PUBLICATIONS. Journal of Geophysical Research: Oceans. Numerical study of solute transport in shallow beach aquifers subjected to waves and tides

Transcription

1 PUBLICATIONS Journal of Geophysical Research: Oceans RESEARCH ARTICLE Key Points: A new approach is developed to address wave effect on solute fate within beaches Additive waves cause solute to move seaward with a longer and deeper trajectory Waves shift the biochemical residence time map downward and seaward in the beach Supporting Information: Supporting Information S1 Correspondence to: M. C. Boufadel, boufadel@gmail.com Citation: Geng, X., and M. C. Boufadel (2015), Numerical study of solute transport in shallow beach aquifers subjected to waves and tides, J. Geophys. Res. Oceans, 120, , doi: / 2014JC Received 27 OCT 2014 Accepted 19 JAN 2015 Accepted article online 27 JAN 2015 Published online 27 FEB 2015 Numerical study of solute transport in shallow beach aquifers subjected to waves and tides Xiaolong Geng 1 and Michel C. Boufadel 1 1 Center for Natural Resources Development and Protection, Department of Civil and Environmental Engineering, New Jersey Institute of Technology, Newark, New Jersey, USA Abstract A numerical study was conducted to investigate the fate of solute in a laboratory beach in response to waves and tides. A new temporal upscaling approach labeled net inflow was introduced to address impacts of waves on solute transport within beaches. Numerical simulations using a computational fluid dynamic model were used as boundary conditions for the two-dimensional variably saturated flow and solute transport model MARUN. The modeling approach was validated against experimental data of solute transport due to waves and tides. Exchange fluxes across the beach face and subsurface solute transport (e.g., trajectory, movement speed, and residence time) were quantified. Simulation results revealed that waves increased the exchange fluxes, and engendered a wider exchange flux zone along the beach surface. Compared to tide-only forcing, waves superimposed on tide caused the plume to be deeper into the beach, and to migrate more seaward. The infiltration into the beach was found to be directly proportional to the general hydraulic gradient in the beach and inversely proportional to the matrix retention (or capillary) capacity. The simulations showed that a higher inland water table would attenuate wave-caused seawater infiltration, which might impact beach geochemical processes (e.g., nutrient recycle and redox condition), especially at low tide zone. The concept of biochemical residence time maps (BRTM) was introduced to account for the net effect of limiting concentration of chemicals on biochemical reactions. It was found that waves shifted the BRTMs downward and seaward in the beach, and subsequently they engendered different biochemical conditions within the beach. 1. Introduction Inland pollutant discharges from human, agricultural, or industrial activities have been known to degrade coastal groundwater ecosystems [Weil et al., 1990; Winter, 1999; Islam and Tanaka, 2004]. Efforts have been dedicated on investigating the fate of solute in nearshore groundwater system [Moore, 1996; Robinson et al., 2006; Li et al., 2007; Li and Boufadel, 2011; Bakhtyar et al., 2013], and the general assessment was that oceanic forcing, such as tides and waves, significantly impacts pollutant discharge across the aquifer-ocean interface. A majority of the work has focused on investigating the impact on the submarine groundwater discharge (SGD) [Moore, 1996; Li et al., 1999; Destouni and Prieto, 2003; Michael et al., 2005]. These studies used largescale models based on the sought interest. Li et al. [2008] addressed beach-scale transport due to tides, but their findings were focused on the SGD. The present paper aims to address beach-scale transport due to tides and waves, due to the importance of this scale to quantification of geochemical reactions such as dissolved organic carbon entrapment [Sawyer et al., 2014] and bioremediation of oil spills [Geng et al., 2014a]. The impact of tides on solute transport in nearshore aquifers has been thoroughly investigated in the last two decades by experiments [Wrenn et al., 1997; Uchiyama et al., 2000; Boufadel et al., 2006, 2011a] and through numerical simulations [Boufadel et al., 1999b; Brovelli et al., 2007; Robinson et al., 2007; Xia et al., 2010]. Compared to tidal forcing, wind-generated waves have high frequency, with wave periods between 6 and 10 s on the eastern coast of the U.S. [Thornton and Guza, 1983]. As a wave approaches land from sea, it encounters shallower depths (i.e., it shoals), which causes the wave height to increase and the wave length GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1409

