UC Berkeley

Optimality principles have been used for investigating physical processes in different areas. This work attempts to apply an optimal principle (that water flow resistance is minimized on global scale) to steady-state unsaturated flow processes. Based on the calculus of variations, we show that under optimal conditions, hydraulic conductivity for steady-state unsaturated flow is proportional to a power function of the magnitude of water flux. This relationship is consistent with an intuitive expectation that for an optimal water flow system, locations where relatively large water fluxes occur should correspond to relatively small resistance (or large conductance). Similar results were also obtained for hydraulic structures in river basins and tree leaves, as reported in other studies. Consistence of this theoretical result with observed fingering-flow behavior in unsaturated soils and an existing model is also demonstrated.