Stagnation lines and its control of nested groundwater flow systems in three-dimensional Tóthian basins
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摘要:
Tóth基于二维剖面流场提出的地下水流系统理论已成为研究盆地尺度地下水循环的理论依据。二维剖面上的驻点可以用于精确划分水流系统的空间分布，然而人们对三维盆地中水流系统的形态以及驻点是否存在等认识尚不清楚。针对2种典型的三维盆地，分别是只在单一方向存在波状起伏的类前陆型盆地和2个正交方向同时存在波状起伏的沙丘型盆地，利用余弦函数建立潜水面起伏的数学表达式，推导水头分布的解析解，利用TECPLOT软件实现了水流系统三维空间分布的可视化。研究发现，2种理想三维盆地内都可以发育驻点，其中类前陆型盆地内驻点构成一条水平延伸的驻线，驻线控制了4个水流系统的空间分布；沙丘型盆地内驻点构成一条圆弧状驻线，驻线控制了6个水流系统的空间分布。通过研究驻线在三维盆地中的分布并且提出了利用驻线划分三维盆地水流系统的方法，加深了对三维盆地地下水循环规律的认识。
Abstract:The theory of groundwater flow systems proposed by Tóth, which was based on the two-dimensional profile flow field, has become the theoretical basis for studying basin-scale groundwater circulation.The stagnation points on the two-dimensional profile can be used to accurately divide the spatial distribution of groundwater flow systems.However, the spatial distribution of groundwater flow systems and whether stagnation points exist in the 3D domain remain unknown.In this study, two typical three-dimensional basins, namely foreland-like basins with undulations only in the x direction and dune-type basins with undulations in both x and y directions, are used as typical examples.By using a combination of cosine functions to characterize the undulating water table, analytical solutions of head distribution in the two basins are derived.Moreover, by employing the TECPLOT software, the spatial distribution of the 3D groundwater flow systems is clearly shown.It is found out that stagnation points can develop in two basins.The stagnation points in the foreland-like basin constitute a horizontally extending stagnation line, which controls the spatial distribution of four flow systems in the basin, while the stagnation points in the dune-type basin form an arc-shaped stagnation line, which controls the spatial distribution of six flow systems in the basin.By studying the distribution of stagnation line in 3D basins and successfully dividing flow systems by using the stagnation line, this study leads to a deepened understanding of groundwater circulation in 3D basins.
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图 1 类前陆型盆地(a)与沙丘型盆地(b)的概念模型示意图
Figure 1. Conceptual model diagram of foreland-like basin (a) and dune-type basin (b)
图 2 三维类前陆型盆地驻线及临界流线三维空间分布图(a)、驻线及4个水流系统分布俯视图(b)
Figure 2. Three-dimensional spatial distribution of stagnation line and dividing streamlines (a), top view of the distribution of stagnation line and four flow systems (b) in the three-dimensional foreland-like basins
图 3 理想沙丘型三维盆地的驻线及水流系统空间分布图
a.驻线及AC剖面流场图；b.驻线及水流系统分布俯视图
Figure 3. Spatial distribution map of standing line and flow system of ideal dune-shaped three-dimensional basins
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