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This article in VZJ

  1. Vol. 10 No. 2, p. 736-740
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    Received: Sept 16, 2010


    * Corresponding author(s): hhliu@lbl.gov
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doi:10.2136/vzj2010.0118

A Conductivity Relationship for Steady-State Unsaturated Flow Processes under Optimal Flow Conditions

  1. Hui-Hai Liu *
  1. Earth Sciences Division, Lawrence Berkeley National Lab., Berkeley, CA

Abstract

Optimality principles have been used to investigate physical processes in different areas. This work applied an optimal principle (that water flow resistance is minimized for the entire flow domain) to steady-state unsaturated flow processes. Based on the calculus of variations, under optimal conditions, hydraulic conductivity for steady-state, gravity-dominated 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). This theoretical result was also consistent with observed fingering-flow behavior in unsaturated soils and an existing model.

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