论文标题
关于耦合的表面表面露水集水区模型的开发和分析。第3部分。分析解决方案和扩展定律
On the development and analysis of coupled surface-subsurface models of catchments. Part 3. Analytical solutions and scaling laws
论文作者
论文摘要
这三部分工作的目的是制定和严格分析许多减少的数学模型，这些模型仍然能够描述河流盆地规模的水文学（即集水区）。考虑了耦合的表面和地下流。在第三部分中，我们着重于开发分析解决方案和缩放定律的基准集水模型，该模型模拟了一次降雨期间产生的河流流量（径流）。我们证明，对于以浅色坚不可摧的基岩为特征的集水区，浅水近似允许将管理公式的公式降低到表面和地下流的一维时间相关方程的耦合系统。渐近分析用于为模型得出半分析溶液。我们提供了描述峰流形成的简单渐近缩放定律，并通过与第2部分中开发的二维模型进行比较来证明其准确性。这些缩放定律可以用作评估其他物理，概念或统计学模型的有效性的分析基准。
The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface and subsurface flows are considered. In this third part, we focus on the development of analytical solutions and scaling laws for a benchmark catchment model that models the river flow (runoff) generated during a single rainfall. We demonstrate that for catchments characterised by a shallow impenetrable bedrock, the shallow-water approximation allows a reduction of the governing formulation to a coupled system of one-dimensional time-dependent equations for the surface and subsurface flows. Asymptotic analysis is used to derive semi-analytical solutions for the model. We provide simple asymptotic scaling laws describing the peak flow formation, and demonstrate its accuracy through a comparison with the two-dimensional model developed in Part 2. These scaling laws can be used as an analytical benchmark for assessing the validity of other physical, conceptual, or statistical models of catchments.
