Optimality and Conductivity for Water Flow: From Landscapes, to Unsaturated Soils, to Plant Leaves
Optimality principles have been widely used in many areas. Based on an optimality principle that any 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 three different flow systems: landscapes, unsaturated soils and plant leaves. The conductivity, the ratio of water flux to energy gradient, is a power function of water flux although the power 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). Numerical simulation results also show that the relationship can capture the key features of hydraulic structure for a plant leaf, although more studies are needed to further confirm its validity. 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 are 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.
- Research Organization:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Organization:
- Earth Sciences Division
- DOE Contract Number:
- DE-AC02-05CH11231
- OSTI ID:
- 1039925
- Report Number(s):
- LBNL-5358E; TRN: US201215%%161
- Country of Publication:
- United States
- Language:
- English
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