗流模型。根据某大坝的实际情况,用FLAC软件中的二相流模块对大坝灌浆过程进行了模拟分析,并与推导公式相比较。由于二相流理论考虑了毛细压力的作用,模拟得到的浆液扩散速率递减得更快。模拟结果表明,浆液和水之间存在着一个过渡带,浆液的饱和度在不同时间和位置上是变化的。随着时间的延长,浆液扩散得越远,但其速率逐渐减小。扩散半径不仅与渗透系数有关,还与孔隙度有关,而且孔隙度较渗透系数对扩散半径有着更大的影响。二相流理论可以更好地模拟帷幕灌浆的浆液扩散情况。     

A mathematical model on depth-averaged <Emphasis Type="Italic">β</Emphasis>-factor in open-channel turbulent flow

The well-known Rouse equation is the most widely used equation to determine the vertical distribution of suspended sediment concentration in an open-channel flow. The exponent of Rouse equation, known as Rouse number, contains the parameter β defined by the ratio of sediment diffusion coefficient to turbulent diffusion coefficient. As such to measure sediment concentration accurately, an appropriate expression for β is essentially needed. The present study, therefore, focuses on the derivation of depth-averaged β through modified expressions of sediment and turbulent diffusion coefficients. A regression analysis is done to establish the relation between β and normalized settling velocity, and the relation is used to determine suspension concentration.     

A double medium model for diffusion in fluid-bearing rock

The concept of a double porosity medium to model fluid flow in fractured rock has been applied to model diffusion in rock containing a small amount of a continuous fluid phase that surrounds small volume elements of the solid matrix. The model quantifies the relative role of diffusion in the fluid and solid phases of the rock. The fluid is the fast diffusion path, but the solid contains the volumetrically significant amount of the diffusing species. The double medium model consists of two coupled differential equations. One equation is the diffusion equation for the fluid concentration; it contains a source term for change in the average concentration of the diffusing species in the solid matrix. The second equation represents the assumption that the change in average concentration in a solid element is proportional to the difference between the average concentration in the solid and the concentration in the fluid times the solid-fluid partition coefficient. The double medium model is shown to apply to laboratory data on iron diffusion in fluid-bearing dunite and to measured oxygen isotope ratios at marble-metagranite contacts. In both examples, concentration profiles are calculated for diffusion taking place at constant temperature, where a boundary value changes suddenly and is subsequently held constant. Knowledge of solid diffusivities can set a lower bound to the length of time over which diffusion occurs, but only the product of effective fluid diffusivity and time is constrained for times longer than the characteristic solid diffusion time. The double medium results approach a local, grain-scale equilibrium model for times that are large relative to the time constant for solid diffusion.     

The use of a mixed scheme: mixed hybrid finite elements method/finite volumes (MHFE/FV), for the modeling of contaminants transport in unsaturated porous mediums

This work is intended for the development of a numerical method to simulate flows and solute transport in multiphasical porous medium taking into consideration the interaction of solid/solute. More precisely, the studied problem is modeled by a coupled system composed of an elliptical equation (for the flow) and an equation convection–diffusion–reaction (for the transfer). Numerical simulations were realistic for two-dimensional problems confirming the stability and efficiency of the combined scheme in the characterization of a pollutant transport through an unsaturated zone of an industrial site.     

顺直河流横向紊动扩散系数

利用垂直紊动扩散系数及水利几何形态关系,借助于抛物线型断面形态方程,提出了顺直河道中局部水深沿横断面的分布,在此基础上确定了横向紊动扩散系数的断面分布及其平均值表达式,阐明了无量纲横向紊流扩散系数间的关系,计算的断面平均横向紊动扩散系数与138组试验资料吻合良好。比较结果表明,建立的顺直河道横向紊流扩散系数计算公式能给出与实测值最接近的预测值。与现有的其它横向紊流扩散系数计算公式相比,其公式在理论上更加合理,机理上更加清楚,并且具有最小的预测误差。     

The effect of heterogeneity of diffusion parameters on chloride transport in low-permeability argillites

Understanding flow and transport in low-permeability media is very important in the context of nuclear waste disposal, oil and gas reservoirs and long term evolution of groundwater systems. In low-permeability media, transport by diffusion is often the most important mass transport process. This study investigates the effect of the heterogeneity of diffusion parameters on mass transport in low-permeability media. A geostatistical approach for integrating heterogeneity of diffusion parameters in groundwater flow and transport models is proposed and applied to the Toarcian argillites in France which are studied in the framework of feasibility of storing radioactive waste in deep clayey massifs. Stochastic fields of the diffusion parameters of the Toarcian argillites (France) are generated based on 64 measured values of diffusion coefficient and diffusion accessible porosity and used as input for a 3D local-scale groundwater flow and transport model. The chloride concentrations computed by these heterogeneous models are compared to the measured chloride concentrations and to concentrations calculated with a model in which the Toarcian argillites are subdivided into several homogeneous zones. The heterogeneous simulations result in a slightly better correspondence between measured and calculated values and have the additional advantage that the measured diffusion coefficient values in the Toarcian are perfectly honored in the model. This study shows that small-scale variability of diffusion parameters has a significant effect on solute concentrations and omitting this heterogeneity may be a problem in transport calculations in low-permeability media, depending on the specific setting and objectives of the study.     

