Flow recession behavior of preferential subsurface flow patterns with minimum energy dissipation

Abstract

Understanding the properties of preferential flow patterns is a major challenge in subsurface hydrology. Most of the theoretical approaches in this field stem from research on karst aquifers, where two or three distinct flow components with different timescales are typically considered. This study is based on a different concept: a continuous spatial variation in transmissivity and storativity over several orders of magnitude is assumed. The distribution and spatial pattern of these properties are derived from the concept of minimum energy dissipation. While the numerical simulation of such systems is challenging, it is found that a restriction to a dendritic flow pattern, similar to rivers at the surface, works well. It is also shown that spectral theory is useful for investigating the fundamental properties of such aquifers. As a main result, the long-term recession of the spring draining the aquifer during periods of drought becomes slower for large catchments. However, the dependence of the respective recession coefficient on catchment size is much weaker than for homogeneous aquifers. Concerning the short-term behavior after an instantaneous recharge event, strong deviations from the exponential recession of a linear reservoir are observed. In particular, it takes a considerable time span until the spring discharge reaches its peak. The order of magnitude of this rise time is one-seventh of the characteristic time of the aquifer. Despite the strong deviations from the linear reservoir at short time spans, the exponential component typically contributes more than 80% to the total discharge. This fraction is much higher than expected for karst aquifers and even exceeds the fraction predicted for homogeneous aquifers.