Water infiltration and unsaturated flow through heterogeneous soil control the distribution of soil moisture in the vadose zone and the dynamics of groundwater recharge, providing the link between climate, biogeochemical soil processes and vegetation dynamics. Infiltration into dry soil is hydrodynamically unstable, leading to preferential flow through narrow wet regions (fingers). In this paper we use numerical simulation to study the interplay between fingering instabilities and soil heterogeneity during water infiltration. We consider soil with heterogeneous intrinsic permeability. Permeabilities are random, with point Gaussian statistics, and vary smoothly in space due to spatial correlation. The key research question is whether the presence of moderate or strong heterogeneity overwhelms the fingering instability, recovering the simple stable displacement patterns predicted by most simplified model of infiltration currently used in hydrological models from the Darcy to the basin scales. We perform detailed simulations of constant-rate infiltration into soils with isotropic and anisotropic intrinsic permeability fields. Our results demonstrate that soil heterogeneity does not suppress fingering instabilities, but it rather enhances its effect of preferential flow and channeling. Fingering patterns strongly depend on soil structure, in particular the correlation length and anisotropy of the permeability field. While the finger size and flow dynamics are only slightly controlled by correlation length in isotropic fields, layering leads to significant finger meandering and bulging, changing arrival times and wetting efficiencies. Fingering and soil heterogeneity need to be considered when upscaling the constitutive relationships of multiphase flow in porous media (relative permeability and water retention curve) from the finger to field and basin scales. While relative permeabilities remain unchanged upon upscaling for stable displacements, the inefficient wetting due to fingering leads to relative permeabilities at the field scale that are significantly different from those at the Darcy scale. These effective relative permeability functions also depend, although less strongly, on heterogeneity and soil structure.

中文翻译：

---

非均质干土中水分入渗过程中不稳定优先流的数值模拟

通过异质土壤的水入渗和非饱和流控制着包气带中土壤水分的分布和地下水补给的动态，提供了气候、生物地球化学土壤过程和植被动态之间的联系。渗入干燥土壤的水动力不稳定，导致优先流过狭窄的潮湿区域（手指）。在本文中，我们使用数值模拟来研究水入渗过程中指法不稳定性和土壤异质性之间的相互作用。我们考虑具有异质固有渗透性的土壤。渗透率是随机的，具有点高斯统计，并且由于空间相关性而在空间中平滑地变化。关键的研究问题是中度或强异质性的存在是否会压倒指法不稳定性，恢复目前在从达西到流域尺度的水文模型中使用的最简化的渗透模型预测的简单稳定位移模式。我们对具有各向同性和各向异性固有渗透率场的土壤进行恒定速率渗透的详细模拟。我们的结果表明，土壤异质性不会抑制指法不稳定性，而是增强了其优先流动和沟道效应。指法模式在很大程度上取决于土壤结构，特别是渗透场的相关长度和各向异性。虽然各向同性场中的相关长度仅略微控制手指尺寸和流动动力学，但分层会导致明显的手指弯曲和凸起，改变到达时间和润湿效率。在将多孔介质中多相流的本构关系（相对渗透率和保水曲线）从指状尺度放大到田间尺度和盆地尺度时，需要考虑指状和土壤非均质性。虽然相对渗透率在稳定位移放大时保持不变，但由于指法导致的低效润湿导致现场尺度的相对渗透率与达西尺度的相对渗透率显着不同。这些有效的相对渗透率函数也依赖于非均质性和土壤结构，尽管不是那么强烈。虽然相对渗透率在稳定位移放大时保持不变，但由于指法导致的低效润湿导致现场尺度的相对渗透率与达西尺度的相对渗透率显着不同。这些有效的相对渗透率函数也依赖于非均质性和土壤结构，尽管不是那么强烈。虽然相对渗透率在稳定位移放大时保持不变，但由于指法导致的低效润湿导致现场尺度的相对渗透率与达西尺度的相对渗透率显着不同。这些有效的相对渗透率函数也依赖于非均质性和土壤结构，尽管不是那么强烈。