Stochastic analysis of the effect of spatial variability of diffusion parameters on radionuclide transport in a low permeability clay layer

Most studies that incorporate subsurface heterogeneity in groundwater flow and transport models only analyze and simulate the spatial variability of hydraulic conductivity. Heterogeneity of the other flow and transport parameters are usually neglected. This approach is often justified, but there are, however, cases in which disregarding the heterogeneity of the other flow and transport parameters can be questionable. In low permeability media, for instance, diffusion is often the dominant transport mechanism. It therefore seems logical to incorporate the spatial variability of the diffusion parameters in the transport model. This study therefore analyses and simulates the spatial variability of the effective diffusion coefficient and the diffusion accessible porosity with geostatistical techniques and incorporates their heterogeneity in the transport model of a low permeability formation. The formation studied was Boom clay (Belgium), a candidate host rock for the deep geological disposal of high-level radioactive waste. The calculated output radionuclide fluxes of this model are compared with the fluxes calculated with a homogeneous model and a model with a heterogeneous hydraulic conductivity distribution. This analysis shows that the heterogeneity of the diffusion parameters has a much larger effect on the calculated output radionuclide fluxes than the heterogeneity of hydraulic conductivity in the low permeability medium under study.     

Condensation of heavy elements on dust grains in interstellar clouds

A possibility of an efficient condensation of heavy elements, such as iron, on the surface of dust grains in interstellar molecular clouds is studied. A high rate of dust destruction in the interstellar medium from one side, and a high degree of heavy elements depletion from the other indicate that the freezing-out of metals should be efficient in interstellar (predominantly molecular) clouds. This is possible only due to betatron acceleration of dust grains behind shocks that originate under intersection of supersonic turbulent flow. Estimates of the heavy elements depletion due to condensation on the surface of dust grains are given.     

Attenuation, transport and diffusion of scalar waves in textured random media

Most theoretical investigations of seismic wave scattering rely on the assumption that the underlying medium is statistically isotropic. However, deep seismic soundings of the crust as well as geological observations often reveal the existence of elongated or preferentially oriented scattering structures. In this paper, we develop mean field and radiative transfer theories to describe the attenuation and multiple scattering of a scalar wavefield in an anisotropic random medium. The scattering mean free path is found to depend strongly on the propagation direction. We derive a radiative transfer equation for statistically anisotropic random media from the Bethe–Salpeter formalism and propose a Monte Carlo method to solve this equation numerically. At longer times, the energy density is shown to obey a tensorial diffusion equation. The components of the diffusion tensor are obtained in closed form and excellent agreement is found between Monte Carlo simulations and analytical solutions of the diffusion equation. The theory has important potential implications for lithospheric models where scatterers are for example flat structures preferentially aligned along the surface. In this simple geometry, analytical expressions of the Coda Q parameter can be given explicitly in the diffusive regime. Our results suggest that pulse broadening and coda decay are controlled by different parameters, related to the eigenvalues of the diffusion tensor. These eigenvalues can differ by more than one order of magnitude. This theory could be applied to probe the anisotropy of length scales in the lithosphere.     

A numerical model of fine sediment transport on the continental shelf

A numerical model of fine-grained sediment dispersion in the New York Bight of the North American continental shelf is presented. Large amounts of waste material have been dumped in this region and the dispersal patterns of this material are of great interest to environmental managers. The model assumes that fine sediment resuspension is determined by surface wave activity and that transport is determined by tidal currents. Considering surface wave activity to be a random process reduces sediment motion to a random walk which is governed by a diffusion equation. The diffusion equation is solved numerically by an implicit time difference, finite element algorithm for a number of initial conditions. Initial conditions corresponding to ocean dumping sites show patterns of dispersal controlled by the geometry of the study region and the anisotropy of the tides. Material dumped at currently used dump sites reaches sensitive coastal areas before it leaves the continental shelf. Examination of the diffusion coefficients suggests an alternative dump site for fine-grained material. This dump site is relatively near sources of dumped material but produces minimal impact on coastal areas. This site should be considered as a possible alternative to expensive direct disposal at deep ocean sites.     

