Outflow Face Research Articles

Numerical simulation for strip-island freshwater lenses involving a precipitation-fed freshwater table

The freshwater table is the upper boundary of the entire freshwater lens and is very important for understanding the formation of freshwater lenses and for managing fresh groundwater on islands. However, little attention has been given to the position of the freshwater table, as it is difficult to visually distinguish it from the unsaturated zone in physical models. Under the natural conditions, the process of rainfall infiltration into soils involves both pore-water flow and air flow in soil voids, and thus, the airflow induced by infiltration has implications for groundwater recharge and formation of freshwater lenses. Therefore, research on the precipitation-fed freshwater table in an oceanic island should consider the water-air two-phase flow induced by rainwater infiltration. This study focuses on simulating the steady-state position of the freshwater table using TOUGH2/EOS7, a model that considers liquid and gas two-phase flow and brine, water and air three-component in unsaturated-saturated porous media, and verifying it by comparing the numerical results with the analytical solutions. The numerical results delineated the entire geometry of island freshwater lenses that involve a freshwater table replenished by precipitation, which were then compared with the Dupuit-Ghyben-Herzberg (DGH) analytical solutions that ignore the outflow face and with Van der Veer's analytical solutions that consider the outflow face. Reasonable fits between the numerical results and the DGH analytical solutions were obtained, with the exception that the lens obtained by the DGH analytical model is smaller in size than that simulated by the numerical model for various cases; a better agreement was found between the results from the numerical model and Van der Veer's analytical solutions for the homogeneous island case. The agreements between the results from the proposed numerical model and the DGH and Van der Veer's analytical models verified the proposed numerical model. The numerical modeling method investigated here enhanced the numerical simulation techniques for studying groundwater movements and the interaction of freshwater and saltwater on oceanic islands and can provide a reference for modeling more complicated island groundwater patterns.

DoD Stabilization of linear hyperbolic PDEs on general cut‐cell meshes

AbstractStandard numerical methods for hyperbolic PDEs require for stability a CFL‐condition which implies that the time step size depends on the size of the elements of the mesh. On cut‐cell meshes, elements can become arbitrarily small and thus the time step size cannot take the size of small cut‐cells into account but has to be chosen based on the background mesh elements.A remedy for this is the so called DoD (domain of dependence) stabilization for which several favorable theoretical and numerical properties have been shown in one and two space dimensions [4, 9]. Up to now the method is restricted to stabilization of cut‐cells with exactly one inflow and one outflow face, i.e. triangular cut‐cells with a no‐flow face (see [4]).We extend the DoD stabilization to cut‐cells with multiple in‐ and outflow faces by properly considering the flow distribution inside the cut‐cell. We further prove L2‐stability for the semi‐discrete formulation in space and present numerical results to validate the proposed extension.

Validation of boundary layer solution for assessing mixing zone dynamics of saltwater wedge in a coastal aquifer

In saltwater intrusion problems of coastal regions, the dynamics of narrower mixing zones are influenced by the amount of dispersive entrainment and its associated marine discharges. Modelling low-fresh water recharge and high-Peclet-number scenarios gives inaccurate results with the available methods. In this study, the physical accuracy of the BL solution provided by Paster and Dagan (2007) and Paster (2010) for such conditions is validated for discharge at outflow face and width of mixing zone (WMZ) with experimentally created datasets and further extended with numerical analysis to quantify the influence of dispersive entrainment on marine discharge and saline circulation. By comparing the measured and estimated saltwater outflows, the average transverse dispersion for all dimensionless freshwater flux rates (a) was calculated, and it ranged from 0.005 cm to 0.062 cm. The study showed that, for buoyancy-dominated, high Peclet number flow circumstances, the boundary layer solutions can be effectively used to predict the marine discharges up to a = 0.5. The combined effects of water flux and dispersion revealed that buoyant force has a considerable impact on the rate of saline circulation as it suppresses the dispersion. The findings lend credence to simplicity of the boundary layer solution in reducing numerical model convergence issues for field problems caused by low recharge and low transverse dispersion flow situations.

