Preliminary discussion on the principle of minimum energy consumption rate controlling hierarchical groundwater flow systems

In the early 1960s, Tóth obtained hierarchical groundwater flow systems by using analytical solution based on given-head upper boundary, which is a milestone breakthrough in hydrogeology and successfully solved a series of theoretical and practical problems.However, the defects of Tóth's analytical solution have been followed for a long time such as focusing solely on mathematical simulation and ignoring the physical mechanism; taking terrain control of water table as a universal law; and ignoring the distortion of the mathematical simulation based on given-head upper boundary.These shortcomings, especially the lack of the physical mechanisms exploration, not only hindered the development of Tótian theory itself, but also made the theory difficult to be understood, so that the theory has not being widely applied yet by the international hydrogeological community.This paper proposes an expression for the minimum energy consumption rate of groundwater flow referring to the principle of minimum energy consumption rate applied in river dynamics.Based on the exited results of "numerical simulation of groundwater flow patterns using flux as upper boundary", the physical mechanism is further explored, and it is concluded that groundwater flow follows the principle of minimum energy consumption rate.