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A Theoretical Study about Ergodicity Issues in Predicting Contaminant Plume Evolution in Aquifers
Water ( IF 3.4 ) Pub Date : 2020-10-20 , DOI: 10.3390/w12102929
Marilena Pannone

A large-time Eulerian–Lagrangian stochastic approach is employed to: (1) estimate centroid position uncertainty of contaminant plumes that originate from instantaneous point sources in statistically stationary and isotropic porous formations; (2) assess the time needed for achieving ergodic conditions, which would allow for the evaluation of local concentration values based on the only ensemble mean distribution; (3) derive the concentration coefficient of variation (CV) as a function of asymptotic macro-dispersion coefficients and centroid trajectory variances. The results indicate that the decay time of plume position uncertainty is so large that there is practically no chance for effective ergodicity. The concentration coefficient of variation is zero at the centroid but rapidly increases when moving away from it. The dissipative effect of local dispersion in the presence of relatively high Peclet numbers is considerably exalted by marked flow field heterogeneity, which confirms the previously postulated synergic, non-additive effect of advection and local dispersion in passive solute dilution. A further result from this study is the derivation of the power law that relates dimensionless concentration micro-scale to dimensionless local dispersive area. The exponent of this power law is the same that appears in the relationship between dimensionless Kolmogorov turbulent micro-scale and flow Reynolds number.

中文翻译:

含水层污染物羽流演化预测中遍历性问题的理论研究

大时间欧拉-拉格朗日随机方法用于: (1) 估计源自统计平稳和各向同性多孔地层中瞬时点源的污染物羽流的质心位置不确定性;(2) 评估实现遍历条件所需的时间,这将允许基于唯一的整体平均分布评估局部浓度值;(3) 导出浓度变异系数 (CV) 作为渐近宏观分散系数和质心轨迹方差的函数。结果表明,羽流位置不确定性的衰减时间如此之大,以至于实际上没有机会获得有效的遍历性。浓度变异系数在质心处为零,但在远离质心时迅速增加。在存在相对较高的 Peclet 数的情况下,局部分散的耗散效应因显着的流场异质性而显着提高,这证实了先前假设的对流和被动溶质稀释中的局部分散的协同、非累加效应。这项研究的另一个结果是幂律的推导,该幂律将无量纲集中微尺度与无量纲局部分散区域相关联。该幂律的指数与在无量纲 Kolmogorov 湍流微尺度和流动雷诺数之间的关系中出现的指数相同。这项研究的另一个结果是幂律的推导,该幂律将无量纲集中微尺度与无量纲局部分散区域相关联。该幂律的指数与在无量纲 Kolmogorov 湍流微尺度和流动雷诺数之间的关系中出现的指数相同。这项研究的另一个结果是幂律的推导,该幂律将无量纲集中微尺度与无量纲局部分散区域相关联。该幂律的指数与在无量纲 Kolmogorov 湍流微尺度和流动雷诺数之间的关系中出现的指数相同。
更新日期:2020-10-20
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