2 to decrease; the wave period remains constant [Dean and Dalrymple, 1984]. At a certain wave slope (ratio of wave height to wave length), the wave becomes unstable and breaks. The generated bore continues landward until the water loses its kinetic energy and runs back. This behavior has been shown to affect the pattern of groundwater flow and associated solute transport in coastal aquifers [Longuet-Higgins, 1983; Baldock and Hughes, 2006; Sous et al., 2013]. Modeling the hydrodynamics of waves is computationally expensive due to the highly transient nature of waves, and the need to track the free surface [Bakhtyar et al., 2009; Geng et al., 2014b] which would require very small temporal and spatial increments. A widely used approach for simulating the effect of waves on beach (i.e., pore water) hydraulics is by using the Mean Water Level (MWL) as a seaward boundary condition. The approach has been labeled phase averaged [Xin et al., 2010], because the MWL is obtained by averaging the temporal variation of the water level in each wave period at each location across the beach. Bakhtyar et al. [2013] simulated the hydrodynamics of waves using Computational Fluid Dynamics (CFD) and obtained the phase-averaged water level at the beach surface, which was used as seaward boundary condition for simulating variable-density groundwater flow and solute transport in nearshore aquifers using model SEAWAT [Langevin, 2008]. Their results suggested that waves superimposed on tide intensified the extent of upper saline plume; to better understand solute fates in nearshore aquifers, both wave and tidal forcing need to be considered. Xin et al. [2010] used the variably saturated groundwater flow model SUTRA [Voss and Souza, 1987] to simulate wave forcing affecting a subterranean estuary. Their results demonstrated that high-frequency waves induced pore water circulations in the nearshore zone of the coastal aquifers, while the combined wave and tide forcing intensified this flow circulation and shifted the freshwater discharge zone farther seaward. Robinson et al. [2014] used the SUTRA model to investigate groundwater flow and salt transport in a subterranean estuary driven by intense waves generated by offshore storms. Their simulation results revealed that the intensified wave conditions significantly perturbed the flow and salt transport in a subterranean estuary. The time for the salt distribution to return to the prestorm condition was up to a 100 days and correlated strongly with the time for seawater to recirculate through the aquifer. Geng et al. [2014b] was the only work to compare numerical simulations of solute transport due to waves to experimental data. They used the MARUN model to simulate the density-dependent subsurface flow and solute transport in the saturated and unsaturated regions of the beach subjected to waves. They also used the CFD software, Fluent, to simulate wave motions on the beach face. Using a phase-resolving approach, their results revealed that wave significantly increased the residence time and spreading of inland-applied solutes in the beach. They also found that due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone constituted a continuous slow release of solute to the saturated zone of the beach. However, to our knowledge, no prior numerical models on subsurface solute transport in response to both waves and tide have been validated against field or experimental data. For this reason, we invested a particular effort in this work to compare our simulation results to experimental data prior to further evaluating the impact of waves on solute transport within the beach. As we are using a variably saturated flow model (i.e., MARUN), which is much more computationally demanding than a saturated flow model, we discuss herein the rationale for using such a model. 2. The Case for Variably Saturated Flow Modeling The studies mentioned above along with other studies [Turner and Masselink, 1998; Austin and Masselink, 2006; Steenhauer et al., 2011, 2012; Heiss et al., 2014] have found that waves would cause infiltration along the swash zone of the beach into the unsaturated zone of the subsurface. Therefore, we argue herein that capillarity effects need to be accounted for in predicting wave-induced groundwater fluctuations and associated solute fate in coastal beaches [Li et al., 1997; Horn, 2006]. Unfortunately, most earlier studies have been based on saturated groundwater flow models [Li and Barry, 2000; Li et al., 2002; Bakhtyar et al., 2009, 2012], where the soil moisture above the water table is assumed to be zero. The approach also makes the water table an impermeable boundary for water flow and solute transport, and thus, as the water table drops it leaves no moisture or solute behind it, which is not what happens in reality where the unsaturated zone holds moisture with solute (i.e., saltwater) in it. The usage of saturated groundwater model might be reasonable for coarse textured media (e.g., gravel and pebbles), but is not realistic for situations where the porous medium is fine textured. Boufadel et al. [1999b] found that the unsaturated flow could be up to GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1410

