On the Coupling Between Channel Level and Surface Ground-Water Flows

Abstract

This paper is devoted to a mathematical analysis of some general models of mass transport and other coupled physical processes developed in simultaneous flows of surface, soil and ground waters. Such models are widely used for forecasting (numerical simulation) of a hydrological cycle for concrete territories. The mathematical models that proved a more realistic approach are obtained by combining several mathematical models for local processes. The water-exchange models take into account the following factors: Water flows in confined and unconfined aquifers, vertical moisture migration allowing earth surface evaporation, open-channel flow simulated by one-dimensional hydraulic equations, transport of contamination, etc. These models may have different levels of sophistication. We illustrate the type of mathematical singularities which may appear by considering a simple model on the coupling of a surface flow of surface and ground waters with the flow of a line channel or river.

Groundwater–Surface Water Interaction—Analytical Approach

“…The assumption was analysed by Nawalany [30] who evidenced that despite a rapidly fluctuating river water table, a slow response of groundwater flow in the adjacent aquifer occurs as a consequence of dumping of high frequency changes in pore pressure by porous rocks. The adequacy of such an assumption was also discussed in more recent literature [26,31,32]. Preliminary field measurements in a real river-aquifer system show that water table fluctuations in the river-H r , and slow response of free water table that follows in the adjacent riparian aquifer-Φ * support the assumption of merely quasi-steady water exchange in the exemplary river-aquifer system.…”

“…The analytical description of water exchange between the river and aquifer has been reviewed from a historical point of view in the available literature [24]. Similar solutions for the improvement of the accuracy of the river-groundwater system interaction have also been published [25,26].…”

“…. , N for z into Equations (26) and (27) leads to a set of (2N + 2) linear algebraic equations, where infinite series are approximated with their finite counterparts…”