Variable‐density flow and mass transport are important processes for a variety of groundwater problems. This study numerically investigated 2‐D vertical unconfined aquifers with horizontal groundwater flow and vertical injection of dense solute from the top. In total, 189 numerical simulation cases were performed with various scenarios of boundary conditions and aquifer properties. Based on the simulation results, three end‐member flow regimes were identified that are dominated by horizontal hydraulically driven flow, vertical hydraulically driven flow, and vertical density‐driven flow, respectively. The regimes can be clearly distinguished by a set of three dimensionless numbers, which are the convective ratios M_x (the ratio of the total flux of the vertical density‐driven flow to the total flux of the horizontal hydraulically driven flow) and M_z (the ratio of the total flux of the vertical density‐driven flow to the total flux of the vertical hydraulically driven flow), and the modified Rayleigh number Ra_d (the ratio of the vertical density‐driven force to the forces caused by dispersion and diffusion). The dimensionless numbers were applied to published numerical and physical experimental results for interpreting their flow behaviors and for classifying their flow regimes. Besides, the analysis of the parameter sensitivity indicated that the shifts among the end‐member regimes are mainly controlled by dimensionless‐number‐related parameters including horizontal groundwater flow velocity, injection rate and concentration of solute, and anisotropy ratio of hydraulic conductivity. The regime shifts are not strongly affected by the unsaturated properties or heterogeneity of hydraulic conductivity within the parameter ranges investigated in this paper.

中文翻译：

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基于数值模拟的多孔介质中变密度流状态识别，无量纲数和参数敏感性

密度变化的流量和质量传输是解决各种地下水问题的重要过程。这项研究通过数值研究了二维垂直无限制含水层，水平地下水流和从顶部垂直注入浓溶质。总共进行了189种数值模拟案例，其中包括边界条件和含水层特性的各种情景。根据模拟结果，确定了三个端部构件流动状态，分别由水平液压驱动流，垂直液压驱动流和垂直密度驱动流控制。可以通过一组三个无因次数来清晰地区分，这是对流比M _x（垂直密度驱动流的总流量与水平液压驱动流的总流量之比）和M _z（垂直密度驱动流的总流量与垂直液压驱动的总流量之比）驱动流），以及修改后的瑞利数Ra _d（垂直密度驱动力与分散和扩散所引起的力之比）。将无量纲数字应用于已发布的数值和物理实验结果，以解释其流动行为并对其流动状态进行分类。此外，对参数敏感性的分析表明，端部成员状态之间的转换主要受与无量纲相关的参数控制，这些参数包括水平地下水流速，注入速率和溶质浓度以及水力传导率的各向异性比。在本文研究的参数范围内，水力传导率的不饱和特性或非均质性不会严重影响状态变化。