Drying front in a sloping aquifer: Nonlinear effects

[1] The profiles for the water table height h(x, t) in a shallow sloping aquifer are reexamined with a solution of the nonlinear Boussinesq equation. We demonstrate that the previous anomaly first reported by Brutsaert [1994] that the point at which the water table h first becomes zero at x = L at time t = t(c) remains fixed at this point for all times t > t(c) is actually a result of the linearization of the Boussinesq equation and not, as previously suggested [Brutsaert, 1994; Verhoest and Troch, 2000], a result of the Dupuit assumption. Rather, by examination of the nonlinear Boussinesq equation the drying front, i.e., the point x(f) at which h is zero for times t greater than or equal to t(c), actually recedes downslope as physically expected. This points out that the linear Boussinesq equation should be used carefully when a zero depth is obtained as the concept of an average'' depth loses meaning at that time.

Experimental observations of watertable waves in an unconfined aquifer with a sloping boundary

Observations of horizontal and vertical variations in piezometric head in a homogeneous, laboratory aquifer are presented and discussed. The observed fluctuations are induced by a simple harmonic oscillation in the clear water reservoir acting across a sloping boundary. The data qualitatively supports existing theories in that higher harmonics are generated in the active forcing zone and that a significant increase in the inland, asymptotic watertable over height (relative to that found for the vertical boundary case) is observed. The observed overheight is shown to be accurately reproduced by existing small-amplitude perturbation theory. Detailed measurements in the vicinity of the sloping boundary reveal that the signal of generated higher harmonics is strongest near the sand surface and that vertical flows are significant in this region. The aquifer is of finite-depth and is influenced by capillary effects, the experimental data therefore exposes limitations of theories which are based on the assumption of a shallow aquifer free of capillary effects. The dispersive properties of the measured pressure wave in the aquifer are comparable to those found from field observations and likewise do not agree with those predicted by the capillary free, shallow aquifer theory. Although some improvement is obtained, discrepancies between the data and theory persist even when a finite-depth aquifer and capillary effects are considered in the theoretical model. Further sand column experiments eliminate a truncated capillary fringe as a possible contributor to these discrepancies. However, the neglect of horizontal flows in the fringe may have caused the discrepancies. (C) 2004 Elsevier Ltd. All rights reserved.

Swash-aquifer interaction in the vicinity of the water table exit point on a sandy beach

The coupling of sandy beach aquifers with the swash zone in the vicinity of the water table exit point is investigated through simultaneous measurements of the instantaneous shoreline (swash front) location, pore pressures and the water table exit point. The field observations reveal new insights into swash-aquifer coupling not previously gleaned from measurements of pore pressure only. In particular, for the case where the exit point is seaward of the observation point, the pore pressure response is correlated with the distance between the exit point and the shoreline in that when the distance is large the rate of pressure drop is fast and when the distance is small the rate decreases. The observations expose limitations in a simple model describing exit point dynamics which is based only on the force balance on a particle of water at the sand surface and neglects subsurface pressures. A new modified form of the model is shown to significantly improve the model-data comparison through a parameterization of the effects of capillarity into the aquifer storage coefficient. The model enables sufficiently accurate predictions of the exit point to determine when the swash uprush propagates over a saturated or a partially saturated sand surface, potentially an important factor in the morphological evolution of the beach face. Observations of the shoreward propagation of the swash-induced pore pressure waves ahead of the runup limit shows that the magnitude of the pressure fluctuation decays exponentially and that there is a linear increase in time lags, behavior similar to that of tidally induced water table waves. The location of the exit point and the intermittency of wave runup events is also shown to be significant in terms of the shore-normal energy distribution. Seaward of the mean exit point location, peak energies are small because of the saturated sand surface within the seepage face acting as a "rigid lid'' and limiting pressure fluctuations. Landward of the mean exit point the peak energies grow before decreasing landward of the maximum shoreline position.

Tidal effects on sea water intrusion in unconfined aquifers

A variable-density groundwater model is used to analyse the effects of tidal fluctuations on sea-water intrusion in an unconfined aquifer. It is shown that the tidal activity forces the sea-water to intrude further inland and it also creates a thicker interface than would occur without tidal effects. Moreover, the configuration of the interface is radically changed when the tidal fluctuations are included. This is because of the dramatic changes in the flow pattern and velocity of the groundwater near the shoreline. For aquifer depths much larger than tidal amplitudes, the tidal fluctuation does not have much effect on how far the sea-water intrudes into the aquifer; nevertheless, a significant change in the configuration of concentration contours because of the effect of tidal fluctuations is observed. This change is more noticeable at the top of the aquifer, near the water table, than at the bottom of the aquifer, and is caused by the infiltration of salt water into the top of the aquifer at higher tidal levels. A flatter beach slope, therefore, intensifies this phenomenon. The interface configurations do not change noticeably over the course of a tidal cycle. Neglecting tidal fluctuation effects results in an inaccurate evaluation of the water table elevation at the land end of the aquifer, although no distinguishable difference is seen between the water tables near the shoreline. Where the landward boundary condition is a constant head, the effects of tidal fluctuations on sea-water intrusion are more pronounced than for cases where the landward boundary condition is a specified flux. Also it is shown that the effects of tidal fluctuations are more significant for a sloping beach than for a vertical shoreline and the salt water intrudes further inland for the sloping case. (C) 1999 Elsevier Science B.V. All rights reserved.

