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

Abstract. Understanding the properties of preferential flow patters is a major challenge in subsurface hydrology. Most of the theoretical approaches in this field stem from research on karst aquifers, where typically two or three distinct flow components with different time scales are considered. This study starts from a different concept, where a continuous spatial variation in transmissivity and storavity over several orders of magnitude is assumed. 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 reduction to a dendritic flow pattern, similar to rivers at the surface, works well. It is also shown that spectral theory can allow 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. This rise time is in an order of magnitude of one-seventh of the e-folding recession time. Despite the strong deviations from the linear reservoir at short times, 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.