Water table waves in an unconfined aquifer: Experiments and modeling

Abstract

[1] Comprehensive measurements are presented of the piezometric head in an unconfined aquifer during steady, simple harmonic oscillations driven by a hydrostatic clear water reservoir through a vertical interface. The results are analyzed and used to test existing hydrostatic and nonhydrostatic, small-amplitude theories along with capillary fringe effects. As expected, the amplitude of the water table wave decays exponentially. However, the decay rates and phase lags indicate the influence of both vertical flow and capillary effects. The capillary effects are reconciled with observations of water table oscillations in a sand column with the same sand. The effects of vertical flows and the corresponding nonhydrostatic pressure are reasonably well described by small-amplitude theory for water table waves in finite depth aquifers. That includes the oscillation amplitudes being greater at the bottom than at the top and the phase lead of the bottom compared with the top. The main problems with respect to interpreting the measurements through existing theory relate to the complicated boundary condition at the interface between the driving head reservoir and the aquifer. That is, the small-amplitude, finite depth expansion solution, which matches a hydrostatic boundary condition between the bottom and the mean driving head level, is unrealistic with respect to the pressure variation above this level. Hence it cannot describe the finer details of the multiple mode behavior close to the driving head boundary. The mean water table height initially increases with distance from the forcing boundary but then decreases again, and its asymptotic value is considerably smaller than that previously predicted for finite depth aquifers without capillary effects. Just as the mean water table over-height is smaller than predicted by capillarity-free shallow aquifer models, so is the amplitude of the second harmonic. In fact, there is no indication of extra second harmonics (in addition to that contained in the driving head) being generated at the interface or in the interior.

Influence of capillarity on a simple harmonic oscillating water table: Sand column experiments and modeling

“…The present data however has highlighted significant limitations in this approach, particularly in the high-frequency limit. Limitations of the model when applied to the 2D case of a propagating water table wave have also been identified [Cartwright et al, 2003[Cartwright et al, , 2004. As such it is suggested that further development of the problem be directed toward improving the understanding of the processes involved in the coupling of the saturated zone with the capillary fringe.…”

“…It does however provide a simple, and computationally efficient way to account for its influence on the nature of water table fluctuations and is easily applied to existing dispersion relation theories to describe water table attenuation [e.g., Nielsen and Turner, 2000;Cartwright et al, 2003].…”

Effects of salinity variations on pore water flow in salt marshes

“…Salt water was pumped from a saltwater tank into the reservoir via a variable height overflow (VHO) column, which generated the tidal fluctuations [Cartwright et al, 2003]. The grain size distribution of the sand used in the experiments is relatively uniform with d 50 5 0.24 mm and d 90 /d 10 5 2.86.…”

“…During the wash, a handheld multiparameter meter (YSI Professional Plus) was used to monitor the pore water salinity. Afterward, the sand was put into the flume and settled by gravity in prefilled salt water of 15 ppt to ensure that the initial pore water salinity was uniform and to avoid trapped air [Cartwright et al, 2003]. …”

Influence of hysteresis on groundwater wave dynamics in an unconfined aquifer with a sloping boundary

“…Lanyon et al, 1982;Nielsen, 1990;Turner et al, 1997;Raubenheimer et al, 1999), laboratory experiments (e.g. Parlange et al, 1984;Nielsen et al, 1997;Boufadel et al, 1998;Ataie-Ashtiani et al, 1999;Cartwright et al, 2003), analytical modelling (e.g. Parlange et al, 1984;Barry et al, 1996;Li et al , 2000;Kong et al, 2013); and numerical modelling (e.g.…”