A simplified equation of approximate interface profile in stratified coastal aquifers

In this study, we provide a simplified equation with a new concise set of parameters defining the approximate interface profile in stratified coastal aquifers. We derive the solution directly by applying the Dupuit-Forchheimer approximation at the outset, and mathematically prove its sameness for the uniform flow in a vertical plane with the interface profile computed using the comprehensive discharge potential theory by Strack and Ausk (2015). We present a surprising result that interface elevation in the case with a seepage and outflow face at the coastal boundary turns out to be same as in which water table and interface coincides with the coastline. The interface profile is a function of the transmissivity-field centroid elevation and the total transmissivity of the freshwater-flow domain above the interface. We found that the boundary potential at the coast in the discharge-potential theory solution represents the first moment of the transmissivity. We also analyzed the differences in the interface profiles in aquifers with different hydraulic-conductivity contrasts for two sets of boundary conditions—constant head and constant flux. For a given-flux boundary, interface profiles in aquifer configurations with different conductivity contrasts converge in the upper part of the aquifer and diverge at the aquifer bottom, leading to different toe-positions. Conversely, for a given-head boundary, interface profiles in aquifer configurations with different conductivity contrasts significantly differ in the upper part of the aquifer, while converge at the aquifer bottom resulting in the same toe-position. We provide explicit solutions for the toe-position and freshwater discharge in unconfined aquifers, an extension to our previous work for confined aquifers. Insights from the newly identified parameters can also potentially help in reducing the uncertainty in the estimation of the real-world SWI extent and optimize the requirement of the extent of the hydraulic conductivity field characterization.

Study of integral characteristics of the turbulent jet elements of power plants

The work represents the results of experimental research of aerodynamics of three dimensional turbulent jets flowing from nozzles with rectangle outflow face. The results of measurements of average and pulse flow characteristics of threedimensional jets are given. The data on axis speed and turbulence intensity are given and an attempt to reveal their interrelation is made. The results of experimental data comparison on axis speed attenuation of three dimensional jets with the data for axis symmetric stream are presented.

Microtidal subterranean estuaries as a source of fresh terrestrial dissolved organic matter to the coastal ocean

This paper reports on the distribution of DOM along the subterranean estuary (STE) of a microtidal beach located in the Gulf of St-Lawrence (Îles-de-la-Madeleine, Quebec, Canada). We combined porewater DOC concentrations as well as CDOM absorbance- and fluorescence-derived indices (SR, SUVA254, FI and BIX) to explore the groundwater-borne DOM transformations along the groundwater flow path to the outflow face of the beach. Based on these optical indices and multivariate analysis, results reveal a highly complex environment where biogeochemical processes and water-rock interaction alter molecular composition of DOM. Marine and groundwater end-members exhibited significantly different optical derived indices. Along the STE, however, DOC and CDOM showed non-conservative behaviour with the production of both “new” high molecular weight (MW) and lignin-derived compounds as well as microbially-derived CDOM. There is no significant relationship between DOC and CDOM optical properties because of the complex and dynamic system. A redundancy analysis (RDA) revealed a relationship between redox conditions and DOM pool signature. The RDA results highlighted a negative correlation between DOC and dissolved Fe, particularly in the suboxic zone of the STE where Fe-oxides are reduced. The RDA showed that the increase of SR and SUVA254, (i.e., from high MW CDOM compounds with low aromaticity to low MW CDOM compounds with high aromaticity) is inversely correlated to dissolved metals, particularly total dissolved Mn. Whatever the processes involved in the carbon behaviour, our results showed the dominance of terrestrial DOM pool all along the STE. Despite the fact that marine-derived particulate solutes are considered as the primary source of DOC in tidal sands, our study illustrated how groundwater-borne solutes may affect reaction in STE and opens questions about the terrestrial DOM export to a coastal bay.

Experiments and modeling of freshwater lenses in layered aquifers: Steady state interface geometry

Summary The interface geometry of freshwater lenses in layered aquifers was investigated by physical 2D laboratory experiments. The resulting steady-state geometries of the lenses were compared to existing analytical expressions from Dupuit–Ghyben–Herzberg (DGH) analysis of strip-island lenses for various cases of heterogeneity. Despite the vertical exaggeration of the physical models, which would seem to vitiate the assumption of vertical equipotentials, the fits with the DGH models were generally satisfactory. Observed deviations between the analytical and physical models can be attributed mainly to outflow zones along the shore line, which are not considered in the analytical models. As unconfined natural lenses have small outflow zones compared to their overall dimensions, and flow is mostly horizontal, the DGH analytical models should perform even better at full scale. Numerical models that do consider the outflow face generally gave a good fit to the physical models.

