Mathematical analysis of nonstationary processes of infiltration into unsaturated soil
Theoretical studies of the movement of moisture in an unsaturated zone are associated with the analysis of the Richards equations. The corresponding mathematical problems are designed to answer practical questions related to the replenishment of groundwater reserves, the degree of their protection from pollution coming from the surface, and the needs of agriculture. The value of surface recharge appears in the problems as a boundary condition at the upper boundary of the soil. It depends on weather conditions, which leads to significant non-stationarity of the infiltration processes. At the same time, for a broad class of surface feeding modes, fluctuations of moisture flows are smoothed out with depth. The depth at which fluctuations in the moisture flow become negligible and the flow becomes almost stationary is of interest for many practical applications. In this work, explicit formulas are derived analytically for this depth, expressing its value through the filtration parameters of the medium and the characteristics of the mode of moisture ingress into the soil.