3 100% of the saturated flow for fine-textured media [see also Naba et al., 2002]. In variably saturated models (such as we are using herein), the water table is simply the locus of points where the water pressure is zero, and thus, water flow and solute can traverse it downward and upward [Boufadel et al., 1999b; Boufadel, 2000; Boufadel et al., 2011b]. In particular, for situations where the water table rises and drops, simulations conducted using a saturated flow model lose water and solute mass, as all cells above the water would have to be deactivated when the water table drops (in other words, water and solute have to be taken out of the mass conservation equations for water and solute). When the water table rises, common saturated flow models assume that the moisture and solute in front of the upward moving water table are equal to zero. This means that more water is displaced vertically in comparison with the case of variably saturated media where initial nonzero moisture exists. In addition, the solute concentration could be either amplified or reduced depending on the real concentration above the water table. Evidently, using a saturated flow model prevents one from addressing transport in the unsaturated zone, and subsequently major geochemical exchanges there. Examples include the transport of nutrients and oxygen for oil biodegradation [Geng et al., 2014a, and citations therein]. The layout of the paper is as follows: first the details for the tracer experiments conducted in a laboratory beach subjected to waves and tides are described. Then the two numerical models are introduced: (i) Fluent, a CFD modeling software that we used for wave simulations, and (ii) MARUN, a finite element model for subsurface flow and solute transport. A new approach, labeled net inflow, is evaluated for temporal upscaling of wave effects on beach hydrodynamics as function of large-scale beach hydraulic gradient. The net inflow approach is compared to the phase-averaged approach, and more importantly to experimental data of water table and tracer concentration in a beach subjected to tides and waves, which has never conducted before. Then, the modeling results are used to reveal the general behaviors of subsurface flow and solute transport in response to waves and tides in coastal aquifers, and the article closes with a discussion on using beach hydrodynamic results to evaluate biochemically active zones in coastal beaches. 3. Methodology 3.1. Experiment of Boufadel et al. [2007] Boufadel et al. [2007] presented a tracer study in a laboratory beach (Figure 1) subjected to waves and/or tides. The beach was 6.3 m long, 1.15 m high, and 0.6 m wide, had a slope of 10% between 0 and 5 m distance, and a 50% slope between 5 and 6.3 m distance. The sand used in the tank was made of silica and was coarse with a median size of 1.0 mm and narrow particle size distribution varying from 0.8 to 1.2 mm. The porosity of the sand was 0.33 (Table 1). Due to the operation of the tank over time, tide, waves, and mechanical compaction [Boufadel et al., 2006], the beach was found to consist of two layers [Boufadel et al., 2011b]. The saturated hydraulic conductivity of the upper layer was m/s and that of the lower layer was m/s. The values of the van Genuchten [1980] unsaturated parameters of upper layer were a 5 25 m 21 and n (Table 1). The experiments started by filling the tank with tap water, whose background ion concentration was 0.15 g/l. A tracer solution (100 L of NaCl solution at a concentration of 2.76 g/l) was applied onto the beach surface. Three experiments were performed using different type of oceanic forcing at sea side: (1) wave-only (T w s, A w cm); (2) tide-only (T t min, A t m); (3) tide 1 wave (T t min, A t m, T w s, A w cm). The duration of tracer application was from time t 5 0tot 5 50 min (50 min) for the wave-only experiment, and from time t 5 22 min to t 5 42 min (20 min) for the tide-only and tide 1 wave experiments. Note that the tide level varied linearly with time between 0.7 and 1.1 m by pumping water in and out of the tank periodically through manifolds. Waves were generated through the movement of a flaptype wavemaker. Four pressure transducers (PT, Model NO. 1151AP, Fisher) and ten Conductivity Meter sensors (CM, CDCN 108, Omega Engineering) were placed at different locations of the beach to measure water pressure and salt concentrations in the beach, respectively (Figure 1). The open water level in the tank was measured using a Wave Gauge (WG, Model NO. LV5900, Omega Engineering). The locations of all sensors are shown in Table S1. Further details of the experimental setup can be found in Boufadel et al.[2007] Numerical Approach The waves were simulated using the CFD software, Fluent ( The output pressure on the beach surface was used as seaward boundary condition for subsurface water flow and solute transport GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1411