Numerical investigation of leakage in sloping aquifers

A sloping aquifer resting on impermeable bedrock is a common paradigm in hydrological modeling. The underlying assumption of this paradigm is examined in this study of leaky hillslope systems. Leakage is simulated with a three-dimensional finite element Richards equation model for a 100 m synthetic hillslope composed of an unconfined and a confined aquifer separated by an aquitard. The simulations examine different configurations of aquifer and aquitard properties (hydraulic conductivity, aquitard thickness), hillslope geometry (uniform, convergent, divergent), hillslope inclination (0.2, 5, and 30%), and boundary conditions (Dirichlet, seepage face), as well as the interplay between leakage, water levels, and outflow. The results show that leakage generally percolates in both directions, with downward (positive) leakage in upslope portions of the aquifer and upward (reverse or negative) leakage in downslope regions. Geometry is found to be a main determinant of the partitioning of leakage along a hillslope, with for instance upward leakage in large portions of convergent slopes but only in a restricted downslope region for divergent slopes. In steep hillslopes, the reverse leakage that occurs downslope as a result of quick upslope drying represents a major component of the water budget. Outflow boundary conditions also exert a major control on the volume and direction of leakage, with the placement and extent of Dirichlet or seepage face nodes along the outflow face being particularly important factors. A dimensional analysis is used to synthesize the main findings and to highlight the differences in response between leaky and non-leaky hillslope conceptualizations. Leakage is also examined for a larger scale aquifer system, in a preliminary assessment of the importance of this exchange process for river basin models that are based on extensions of simple hillslope conceptualizations.

Seepage caused tension failures and erosion undercutting of hillslopes

Summary Seepage has been suggested as an important factor in gully and river bank erosion. This study investigated the underlying mechanisms of instability by seepage in laboratory studies. A 25-cm tall, 50-cm wide, and 20-cm long soil block with a focused inflow reservoir was constructed to investigate seepage gradient forces and the three-dimensional nature of seepage particle mobilization (i.e., seepage erosion) and undercutting. Experiments included sand and loamy sand soil blocks packed at prescribed bulk densities (1.30–1.70 Mg m−3) and with an outflow face at various angles (90°, 75°, and 60°). Constant heads of 15, 25, and 35 cm were imposed on the soil to induce flow. A laser scanner was utilized to obtain the three-dimensional coordinates of the bank and undercut surfaces at approximately 15–30 s intervals. The bulk density of the two different soil types controlled which seepage failure mechanism occurred: (1) tension or “pop-out” failures due to the seepage force exceeding the soil shear strength which was being concurrently reduced by increased soil pore-water pressure, or (2) particle entrainment in the seepage flow, particle mobilization, bank undercutting, and bank collapse when the initial seepage force gradient was less than the resistance of the soil block. For cases experiencing particle mobilization and undercutting, seepage erosion initiated as unimodal (i.e., concentrated at one point) or as multimodal (i.e., initiating at several locations across the bank face), and this result was largely controlled by the bank angle. A five parameter Gaussian function was fitted to the measured three-dimensional undercut shapes to derive parameters for the maximum depth of undercutting, position of the center of the peak, and the vertical and lateral spreads of the undercut. The parameters of this distribution can be useful in the development of improved sediment transport functions and the incorporation of this failure mechanism into hillslope stability models.

Episodic high intensity mixing events in a subterranean estuary: Effects of tropical cyclones

Hydrostatic balances between fresh and saline groundwater and saline surface water control the physical and chemical framework of subterranean estuaries, but they are responsive to high frequency (waves and tides), low frequency (seasonal recharge patterns), and episodic (storm) events. In this study, we document a salinity and pressure perturbation to the subterranean estuary in east‐central Florida during and after the passage of Tropical Storm Tammy on 04 Oct 2005–05 Oct 2005 and Hurricane Wilma on 24 Oct 2005. These storms reversed hydraulic gradients, forced lagoon water into the aquifer, and shifted the outflow face landward. Salinity at 1.5 m and 2.5 m below a common datum converged on similar values intermediate between fresh and lagoon water salinities. The outflow face reestablished pre‐storm conditions after 80 days at 15 m offshore, but more than 160 days at 30 m offshore, confirming that both the flow field and fluid sources control the position of the subterranean estuary. Episodic, high intensity events could influence the biogeochemical setting of the subterranean estuary and the overlying water body by altering redox conditions in the subterranean estuary during the landward migration of the dispersive mixing zone, increasing short‐term discharge of potentially contaminated groundwater, and/or changing pore fluid residence time within the seepage face and along the mixing zone‐seepage face front.