Numerical and experimental study of seepage in unconfined aquifers with a periodic boundary condition

The assessment of groundwater conditions within an unconfined aquifer with a periodic boundary condition is of interest in many hydrological and environmental problems. A two-dimensional numerical model for density dependent variably saturated groundwater flow, SUTRA (Voss, C.I., 1984. SUTRA: a finite element simulation model for saturated-unsaturated, fluid-density dependent ground-water flow with energy transport or chemically reactive single species solute transport. US Geological Survey, National Center, Reston, VA) is modified in order to be able to simulate the groundwater flow in unconfined aquifers affected by a periodic boundary condition. The basic flow equation is changed from pressure-form to mixed-form. The model is also adjusted to handle a seepage-face boundary condition. Experiments are conducted to provide data for the groundwater response to the periodic boundary condition for aquifers with both vertical and sloping faces. The performance of the numerical model is assessed using those data. The results of pressure- and mixed-form approximations are compared and the improvement achieved through the mixed-form of the equation is demonstrated. The ability of the numerical model to simulate the water table and seepage-face is tested by modelling some published experimental data. Finally the numerical model is successfully verified against present experimental results to confirm its ability to simulate complex boundary conditions like the periodic head and the seepage-face boundary condition on the sloping face. (C) 1999 Elsevier Science B.V. All rights reserved.

Submarine groundwater discharge and associated chemical input to a coastal sea

This paper presents a theoretical model of flow and chemical transport processes in subterranean estuaries (unconfined brackish groundwater aquifers at the ocean-land interface). The model shows that groundwater circulation and oscillating flow, caused by wave setup and tide, may constitute up to 96% of submarine groundwater discharge (SGWD) compared with 4% due to the net groundwater discharge. While these local flow processes do not change the total amount of land-derived chemical input to the ocean over a long period (e.g., yearly), they induce fluctuations of the chemical transfer rate as the aquifer undergoes saltwater intrusion. This may result in a substantial increase in chemical fluxes to the ocean over a short period (e.g., monthly and by a factor of 20 above the averaged level), imposing a possible threat to the marine environment. These results are essentially consistent with the experimental findings of Moore [1996] and have important implications for coastal resources management.

Beach water table fluctuations due to spring-neap tides: moving boundary effects

Tidal water table fluctuations in a coastal aquifer are driven by tides on a moving boundary that varies with the beach slope. One-dimensional models based on the Boussinesq equation are often used to analyse tidal signals in coastal aquifers. The moving boundary condition hinders analytical solutions to even the linearised Boussinesq equation. This paper presents a new perturbation approach to the problem that maintains the simplicity of the linearised one-dimensional Boussinesq model. Our method involves transforming the Boussinesq equation to an ADE (advection-diffusion equation) with an oscillating velocity. The perturbation method is applied to the propagation of spring-neap tides (a bichromatic tidal system with the fundamental frequencies wt and wt) in the aquifer. The results demonstrate analytically, for the first time, that the moving boundary induces interactions between the two primary tidal oscillations, generating a slowly damped water table fluctuation of frequency omega(1) - omega(2), i.e., the spring-neap tidal water table fluctuation. The analytical predictions are found to be consistent with recently published field observations. (C) 2000 Elsevier Science Ltd. All rights reserved.

A two-dimensional analytical solution of groundwater responses to tidal loading in an estuary and ocean

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a configuration that is essentially one-dimensional. Aquifers at natural coasts can also be influenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head fluctuations in the aquifers. We present an analytical solution to the two-dimensional depth-averaged groundwater flow equation for a semi-infinite aquifer subject to oscillating head conditions at the boundaries. The solution describes the tidal dynamics of a coastal aquifer that is adjacent to a cross-shore estuary. Both the effects of oceanic and estuarine tides on the aquifer are included in the solution. The analytical prediction of the head fluctuations is verified by comparison with numerical solutions computed using a standard finite-difference method. An essential feature of the present analytical solution is the interaction between the cross- and along-shore tidal waves in the aquifer area near the estuary's entry. As the distance from the estuary or coastline increases, the wave interaction is weakened and the aquifer response is reduced, respectively, to the one-dimensional solution for oceanic tides or the solution of Sun (Sun H. A two-dimensional analytical solution of groundwater response to tidal loading in an estuary, Water Resour Res 1997;33:1429-35) for two-dimensional non-interacting tidal waves. (C) 2000 Elsevier Science Ltd. All rights reserved.

Driving mechanisms for groundwater flow and salt transport in a subterranean estuary

This paper presents field measurements and numerical simulations of groundwater dynamics in the intertidal zone of a sandy meso-tidal beach. The study, focusing on vertical hydraulic gradients and pore water salinities, reveals that tides and waves provide important forcing mechanisms for flow and salt transport in the nearshore aquifer. Such forcing, interacting with the beach morphology, enhances the exchange between the aquifer and ocean. The spatial and temporal variations of vertical hydraulic gradients demonstrate the complexity and dynamic nature of the processes and the extent of mixing between fresh groundwater and seawater in a subterranean estuary''. These results provide evidence of a potentially important reaction zone in the nearshore aquifer driven by oceanic oscillations. Land-derived contaminants may undergo important biogeochemical transformations in this zone prior to discharge.