4 Figure 1. Experimental laboratory beach setup showing conductivity meters (CMs) for measuring the tracer concentration, pressure transducers (PTs), and the wave gauge (WG). This beach was found to consist of two layers [Boufadel et al., 2011b]. within the beach to be simulated using the variably saturated model MARUN (marine unsaturated) [Boufadel et al., 1999b]. The MARUN model has been verified and validated extensively in previous studies [Guo et al., 2010; Li and Boufadel, 2010; Xia et al., 2010] Wave Motion The wave-induced sea level oscillations were simulated using Fluent, which has been thoroughly adopted for nearshore wave motion simulations [Bakhtyar et al., 2010; Dimakopoulos and Dimas, 2011; Geng et al., 2014b]. The hydrodynamic model defined in Fluent for the simulation was based on the Reynolds-Averaged Navier-Stokes (RANS) equations, the Volume of Fluid (VOF) module and k-e turbulence closure. The VOF module [Hirt and Nichols, 1981] was used to solve for the location of the free surface at each time step. The k-e turbulence closure was selected due to its simplicity and robustness [Jones and Launder, 1972; Mohammadi and Pironneau, 1993; Wilcox, 1998]. The setup of the hydrodynamic model was described in detail in Geng et al. [2014b]. A time step of s was selected to accurately capture the change in pressure at the beach surface, and to keep the grid Courant number less than 1.0 (it was generally around 0.25). The parameter values used for k-e closure turbulence model are reported in Table Variable-Density Subsurface Flow and Solute Transport Subsurface flow and solute transport were simulated using MARUN model. On the landward side, the head recorded in PT1 was used as boundary condition. On the seaward side: a no-flow boundary was used on the beach surface when it was exposed to air, with the exception of the tracer application zone during the application which was assigned a Neumann flux equal to m 2 /s for the wave-only case and m 2 /s for the tide-only and tide 1 wave. As observed by Boufadel et al. [2011b], the formation of the seepage face did not have great effects on solute hydrodynamics in this beach system, and therefore, Table 1. Model Parameter Values Used in the Numerical Simulations Symbol Definition Units Value k-e Closure Turbulence Model C m Model constant C 1n Model constant 1.42 C 2n Model constant 1.68 k Turbulence kinetic energy m 2 s e Turbulence dissipation rate m 2 s MARUN Model a Sand capillary fringe parameter of the m van Genuchten [1980] model n Sand grain size distribution parameter of the 3.5 van Genuchten [1980] model K 0 Saturated freshwater hydraulic conductivity m s (Upper layer) (Lower layer) a L Longitudinal dispersivity m 0.03 a T Transverse dispersivity m n Fitting parameter of density concentration Lg relationship S 0 Specific storage m S r Residual soil saturation 0.01 U Porosity 0.33 CONVP The convergence criterion of pressure head in the m Picard iterative scheme of MARUN code sd m Product of tortuosity and diffusion coefficient m 2 s GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1412

5 the seepage face module within MARUN was inactivated for these simulations. For the submerged beach surface, the head recorded in WG was assigned for the tide-only experiment. For the tide 1 wave experiment, an additional Neumann boundary condition was assigned to the swash zone, which was generated based on net inflow approach, introduced in this paper. Finally, a no-flow boundary condition was used for the bottom of the beach for all experiments, which represents the impermeable steel bottom of the tank. For the solute transport equation, at the landward side (x 5 0), a Neumann boundary condition with zero dispersive flux, was where n is the outward normal vector. At the seaward side, a Neumann boundary condition with a zero dispersive flux was when the beach surface was exposed to the air (as no advective flow leaves the beach from the unsaturated zone, this boundary condition implies no solute leaves the beach from the unsaturated zone). In the application zone on the beach surface during tracer application, a Dirichlet boundary condition with the concentration of 2.76 g/l was assigned. For the submerged beach surface, a check on the water velocity was conducted; if the water is entering the beach, then a Dirichlet boundary condition was assigned at the seawater concentration (i.e., 0.15 g/l). If water is leaving the beach, then a Neumann boundary condition was which represents the so-called outflowing boundary condition, where water leaves the porous domain without a change in concentration. This boundary condition was discussed further by Galeati et al. [1992] and Boufadel et al. [1999b]. In the tracer application segment (25 cm, between x m and x m), a flux (Neumann) boundary condition was used during the application period. The value was m 2 /s for the tide-only experiment and m 2 /s for the experiments with waves. These values were obtained by dividing the applied flow rate by the application zone and integrating through the width of the tank (0.60 m). A mesh of 106 nodes in the horizontal and 58 nodes in the vertical directions was employed in the domain, which gave a total of 6148 nodes, and 11,970 triangular elements. Mesh resolution was 0.06 m horizontally and 0.02 m vertically. The spacing was small enough to meet the strict criterion for the grid Peclet number to be less than or equal to 2.0 [Zheng and Bennett, 2002]. For all the experiments, MARUN was first run for a 10 h simulation in absence of waves until the hydraulic regime reached a quasi-steady state. The pressure and salinity distributions then were used as initial conditions for the simulations of tracer application. The time step selected for the MARUN simulations was 10.0 s. Under such time step, the grid Courant number was less than 0.3. The small step is not only important for stability considerations, but also for accuracy, as a large time step might