Theory for Source‐Responsive and Free‐Surface Film Modeling of Unsaturated Flow

Abstract

A new model explicitly incorporates the possibility of rapid response, across significant distance, to substantial water input. It is useful for unsaturated flow processes that are not inherently diffusive, or that do not progress through a series of equilibrium states. The term source‐responsive is used to mean that flow responds sensitively to changing conditions at the source of water input (e.g., rainfall, irrigation, or ponded infiltration). The domain of preferential flow can be conceptualized as laminar flow in free‐surface films along the walls of pores. These films may be considered to have uniform thickness, as suggested by field evidence that preferential flow moves at an approximately uniform rate when generated by a continuous and ample water supply. An effective facial area per unit volume quantitatively characterizes the medium with respect to source‐responsive flow. A flow‐intensity factor dependent on conditions within the medium represents the amount of source‐responsive flow at a given time and position. Laminar flow theory provides relations for the velocity and thickness of flowing source‐responsive films. Combination with the Darcy–Buckingham law and the continuity equation leads to expressions for both fluxes and dynamic water contents. Where preferential flow is sometimes or always significant, the interactive combination of source‐responsive and diffuse flow has the potential to improve prediction of unsaturated‐zone fluxes in response to hydraulic inputs and the evolving distribution of soil moisture. Examples for which this approach is efficient and physically plausible include (i) rainstorm‐generated rapid fluctuations of a deep water table and (ii) space‐ and time‐dependent soil water content response to infiltration in a macroporous soil.