Optimal Convergence of the Original DG Method for the Transport-Reaction Equation on Special Meshes

We show that the approximation given by the original discontinuous Galerkin method for the transport-reaction equation in d space dimensions is optimal provided the meshes are suitably chosen: the $L^2$-norm of the error is of order $k+1$ when the method uses polynomials of degree k. These meshes are not necessarily conforming and do not satisfy any uniformity condition; they are required only to be made of simplexes, each of which has a unique outflow face. We also find a new, element-by-element postprocessing of the derivative in the direction of the flow which superconverges with order $k+1$.

Magnitudes of submarine groundwater discharge from marine and terrestrial sources: Indian River Lagoon, Florida

Magnitudes of terrestrial (fresh) and marine (saline) sources of submarine groundwater discharge (SGD) are estimated for a transect across Indian River Lagoon, Florida. Two independent techniques (seepage meters and pore water Cl− concentrations) show terrestrial SGD decreases linearly to around 22 m offshore, and these techniques, together with a model based on the width of the outflow face, indicate a cumulative discharge of between 0.02 and 0.9 m3/d per meter of shoreline. Seepage meters and models of the deficiencies in 222Rn activity in shallow sediments indicate marine SGD discharges of roughly 117 m3/d per meter of shoreline across the entire 1800‐m‐wide transect. Two surface streams nearest the transect have an average discharge of about 28 m3/d per meter of shoreline. Marine SGD is thus 4 times greater then surface water discharge and more than 2 orders of magnitude greater than terrestrial SGD. The magnitude of the terrestrial SGD is limited by the amount of regional precipitation, evaporation, recharge, and groundwater usage, while marine SGD is limited only by processes circulating marine water into and out of the sediments. The large magnitude of marine SGD means that it could be important for estuarine cycling of reactive components such as nutrients and metals with only slight modification from estuarine water compositions. The small magnitude of terrestrial SGD means that large differences from estuarine water composition would be required to affect chemical cycling.

The size of the freshwater zone below an elongated island with infiltration

An exact solution is derived for two‐dimensional, steady interface flow below an elongated island with infiltration. The exact solution is obtained with the hodograph method in combination with conformal mapping; the complex specific discharge function and the reference function are used as auxiliary functions. A new procedure is presented for the solution of the parameter problem in the conformal map of the upper half plane onto the domain in the specific discharge plane. The exact solution is used to compute the depth of the interface for both isotropic and anisotropic aquifers. The depth of the interface at the center of the island is independent of the vertical hydraulic conductivity; the length of the outflow face at the beach is independent of the horizontal hydraulic conductivity. The exact solution can only be evaluated numerically for values of the infiltration rate that are at least an order of magnitude larger than may be expected realistically. For practical problems it is proposed to approximate the shape of the interface with a semiellipse; explicit equations are given for the size of the ellipse in terms of the aquifer parameters. The approximate solution is compared to the exact solution for a number of cases with large infiltration rates (so that the exact solution could be evaluated). The approximate and exact solutions produce results that are identical for at least six significant digits for all cases investigated, which suggests that it may be reasonable to use the approximate formulas outside the range of comparison. Solutions for isotropic and anisotropic aquifers obtained with the approximate formulas are compared to results obtained with a Dupuit solution for a set of realistic aquifer parameters; the interface is approximated well with the Dupuit solution.

Modeling Sea‐Water Intrusion with Open Boundary Conditions

AbstractThe present study concerns the application of a new numerical approach to describe the fresh‐water /sea‐water relationships in coastal aquifers. Essentially, a solution to the partial differential equation governing the regional motion of a phreatic surface and the resulting interface between fresh water and salt water is analyzed by a Galerkin finite‐element formulation. A single‐phase steady numerical model was applied to approximate, with simple triangular elements, the regional behavior of a coastal aquifer under appropriate sinks, sources, Neumann, outflow face, and open boundary conditions. On the one hand, outflow open boundaries at the coastline were not treated with other classical boundary conditions (Dirichlet or the outflow face approach), but instead with a formal numerical approach for open boundaries inspired in this particular case by the Dupuit approximation of horizontal outflow at the boundary. The solution to this numerical model, together with the Ghyben‐Herzberg principle, allows the correct simulation of fresh‐water heads and the position of the salt‐water interface for a steeply sloping coast. Although the solutions were precise and do not present classical numerical oscillations, this approach requires a previous solution with Dirichlet boundary conditions at the coastline in order to find a good convergence of the solution algorithm. On the other hand, the same precise results were obtained with a more restrictive open boundary condition, similar in a way to the outflow face approach, which required less computer time, did not need a prior numerical solution and could be extended to different coastline conditions. The steady‐state problem was solved for different hypothetical coastal aquifers and fresh‐water usage through three types of numerical tests. Calculated fresh‐water heads, interface positions and discharges show very precise results throughout the domain and especially at the coastline when compared to analytical, experimental, and numerically correct solutions. Therefore, interface positions, fresh‐water heads, and discharges originating from the steady regional behavior of coastal aquifers can be precisely predicted by numerical modeling when open boundaries towards the sea are properly treated for the likely conditions of the coastline.