高塌落度防渗墙填料扩散系数快速测定的透析试验

扩散是低渗透系数情况下溶质迁移的主要方式,目前尚没有测定高塌落度防渗墙填料扩散系数的试验方法。根据沥出试验原理,将处于流动状态的填料用半透膜包裹进行透析试验,通过有限圆柱中溶质迁移解析解对溶质迁移过程进行拟合求其扩散系数,探讨了试验和数据处理的相关问题,研究了膨润土含量和盐浴浓度对扩散系数的影响规律。结果表明,随拟合天数增加,填料中NaCl有效扩散系数减小,而误差增大;高塌落度填料中溶质迁移明显比压实土样中快,按拟合误差小于0.5%作为试验数据取舍依据,这一误差要求实际上是对溶质迁移以扩散为主导这一条件的量化,保证了采用纯扩散解析解进行数据拟合的合理性;扩散系数随填料中膨润土含量增加而减小,随盐浴浓度增加而减小,但在试验范围内数值变化不大,透析试验是快速测定防渗墙填料中溶质有效扩散系数的可行方法。     

Toward a unified theory of tidally-averaged estuarine salinity structure

Equations are developed for the tidally-averaged, width-averaged estuarine salinity and circulation in a rectangular estuary. Width and depth may vary along the length of the channel, as may coefficients of vertical turbulent mixing and along channel diffusion. The system is reduced to a single first-order, nonlinear, ordinary differential equation governing the section-averaged salinity. A technique for specifying the ocean boundary condition is given, and solutions are found by numerical integration. Under different assumptions for the diffusion it is possible to reproduce the few existing analytical solutions, in particular the Hansen and Rattray (1965) Central Regime solution, and Chatwin's (1976) solution. The mathematical framework allows easy comparison of the results of different channel geometries and mixing coefficients. Of particular interest is the along-channel distribution of the diffusive fraction of up-estuary salt flux. It is shown that the Hansen and Rattray solution is always diffusion-dominated near the mouth. A theory is presented for estimating the diffusion coefficient within a tidal excursion of the mouth. It is shown that the resulting rapid along-channel increase of diffusion may explain some observed patterns of salinity structure: a decrease in both stratification and along-channel salinity gradient near the mouth. The theory is applied to the Delaware Estuary and Northern San Francisco Bay, and shows reasonable agreement with observed sensitivities of salt intrusion distance to river flow.     

北京市朝阳区沙子营垃圾污染物在潜水含水层中迁移规律的现场模拟实验

选择北京平原区水文地质、环境地质等方面都比较典型的沙子营垃圾堆放场,建立了其水文地质模型。在充分收集资料、分析得出部分计算所需参数后,采用现场弥散实验、勘查取样测试等方法,求得了该含水层的弥散系数等参数;用二维非稳定流溶质运移方程对污染物在此含水层中的迁移扩散规律、速度和污染范围等进行了模拟计算;采用现场钻探、取样测试分析等方法,评价了该含水层的实际污染状况。实验模拟计算和现场调查结果表明:污染物在潜水含水层中的运移规律遵循二维非稳定流场中的溶质运移方程,污染物在潜水含水层中的运移速度约为86.25m/a,迁移扩散主要发生在地下水流向上,侧向扩散宽度极小,是地下水流向上的1/17。     

多尺度多孔介质有效气体输运参数的分形特征

非常规油气资源的孔隙结构及其连通性非常复杂,其孔隙尺度从毫米到纳米跨越多个量级.多孔介质中气体的输运过程不仅依赖于介质的多尺度微观结构特征,还依赖于气体的相关属性.气体在多尺度多孔介质中的输运过程包括无滑流、滑脱流和过渡流,涉及分子扩散和努森扩散等多种机制,因此很难用唯一的连续介质理论来描述气体的输运特征.大量的数据表明真实多孔介质中的内部孔隙具有分形标度特征,因此采用分形几何表征多尺度多孔介质的孔隙结构,引入孔隙分形维数和迂曲度分形维数定量表征多孔介质的微结构和弯曲流道,建立多尺度多孔介质气体输运过程的细观模型;推导了多尺度多孔介质中气体的有效渗透率和有效扩散系数,并讨论了多尺度多孔介质微结构参数和气体属性对于气体等效输运特性的定量影响.该研究不仅可以丰富渗流理论,且有利于深入理解非常规油气藏的产出机制.      

Error Estimates for a Time Discretization Method for the Richards' Equation

We present a numerical analysis of a time discretization method applied to Richards' equation. Written in its saturation-based form, this nonlinear parabolic equation models water flow into unsaturated porous media. Depending on the soil parameters, the diffusion coefficient may vanish or explode, leading to degeneracy in the original parabolic equation. The numerical approach is based on an implicit Euler time discretization scheme and includes a regularization step, combined with the Kirchhoff transform. Convergence is shown by obtaining error estimates in terms of the time step and of the regularization parameter.     

基于最小作用原理的Richards方程变分解

经典的Richards入渗控制方程属于偏微分方程,具有强烈的非线性,难以求得解析解。以入渗时间为最小作用量,基于Richards方程建立关于入渗路径的时间泛函,将考虑重力项的非饱和土垂直入渗问题转化为泛函极值问题,并构造等价的Euler-Lagrange方程进行求解。计算结果表明,扩散系数D（?）与概化湿润锋距离具有函数关系,当扩散系数D（?）形式已知时,可求得最优路径下湿润锋处含水率、较远处湿润锋最小含水率、土壤含水率最大熵分布3个问题,并基于最优路径检验了本研究条件下,Boltzmann变换和线性变换求解Richards方程的精度。求解过程未引进新变量化简Richards方程,不改变原方程结构,因此其解具有普遍性,可作为非饱和土力学计算的一个补充。