One‐dimensional airflow in unsaturated zone induced by periodic water table fluctuation

Abstract

This paper investigates the vertical airflow driven by fluctuating water table within the lower layer of a coastal two‐layered system. The upper layer is unsaturated and semipermeable, while the lower is permeable. An analytical solution of the subsurface air pressure fluctuation is derived on the basis of model simplification assumptions, the reasonability of which was examined by numerical solutions of the original nonlinear model. The airflow in the upper layer is controlled from the top by the constant atmospheric pressure and from the bottom by a temporally fluctuating air pressure P0(t), which is spatially constant in the unsaturated zone of the lower layer. For a sinusoidal head the amplitude of P0(t) increases with the frequency of the head fluctuation, the upper layer's thickness, and the unconfined aquifer's air‐filled porosity and decreases with the upper layer's permeability. The phase shift of P0(t) ranges from 0 to π/2, indicating a “time advance.” Particularly, P0(t) is approximately proportional to the temporal derivative of the head for sufficiently thin or permeable upper layer and to the head itself for sufficiently thick or less permeable one. The fluctuation amplitude of the water table is always less than that of the head and can be only one tenth of the latter if the upper layer is sufficiently thick or less permeable, which may slow significantly the landward attenuation speed of the tide‐induced head fluctuation in a coastal “air‐confined” aquifer. The analytical solution was used to estimate the value range of the air permeability of the marine sand fill at a coastal reclamation area of Hong Kong.