Centrifuge Measurements of Capillary Pressure: Part 1-Outflow Boundary Condition

Summary The capillary pressure curve is estimated from centrifuge measurements with the assumption that Pc =0 at the outflow end of the core. With the proper end piece to support the core sample, this boundary condition is valid in practically all circumstances. If the end piece is wetted by the produced liquid, however, experiments show that the capillary pressure curve is altered significantly. Theoretical analysis demonstrates that film drainage can displace the zero-capillary-pressure boundary condition to the bottom of the end piece or farther. Accordingly, we recommend that the displaced phase not wet the end piece; in the case of water, a teflon end piece is recommended over the commonly used rubber one. When the end piece is not a problem, the condition for 100% liquid saturation at the outflow face can be expressed as a critical Bond number, which is rarely exceeded. Saturation profiles for an experiment just below the critical Bond number were in excellent agreement with predictions. Pendant drops at the outflow face can result in a nonzero capillary pressure at the outflow face, but this effect is insignificant. Good agreement was obtained between mercury injection and centrifuge-measured capillary pressure curves. Attention is drawn to the importance of core jacketing, core cleaning, and equilibration times in providing reliable centrifuge-measured capillary pressure curves.

A new approximate technique for the hodograph method in groundwater flow and its application to coastal aquifers

The solution to a steady, two‐dimensional problem of flow in a coastal aquifer is derived to illustrate the application of a new approximate analytical technique. The problem involves the determination of a phreatic surface, an interface separating flowing freshwater from salt water at rest, a seepage face, and an outflow face where freshwater leaves the homogeneously permeable porous medium to flow into the sea. The solution which expresses the relation between the complex potential Ω and the complex variable z, defined in the flow domain, is obtained by application of conformal mapping techniques using the hodograph method. Three auxilliary planes are introduced: the ζ plane, a reference half plane, the plane of the specific discharge function w, which is the complex conjugate of the hodograph, and the plane of the reference function R, a function of the first derivative of z and w with respect to ζ. The boundary of the flow domain, which is not known beforehand, corresponds to a polygon composed of circular arcs and straight line segments in the w plane and to a polygon of straight lines through the origin in the R plane. The function that maps the ζ plane onto the R plane is expressed analytically. In the proposed technique, the analytic function ζ=ζ(w) is evaluated using a new boundary element approximation. It is shown that the solution to the flow problem may be derived from those two relations in terms of w.

Dupuit-Ghyben-Herzberg analysis of strip-island lenses

Dupuit-Ghyben-Herzberg analysis follows from combination of the continuity equation and Darcy's Law with the Ghyben-Herzberg Principle and the Dupuit assumptions of horizontal flow. The analysis is used to derive the position of the water table and salt-water interface in island lenses in terms of island geometry, distribution of hydraulic conductivity (K), and distribution of recharge (R). For small islands and cases for which the salt-water head is zero, application of Dupuit-Ghyben-Herzberg analysis gives good results because the low R/K ratios of natural lenses assure that height/width ratios of natural lenses are extremely low, 1:30 to 1:100. In earlier publications, the Dupuit-Ghyben-Herzberg differential equation has been integrated with the boundary condition that the water table and interface meet at sea level at the shoreline (that is, no outflow face). The dimensions of an outflow face, however, are known from results of potential-theory analysis. Integration of the Dupuit- Ghyben-Herzberg equation with a boundary condition consistent with the potential-theory outflow face (a) places the interface indistinguishably close to its position given by potential theory and (b) allows calculation of Ghyben-Herzberg ratios (interface depth to water-table elevation), which in this case, depart from their usual value of 40 because equipotentials are curved close to the outflow face. For natural-sized lenses, however, such analysis is necessary only within a narrow strip within 1% to 5% of the island width of the shoreline. Outside this strip, the regular analysis that ignores the presence of the outflow face positions the interface indistinguishably close to that of the potential-theory solution. Analytical solutions are developed for a number of infinite-strip islands. It is shown by analysis of the homogeneous, rectangular-island case that an island can be considered an infinite strip (to 0.1% accuracy) if its length/width ratio is larger than 4.4. Asymmetric lenses occur if the island is composed of strips of different K or different R, with the greater asymmetry occurring with differences in K. A high-K basement compresses the root of the lens and thereby decreases the water table in the island. A lens perched on impermeable basement has a higher water table than would otherwise occur in the island, but the volume of the lens is less.

