空隙介质水动力弥散尺度效应的分形特征及弥散度初步估计

通过时空隙介质中水动力弥散尺度效应近期研究成果的总结和分析，阐述了不同尺度下空隙介质的空间非均质的自相似性，提出了水动力弥散的尺度效应在统计意义上具有分形特征，按计算方法（解析模型与数值方法）与岩性特征（孔隙介质与非孔隙介质）及计算模型维数的不同，对世界范围内所收集到的百余个纵向弥散度数据求出了尺度效应的分维数并进行了分析与讨论，为地下水污染模型研究提供了一种参数的初步估计方法。     

Experimental Investigation into the Scale Dependence of Fluid Transport in Heterogeneous Rocks

We investigated the dependence of hydraulic properties on the spatial scale of intrinsic and artificial heterogeneity, applying harmonic pore pressure testing to two varieties of Fontainebleau sandstone at various periods and effective pressures. Blocks with porosities of about 5 and 8% were chosen exhibiting a permeability of about 2·10⁻¹⁹ and 1·10⁻¹³ m², respectively. The permeability of the less permeable variety strongly depends on sample size. Artificial heterogeneous rock samples were prepared by stacking pieces of the two sandstone varieties perpendicular and parallel to the main flow direction. The perturbation of the fluid flow owing to the interfaces between pieces of the same variety is controlled by the orientation of and subordinately by the effective stress on the interfaces. Constraints on conduit geometry derived from the effect of interfaces indicate that interconnectivity is more important than pore radius at the lower porosity. The effective permeability of alternating stacks of the two varieties differs tremendously for the two interface orientations; arithmetic and harmonic averages coincide with the effective properties parallel and perpendicular to the main flow, respectively. When the oscillation period is varied two regimes are observed, one with constant permeability at long periods and a second with decreasing permeability for decreasing period at short periods. Order of magnitude considerations of penetration depth suggest that this period dependence may be related to heterogeneity.     

黑河流域地理观测分析——复杂性科学视角（英文）

Since 2005,dozens of geographical observational stations have been established in the Heihe River Basin(HRB),and by now a large amount of meteorological,hydrological,and ecological observations as well as data pertaining to water resources,soil and vegetation have been collected.To adequately analyze these available data and data to be further collected in future,we present a perspective from complexity theory.The concrete materials covered include a presentation of adaptive multiscale filter,which can readily determine arbitrary trends,maximally reduce noise,and reliably perform fractal and multifractal analysis,and a presentation of scale-dependent Lyapunov exponent(SDLE),which can reliably distinguish deterministic chaos from random processes,determine the error doubling time for prediction,and obtain the defining parameters of the process examined.The adaptive filter is illustrated by applying it to obtain the global warming trend and the Atlantic multidecadal oscillation from sea surface temperature data,and by applying it to some variables collected at the HRB to determine diurnal cycle and fractal properties.The SDLE is illustrated to determine intermittent chaos from river flow data.     

Analyses of geographical observations in the Heihe River Basin: Perspectives from complexity theory

Journal of Geographical Sciences - Since 2005, dozens of geographical observational stations have been established in the Heihe River Basin (HRB), and by now a large amount of meteorological,...     

一维均质与非均质土柱中溶质迁移的分数微分对流-弥散模拟

分数微分对流-弥散方程(FADE)是模拟溶质迁移问题的新理论,但应用FADE来模拟溶质迁移时能否克服弥散的尺度效应尚待验证。利用长土柱实验资料结合FADE的解析解拟合推求FADE的弥散系数,并分析其与尺度之间的相关关系。研究结果表明,FADE的弥散系数具有随尺度增大而增大的现象,且均质土柱中FADE的弥散系数尺度效应小于非均质土柱中弥散系数尺度效应。在均质土柱中,弥散系数与尺度之间成指数相关关系,在非均质土柱中,弥散系数与尺度之间成幂相关关系。考虑了弥散系数分别与迁移时间和迁移距离呈线性递增两种相关关系,进而分别构建了3种考虑弥散尺度效应的FADE模型,并提出了求解的差分方法。利用上述3种考虑弥散尺度效应的FADE来模拟和预测不同空间位置处的溶质迁移过程。结果表明,对均质土柱中的溶质迁移可得到较好的模拟结果;对于非均质土柱,其模拟结果与实测结果仍然存在一定的差异。     

土壤水分运动空间变异性尺度效应的染色示踪入渗试验研究

探讨了土壤水非均匀流动特性和描述方法,通过染色示踪剂调查了三种试验尺度条件下非均匀流动模式,并采用随机层叠模型对不同实验尺度条件下非均匀流动模式进行了模拟。随机层叠模型中具有对数正态分布性质的随机层叠发生器被用来描述水流入渗过程,不同的方法被用于模型参数求解。试验观测和模拟计算结果均表明,尺度特性是非均匀流动的重要影响因素之一,准确的描述不同研究尺度下的非均匀流动特征,须同时考虑流动在水平和垂直方向的变异性。随着研究尺度的增加,流动的非均匀性变异程度更加明显。     

Nonlocal transport models for capturing solute transport in one-dimensional sand columns: Model review,applicability, limitations and improvement

Modelling pollutant transport in water is one of the core tasks of computational hydrology, and various physical models including especially the widely used nonlocal transport models have been developed and applied in the last three decades. No studies, however, have been conducted to systematically assess the applicability, limitations and improvement of these nonlocal transport models. To fill this knowledge gap, this study reviewed, tested and improved the state-of-the-art nonlocal transport models, including their physical background, mathematical formula and especially the capability to quantify conservative tracers moving in one-dimensional sand columns, which represents perhaps the simplest real-world application. Applications showed that, surprisingly, neither the popular time-nonlocal transport models (including the multi-rate mass transfer model, the continuous time random walk framework and the time fractional advection-dispersion equation), nor the spatiotemporally nonlocal transport model (ST-fADE) can accurately fit passive tracers moving through a 15-m-long heterogeneous sand column documented in literature, if a constant dispersion coefficient or dispersivity is used. This is because pollutant transport in heterogeneous media can be scale-dependent (represented by a dispersion coefficient or dispersivity increasing with spatiotemporal scales), non-Fickian (where plume variance increases nonlinearly in time) and/or pre-asymptotic (with transition between non-Fickian and Fickian transport). These different properties cannot be simultaneously and accurately modelled by any of the transport models reviewed by this study. To bypass this limitation, five possible corrections were proposed, and two of them were tested successfully, including a time fractional and space Hausdorff fractal model which minimizes the scale-dependency of the dispersion coefficient in the non-Euclidean space, and a two-region time fractional advection-dispersion equation which accounts for the spatial mixing of solute particles from different mobile domains. Therefore, more efforts are still needed to accurately model transport in non-ideal porous media, and the five model corrections proposed by this study may shed light on these indispensable modelling efforts.