Basic postulates of groundwater occurrence and movement
For nearly two centuries, the partial differential equation of heat conduction has constituted the foundation for analyzing many physical systems, including those involving the flow of water in geologic media. Even as the differential equation continues to be a powerful tool for mathematical analysis in the earth sciences, it is useful to look at the groundwater flow process from other independent perspectives. The physical basis of the partial differential equation is the postulate of mass conservation. Alternatively, it is possible to understand groundwater movement in terms of energy and work because mechanical work has to be done in moving water against the resistance to flow offered by the solid material and to store water by opening up pore spaces. To this end, the behaviors of steady-state and transient groundwater systems are sought to be understood in terms of postulates concerning the state of a groundwater system, its tendency to optimally organize itself in response to impelling forces and its ability to store and release energy. This description of groundwater occurrence and flow, it is shown, is equivalent to the variational statement of the Laplace equation for the steady-state case and is similar to Gurtin’s (1964) variational principle for the transient case. The approach followed here has logical similarities with Hamilton’s principle for dynamical systems. Though the variational statement of the transient groundwater flow process is appealing in that it provides a rationale for deriving the parabolic equation, intriguing questions arise when one attempts to understand the physical significance of the variational statement. This work is motivated in part by a desire to develop a better understanding of the groundwater flow process from an intuitive base pertaining to discrete systems. Also, as we show an increasing preference to numerically solve groundwater flow problems on the basis of integro-differential equations, it is likely that the work presented here may contribute to improving such integral solution techniques.