Steady Interface Upconing Beneath a Coastal Infiltration Gallery

ABSTRACTThe upconing of the salt‐water interface in an unconfined coastal aquifer due to water withdrawal by an infiltration gallery is analyzed numerically based on the variational formulation of the problem. Sometimes in coastal areas, from the point of view of safe withdrawal of water on a long‐term basis, the use of an infiltration gallery is found to be feasible in preventing severe upconing of the interface that would have resulted from heavy pumpage by a vertical well. The numerical procedure presented here is capable of delineating profiles of the free surface and interface along with the length of the outflow face and quantity of freshwater flow to the sea. Full consideration of the nonlinear boundary conditions on the free surface and interface is included for a steady flow towards a gallery in both isotropic and anisotropic aquifers. The extent of upconing of the interface under different operating conditions of the gallery for different aquifer geometries has been studied. A general understanding of the flow phenomenon in the vicinity of the gallery has been established. The results of the analysis can be used to plan a water withdrawal scheme without causing contamination by salt water.

Effect of subsoil conductivity and thickness on interflow pathways, rates and source areas for chemicals in a sloping layered soil with seepage face

The effects of relative hydraulic conductivities and thicknesses of topsoil and subsoil layers and leakage rate of a compact base material on the saturated steady water flow through a sloping soil to an outflow face (interflow) were investigated theoretically. The water was assumed to be supplied from the surface, at a rate adequate to keep the entire soil saturated. Simplified descriptions of the interflow characteristics were sought wherever possible. A Gram-Schmidt orthonormalization procedure of W.L. Powers, D. Kirkham and G. Snowden provided a potential-theory solution of the problem, even though the outflow seepage face existed over two soil layers. As reported earlier by the present authors for a nonlayered soil, two regions of water entry and flow could be distinguished when the base material was not leaky: (1) flow in the main body of soil (region 1); and (2) additional infiltration and flow near the seepage face (region 2). For a slope length)/(soil depth) ratio of 20 or greater, the flow in region 1 could be approximated as a one-dimensional flow downslope in each soil layer. The length of slope that contributed to flow in region 2 was linearly related to the ratio of the hydraulic conductivity of the subsoil to that of the topsoil. A subsoil of higher conductivity than that of the topsoil increased several fold the rate of infiltration and interflow and the soil (both topsoil and subsoil) volume that was traversed by interflow near the seepage face. It also increased the area and rates of water entry and flow through the topsoil near the upper end of the slope. A significant finding of this analysis is that the transport of topsoil chemicals to field runoff will be speeded up from certain, now predictable, portions of the slope length. When the underlying base material was leaky, some water entering the soil surface seeped into the base material and the soil volume traversed by the interflow was greatly reduced. Amounts of chemicals carried to the outflow face would also be reduced. There were several situations of base leakage rates, soil conductivities and thicknesses considered. For leakage rates of practical interest, the source areas and the soil volume traversed by the interflow could be predicted adequately by a simple procedure. The total rates of water interflow in both the nonleaky- and leaky-base cases could be predicted adequately from known reference values of a nonlayered soil by using a weighted average hydraulic conductivity of the layered profile. However, for prediction of chemicals transported with interflow, knowledge of the flow directions and rate variation along the slope length will be required.

The Björk-Shiley heart valve prosthesis. Flow characteristics of the new 70 degrees model.

Thrombus formation on the outflow face and tissue overgrowth along the sewing ring adjacent to the minor outflow region are major clinical pathologic problems observed with the Björk-Shiley tilting disc valve. In the hope of reducing these pathologic conditions the convexo-concave Björk-Shiley valve was designed. A new modification to the convexo-concave model has further improved most of the fluid dynamic characteristics of the valve. In vitro flow studies indicate an average improvement in pressure drop characteristics of about 20 to 30%. Velocity measurements made with a laser-Doppler anemometer in the immediate downstream vicinity of the modified convexo-concave valve indicate that the design changes have further reduced the size of the stagnation zone near the outflow face of disc. It was observed, however, that the regurgitation across the valve increased by about one to two percentage points.