J.-Y. Parlange

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.

Physics of water repellent soils

Although it is generally well known that water repellent soils have distinct preferential flow patterns, the physics of this phenomenon is not well understood. In this paper, we show that water repellency affects the soil water contact angle and this, in turn, has a distinct effect on the constitutive relationships during imbibing. Using these constitutive relationships, unstable flow theory developed for coarse grained soils can be used to predict the shape and water content distribution for water repellent soils. A practical result of this paper is that with a basic experimental setup, we can characterize the imbibing front behavior by measuring the water entry pressure and the imbibing soil characteristic curve from the same heat treated soil. q 2000 Elsevier Science B.V. All rights reserved.

Wetting front instability as a rapid and far-reaching hydrologic process in the vadose zone

Abstract Wetting front instability in the vadose zone causes the formation of fingers which can rapidly transport both water and solute to the phreatic surface. The development of the unstable flow field in laboratory experiments is described for an initially dry, two-layer sand system, in which the top layer has a finer texture than the bottom layer. The effect of repeated infiltration cycles and of initial moisture content at field capacity are presented. Fingers once formed in the dry porous media are found to not change location even after several infiltration events. Only saturation and subsequent drainage alters the finger structure within the chamber. In Eastern Long Island, New York, USA, field infiltration experiments using the combination of two dyes showed that water moved through finger-like structures.

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

Infiltration under ponded conditions: 3. A predictive equation based on physical parameters.

We derived a new infiltration equation that takes into account the possibility of an infinite diffusivity near saturation. Using the example of two soils (clay and coarse sand), we showed that this new infiltration equation has a sound physical basis. In particular, all parameters used are true soil properties that are constant with time and independent of the water depth imposed as a surface boundary condition. Compared with analytical, numerical, and experimental results, the equation shows a great precision (σ2 < 5.10-3 cm2) at all times. The present law introduces a significant improvement over the law obtained in part 1 of this series dealing with ponded infiltration by introducing the physical effect of an infinite diffusivity at saturation.

Interpretation of two-region model parameters

Apart from advection and diffusion/dispersion, other physical and chemical processes can affect the movement of solute through a porous medium. The classical advection-dispersion equation does not usually model adequately the breakthrough curves resulting from such effects. The two-region model (TRM) is an attempt to model succinctly and easily the effects of physical and/or chemical nonequilibrium. Physical nonequilibrium is the focus of this paper. The additional parameters appearing in the TRM are the ratio of mobile to total pore fluid, β, and the apparent transfer rate of the solute between the mobile and the immobile regions, α. Meaning is ascribed to these parameters by identifying the various ways in which physical nonequilibrium can arise. An examination of published data shows that the dominant trend is a linear variation of the transfer rate α with mobile fluid velocity Vm . In order to develop an approach incorporating all porous media types, timescales of solute transport are identified and compared to the mass transfer timescale (1/α). It was found that the local advection timescale best characterizes the mass transfer timescale. Two trends were observed for the mobile water fraction β. For aggregated/saturated porous media, β was found to be constant or decreased with increasing pore water velocity, while for partially saturated soils, β was constant or increased with increasing moisture content.

Fingered Flow in Two Dimensions 1. Measurement of Matric Potential

Precise management of the changing matric potential during infiltration into unsaturated soil required the development of miniature, high-speed, planar tensiometers. A novel design was developed, with response time of less than 1 s. The applicability of the devices is shown through measurements of the matric potential in growing instabilities, both in the induction zone and along the vertical finger profile. Tensiometry is demonstrated to be a practical method of obtaining data with high temporal and spatial resolution for the study of dynamic flow fields and facilitates testing of theoretical results for unstable flow fields.

Funneled flow mechanisms in a sloping layered soil : Laboratory investigation

Artificial capillary barriers are being used to divert water away from sensitive underground regions. Conversely, funneled flow over natural capillary barriers may increase the danger of groundwater contamination by decreasing the travel time and contact area. There have been relatively few experimental studies of capillary barrier flow patterns. In this study, water was applied uniformly across the top surface of a backlit tilting chamber, 1 cm thick, 110 cm high, and 180 cm long, in which a coarse sand layer was imbedded in a fine sand. Bedding slope and water application rates were varied between 0° and 12° and 1 and 3 cm h−1, respectively. After attaining steady state, matric potential was measured along the textural interface, and photos of dye traces were taken in order to visualize streamlines. The funneled flow was characterized by three discrete regions: an initial capillary diversion, a breakthrough region, and a toe diversion. The breakthrough region consisted of a significant zone of partial breakthrough where the vertical flux into the coarse layer was less than the water application rate. The lateral distance of the capillary diversion was explained well by previously published relationships when the water entry value at the textural interface was replaced by lower, observed matric potential at which breakthrough occurred at the most upslope point. The length of the capillary diversion was overpredicted using the air entry value. Finally, the toe of the coarse layer had significant, observed effects on funneled flow patterns, which have previously received little, if any, attention. The results of this study imply that the slope of the coarse layer and infiltration rate will largely govern the effectiveness of capillary barriers and that capillary barriers are less effective than previously assumed.

INFILTRATION UNDER PONDED CONDITIONS: 1. OPTIMAL ANALYTICAL SOLUTION AND COMPARISON WITH EXPERIMENTAL OBSERVATIONS

Under ponded infiltration the cumulative infiltration is a function of soil properties, initial conditions, and water layer thickness above the soil surface. For arbitrary soil properties and arbitrary dependence of water layer thickness on time but uniform initial water content, an optimization technique predicts the cumulative infiltration from the integration of an ordinary differential equation. If the thickness of the water layer is constant with time, a fully analytical result is obtained. Careful experimental observations carried out in the laboratory illustrate the validity and accuracy of the result.

Unsteady soil erosion model, analytical solutions and comparison with experimental results

Hairsine and Rose developed a soil erosion model which described the erosion transport of the multiparticle sizes in sediment for rain-impacted flows in the absence of entrainment in overland flow. In this paper we extend their steady-state solutions to account for the time variation of suspended sediment concentration during an erosion event. A very simple approximate analytical solution is found which agrees extremely well with experimental data obtained from nine experiments. We are able to reproduce the rapid initial increase to a peak in the total sediment concentration, which occurs about 3–5 min after the commencement of rainfall, as well as the subsequent declining exponential tail towards steady-state conditions. We are also able to show that the fraction of shielding of the original soil bed resulting from depositing sediment reaches its equilibrium value on about the same time-scale as the total peak suspended sediment concentration. Interestingly, we find that the masses of the individual particles which form this deposited layer are far from equilibrium, and that there is a great deal of continuous reworking and sorting of this material during the erosion event. Finally, our solution shows that the initial peak in the total sediment concentration is due to the enrichment of this sediment by the finer size classes and that as the event continues their percentage contribution diminishes.