Free convection usually happens in variable-density groundwater flow systems, and it favors contaminant transport by enlarging length scales and shortening timescales compared to advection and diffusion/dispersion alone. Previous studies have demonstrated that heterogeneity with multi-variate Gaussian distribution for logarithmic permeabilities (log10k) plays an important role in the onset, growth, and/or decay of instability during the density-driven convective process. Nevertheless, the connectivity features (i.e., connected structures of extremely high/low-k values), which are common in natural aquifers, have received little attention. In this study, the classical problem of transient free convection has been modified and numerically simulated by Monte Carlo approach to investigate the effects of connectivity features in heterogeneity on the unstable convective processes. Results show that free convection is promoted by the connected high-k structures and retarded by the connected low-k structures during mainly the early-stage mass loading. The impacts of connectivity features tend to be amplified by higher variation in log10k distributions, and can be secondarily influenced by correlation lengths and anisotropy. Under the multi-variate Gaussian assumption, the existence of connected high-k structures leads to underestimation of density-driven instability, in which the risk differs based on the statistics of permeability fields, metrics of interest and timeframe. This study highlights the importance of understanding connectivity features in heterogeneous geological media when assessing density-dependent solute transport in groundwater systems.

中文翻译：

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具有连通性特征的非均质含水层中的密度驱动自由对流


自由对流通常发生在可变密度的地下水流系统中，与单独的平流和扩散/扩散相比，它通过扩大长度尺度和缩短时间尺度来促进污染物的输送。以前的研究表明，对数磁导率 （log10k） 的多变量高斯分布的非均质性在密度驱动对流过程中不稳定性的发生、增长和/或衰减中起着重要作用。然而，天然含水层中常见的连通性特征（即极高/低 k 值的连通结构）很少受到关注。在本研究中，通过蒙特卡洛方法对瞬态自由对流的经典问题进行了修正和数值模拟，以研究非均质性中的连通性特征对不稳定对流过程的影响。结果表明，在主要早期质量载荷期间，连接的高 k 结构促进了自由对流，而连接的低 k 结构则阻碍了自由对流。连通性特征的影响往往会被 log10k 分布的较高变化放大，并且可能受到相关长度和各向异性的影响。在多变量高斯假设下，连通高 k 结构的存在导致对密度驱动的不稳定性的低估，其中风险根据渗透率场的统计数据、感兴趣的指标和时间框架而有所不同。本研究强调了在评估地下水系统中密度依赖性溶质运移时，了解非均质地质介质中的连通性特征的重要性。