ABSTRACT

The present study proposes two analytical solutions for a layered ponded ditch drainage system with Dirichlet and lagging Robin boundary conditions. The flow domain is assumed to be saturated, layered, and anisotropic. The first analytical model considers flow to a ditch drainage network from a ponded field through a two-layered soil considering the Dirichlet boundary condition, whereas the second model is developed considering a lagging Robin condition at the ditch face and surface of the soil. The study highlights that the lagging Robin condition can better mimic the actual flow scenario as compared to the standard Robin boundary condition. A comparison study has been carried out to assess the top layer’s permissible depth under which a homogeneous drainage system with Robin boundary condition can approximate a layered drainage system. Further, the residence time distributions are observed to follow power-law-like distributions with heavier tails for both single and two-layered ditch drainage systems.

摘要

本研究针对具有 Dirichlet 和滞后 Robin 边界条件的分层蓄水沟排水系统提出了两种解析解。假定流域是饱和的、分层的和各向异性的。第一个分析模型考虑了狄利克雷边界条件下从蓄水田通过双层土壤流向沟渠排水网络的流量，而第二个模型是考虑到沟渠面和土壤表面的滞后 Robin 条件而开发的。该研究强调，与标准 Robin 边界条件相比，滞后 Robin 条件可以更好地模拟实际流动场景。已经进行了一项比较研究，以评估顶层的允许深度，在该深度下，具有 Robin 边界条件的均质排水系统可以近似于分层排水系统。更远，