Emergent Conductivity Relationship for Water Flow Based on Minimized Dissipation: From Landscapes to Unsaturated Soils.

摘要

Optimality principles have been widely used in many areas. Based on an optimality principle that a flow field will tend toward a minimum in the energy dissipation rate, this work shows that there exists a unified form of conductivity relationship for two different flow systems: landscapes and unsaturated soils. The conductivity, the ratio of water flux to water head (energy) gradient, is a power function of water flux where the exponent value is system dependent. This relationship indicates that to minimize energy dissipation rate for a whole system, water flow has a small resistance (or a large conductivity) at a location of large water flux. Empirical evidence supports validity of the relationship for landscape and unsaturated soils (under gravity dominated conditions). Especially, it is of interest that according to this relationship, hydraulic conductivity for gravity-dominated unsaturated flow, unlike that defined in the classic theories, depends on not only capillary pressure (or saturation), but also the water flux. Use of the optimality principle allows for determining useful results that may be applicable to a broad range of areas involving highly non-linear processes and may not be possible to obtain from classic theories describing water flow processes.