eliminate information on the tide near the maximum, which could greatly affect the results as noted by Boufadel et al. [2011b]. The parameter values used for the simulation are summarized in Table Centroid Location It is sometimes needed to use metrics to quantify the movement of plumes, and we have such an approach in our earlier work [Boufadel et al., 1999b]. In particular, one computes spatial moments and uses them to track the location of the plume centroid with time. In a two-dimensional vertical slice, the location of the! centroid is X! c 5XG x 1Z! G z, where! x and! z are the unit vectors in the horizontal and vertical directions, respectively, and X G and Z G are the centroid coordinates obtained using the following equations: where M represents the spatial moment in the x or z direction evaluated as X G 5 M x;1 M x;0 (1) Z G 5 M z;1 M z;0 (2) M s;q 5 XN node s q i c i (3) i51 where q 5 0or1,s 5 x or z, c i 5 concentration at the ith node; and N node 5 total number of nodes in the domain Net Inflow Approach The phase-resolving approach is very accurate but too demanding for a computational point of view. It is currently cost prohibitive to simulate the combined wave and tide experiment. For instance, to simulate wave motions for the separate wave case, the time step of s is needed to accurately capture the GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1413

6 change in pressure at the beach surface, and to keep the grid Courant number less than 1.0 [Geng et al., 2014b], which requires that MARUN runs at the same time step s if one wants to avoid interpolating over time. Thus, 12,000 time steps are needed to obtain a simulation of one minute in real time. Based on the present tidal range and period, 1 min corresponds to a change in the tide level of 2.0 cm, which is too small to allow one to evaluate the variability due to both waves and tide (recall that the wave height before breaking is around 4.0 cm). To allow one to simulate both waves and tide, we consider herein a new approach for temporal upscaling that we label the net inflow approach. Within this approach, the models were run for 120 s (but any sufficiently long duration should work) for the situation where the water table far landward of the beach was equal to the SWL. Using the water pressure from Fluent as boundary condition for the beach, MARUN simulations were obtained and the inflow into the beach at each spatial location (actually segment) was calculated based on phase-resolving approach for the duration of the forcing. Finally, the temporal average of inflow was obtained at each location. Thus, while the phase-averaged approach provides the mean water pressure at each location, the net inflow method provides the mean inflow into the beach at each location. We believe such an approach captures information on both the waves and beach hydrodynamics (water table and beach properties). The averaged infiltration rate would then be used as a Neumann boundary condition in the MARUN model with larger time steps (e.g., 10 and 30 s) to represent the effects of waves on the subsurface water flow and solute transport. The approach above is for the situation where a zero large-scale hydraulic gradient exists in the beach (i.e., the landward water table elevation is equal to that of the SWL). But such is too restrictive, and it is desired to obtain the infiltration for other large-scale gradients to simulate a broad range of situations, namely tidally influenced beaches. For these reasons, we sought and found a physical relation between the infiltration rate and the large-scale hydraulic gradient in the beach Particle Tracking Particle tracking was performed to reveal the flow pathways and associated transit time in the beach subjected to waves and tide. A particle tracking code, NEMO3D, was developed based on the random walk particle tracking algorithm. Random walk particle tracking is a well-established and efficient alternative to simulate advection-dispersion transport problem in porous media [Tompson, 1993; LaBolle et al., 1996; Delay et al., 2005; Bechtold et al., 2011]. 4. Results and Discussion 4.1. The Net Inflow Method: Validation For the wave-only experiment, Figures 2a and 2b show the residence time of the normalized mass and centroid location, respectively, which were obtained using the phase-resolving, net inflow, and phase-averaged approaches. Figure 2a shows that residence time of the plume by the net inflow method matched closely the phase-resolving residence time at earlier time (t < 2.0 h) but slightly underestimated it at later time. The phase-averaged residence time slightly overestimated that of the phase resolving at t < 2.0 h, and matched it closely at later time. Figure 2b shows the trajectory of the centroid after a simulated time of 6 h. The net inflow approach trajectory closely matched that of the phase-resolving approach, and the phase-averaged approach trajectory overestimated the vertical location of the phase-resolving trajectory by a few centimeters, approximately 20% of the vertical trajectory. To better understand Figure 2b (of centroids), we reported in Figure 3 the concentration contours at 0.3C 0 and 0.8C 0 (C g/l). For the 0.3C 0 contour (Figure 