Dissolved-phase contaminants experiencing enhanced diffusion (i.e., “super-diffusion”) with a pronounced leading plume edge can pose risk for groundwater quality. The drivers for complex super-diffusion in geological media, however, are not fully understood. This study investigates the impacts of hydrofacies’ mean lengths and the initial source geometry, motivated by a hydrofacies model built recently for the well-known MADE aquifer, on the spatial pattern of super-diffusion for two-dimensional alluvial aquifer systems. Monte Carlo simulations show that the bimodal velocity distribution, whose pattern is affected by the hydrofacies’ mean lengths, leads to super-diffusion of solutes with a bi-peak plume snapshot in alluvial settings where advection dominates transport. A larger longitudinal mean length (i.e., width) for hydrofacies with high hydraulic conductivity (K) enhances the connectivity of preferential pathways, resulting in higher values in the bimodal velocity distribution and an enhanced leading front for the bi-peak plume snapshot, while the opposite impact is identified for the hydrofacies’ vertical mean length (i.e., thickness) on the bi-peak super-diffusion. A multi-domain non-local transport model is then proposed, extending upon the concept of the distributed-order fractional derivative, to quantify the evolution of bi-peak super-diffusion due to differential advection and mobile-mobile mass exchange for solute particles moving in hydrofacies with distinct K. Results show that the bi-peak super-diffusion identified for the MADE site and perhaps the other similar aquifers, which is affected by the initial source geometry at an early stage and the thickness and width of high-K hydrofacies during all stages, can be quantified by the mobile-mobile fractional-derivative model. Porous medium dimensionality and stochastic model comparison are also discussed to further explore the nature of bi-peak super-diffusion in alluvial systems.

中文翻译：

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冲积环境中受水相平均长度和源几何形状影响的超扩散

溶解相污染物经历增强扩散（即“超扩散”）并具有明显的前缘羽流可能对地下水质量构成风险。然而，地质介质中复杂超扩散的驱动因素尚不完全清楚。本研究调查了水相平均长度和初始源几何形状对二维冲积含水层系统超扩散空间格局的影响，受最近为著名的 MADE 含水层建立的水相模型的启发。Monte Carlo 模拟表明，双峰速度分布（其模式受水相平均长度的影响）导致溶质的超扩散，在冲积环境中，在平流主导运输的情况下，具有双峰羽流快照。较大的纵向平均长度（即 宽度）对于具有高导水率 (K) 的水相增强了优先路径的连通性，导致双峰速度分布的更高值和双峰羽流快照的增强前缘，而对水相的影响则相反双峰超扩散的垂直平均长度（即厚度）。然后提出了一个多域非局部传输模型，扩展了分布式阶分数导数的概念，以量化由于微分平流和移动-移动质量交换对溶质颗粒移动的双峰超扩散的演变在具有不同 K 的水相中。 结果表明，为 MADE 站点和其他类似的含水层确定的双峰超扩散，受早期初始源几何形状和所有阶段高 K 水相的厚度和宽度的影响，可以通过移动-移动分数导数模型进行量化。还讨论了多孔介质维数和随机模型比较，以进一步探索冲积系统中双峰超扩散的性质。