Capillary effect on water table fluctuations in unconfined aquifers

Abstract

[1] Parlange and Brutsaert (1987) derived a modified Boussinesq equation to account for the capillary effect on water table dynamics in unconfined aquifers. Barry et al. (1996) solved this equation subject to a periodic boundary condition. Their solution shows significant influence of capillarity on water table fluctuations, which evolve to finiteamplitude standing waves at the high frequency limit. Here we propose a new governing equation for the water table, which considers both horizontal and vertical flows in an unsaturated zone of finite thickness. An approximate analytical solution for periodic water table fluctuations based on the new equation was derived. In agreement with previous results, the analytical solution shows that the unsaturated zone's storage capacity permits water table fluctuations to propagate more readily than predicted by the Boussinesq equation. Furthermore, the new solution reveals a capping effect of the unsaturated zone on both the amplitude and phase of the water table fluctuations as well as the water table overheight. Due to the finite thickness of the unsaturated zone, the capillary effect on water table fluctuations is modified mainly with reduced amplitude damping and phase shift.

Effects of vadose zone on groundwater table fluctuations in unconfined aquifers

“…Here, we neglected the effect of sloping beach and associated moving boundary, as done in most previous studies (Jeng et al, 2002;Li and Jiao, 2003;Xia et al, 2011), to focus on the effect of vadose zone in the first instance. Also note that although the density effect due to the presence of seawater can influence significantly nearshore groundwater flow, it is of secondary importance for water table fluctuations associated with inland propagation of tidal oscillations in coastal aquifers and has been neglected in previous studies (Guo et al, 2010;Kong et al, 2013;Li et al, 1997;Nielsen et al, 1997;Stojsavljevic et al, 2012). Thus we also neglected the density effect in the present study.…”

“…(11) is based on a rigorous water balance in comparison with previous studies (e.g., Li et al, 1997;Kong et al, 2013) which assumed a negligible water change in the vadose zone. Compared with Xin et al (2013a) and Kong et al (2013), this study aims to explore the underlying mechanism of water exchange between the saturated and vadose zone. Furthermore, the Laplace equation for the saturated zone simulates both the horizontal and vertical flow.…”

“…While the model developed by Kong et al (2013) represents reasonably well the effects of the vadose zone on groundwater table fluctuations, the non-hydrostatic pressure correction term developed in Kong et al (2013) do not satisfy the mass conservation principle as the non-hydrostatic pressure in the vadose zone does not respond to the drying and wetting process. Moreover, this study and others (Li et al, 2000b;Nielsen et al, 1997) did not examine the overall groundwater-surface water exchange across the aquifer boundary (e.g., beach surface).…”

“…By fixing the upper bound of the integral, the truncation effect of ground surface on the vadose zone was considered. This 1-D model was subsequently improved by Kong et al (2013) who used an additional correction term to include the effects of vertical flow in both the saturated zone and the vadose zone of finite thickness. Kong et al (2013) further derived an analytical solution, which shows that the storage capacity of the vadose zone permits groundwater wave to propagate more readily than predicted by the traditional Boussinesq equation.…”

“…This 1-D model was subsequently improved by Kong et al (2013) who used an additional correction term to include the effects of vertical flow in both the saturated zone and the vadose zone of finite thickness. Kong et al (2013) further derived an analytical solution, which shows that the storage capacity of the vadose zone permits groundwater wave to propagate more readily than predicted by the traditional Boussinesq equation. Furthermore, the new solution reveals that for low-frequency groundwater table fluctuations, a capping effect of the vadose zone associated with the finite thickness alters significantly the behavior of the groundwater table fluctuations.…”