3a), the phase-averaged approach overestimated the upper location of the plume (i.e., the one obtained using phase resolving) seaward of x m while the net inflow slightly underestimated that location. But it is fair to assume that both approaches are comparable in that region. For the landward side of the plume, the net inflow approach seemed to closely match the location of the plume. For the 0.8C 0 contour (Figure 3b), the net inflow approach closely matched that of the phaseresolving approach, while the phase-averaged approach resulted in an upward movement of the plume accompanied with a seaward displacement. Considering that the larger the concentration the larger the impact on the location of the centroid, Figure 3 explains the upward movement of the centroid in Figure 2b. Apparently, the net inflow approach depends on beach hydraulics, which is nonlocal (i.e., the solution at any location in the domain depends on the rest of the domain). Thus, it is reasonable to posit that the GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1414

7 Normalized mass of the plume inside of the beach (a) Phase-resolving Net inflow Phase-averaged Time, hours (b) Phase-resolving Net inflow Elevation, m Phase-averaged SWL Distance, m Figure 2. Tracer movement in the wave-only experiment for T s and H cm. (a) Variation of normalized mass of the plume as a function of time. The mass of the plume is normalized by its maximum value, which occurred 50 min after the tracer application; (b) simulated trajectories of the plume centroid in the beach by using different approaches (phase resolving, net inflow, and phase averaged). inflow depends on the large-scale hydraulic gradient in the beach, whose surrogate would be the gradient between the landward groundwater table and the SWL. This is important for the situations where the waves on a particular beach are more or less constant with time, but the beach is subjected to tide. This is also important even for beaches that are subjected to small tides, but the regional water table changes due to recharge [Destouni and Prieto, 2003; Li and Boufadel, 2010; Xia et al., 2010]. For these reasons, we conducted phase-resolving numerical simulations using the same waves, and we varied the landward water table from 0.7 to 1.1 m, which means that the large-scale hydraulic gradient was changed from 0.08 to (positive denotes SWL is higher than inland groundwater table), and for each gradient, we computed the net inflow rate over 120 s at each location of the swash zone. The maximum hydraulic gradient magnitude in the seaward direction was set at 0.08 (i.e., 20.08) as the slope of the beach is 0.1; a large-scale hydraulic gradient of 20.1 implies that the water table is ponding throughout the swash zone, an extreme case that would GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1415

8 Figure 3. Concentration (ratio of initial solution concentration C 0, 2.76 g/l) contours at time t h for (a) 0.3C 0 and (b) 0.8C 0 using phase-resolving (color contours), net inflow (black dashed lines), and phase-averaged approaches (white dashed lines). Note the agreement between net inflow and the phase-resolving approaches, especially at t h. lead to the development of a permanent seepage face along the swash zone, which is a trivial case. More information on the development of the transient seepage face is found in Naba et al. [2002]. Two wave-only experiments were conducted one with a wave period T s and wave height H cm (in deep water) and the other with T s and H cm (in deep water). Figures 4 and 5 report the simulated average infiltration rates as function of the distance along the swash zone for the two experiments. The results within each graph show visual self-similarity with the following traits: the maximum infiltration rate occurred for the highest hydraulic gradient (i.e., s ), which occurred when the landward water table was 0.20 m below the SWL (which remained at 0.9 m throughout). As the gradient decreased (i.e., landward water table rose), the beach inflow decreased, which could be due to two complementary mechanisms. The first and major one is that the increase of the seaward hydraulic gradient occurred through the rise of the landward water table, which means that volume available to be filled up by the infiltrating water decreased. A secondary factor is the reduction of water entering the beach through the mechanism of pumping [Riedl et al., 1972; Li et al., 1999]. The second factor exists even for fully saturated beaches or even confined aquifers. In each of Figures 4 and 5, the infiltration profiles for each wave period occurred at the same location for all large-scale gradients; in Figure 4, the maximum magnitude occurred at approximately 2.0 m and the minimum magnitude (around zero) occurred at approximately 2.35 m. In Figure 5, the maximum magnitude of infiltration occurred at 2.2 m and the minimum magnitude 0 occurred at 2.62 m, respectively. This suggests that the -1 inflow at one gradient can be -2 related to that of another gradient by a multiplicative constant. For this reason, we used -3 F/F the following expression to fit -4 0 =1+11s the infiltration rates in Figures R 2 = and 5: Infiltration rate, m 3 /(m day) Distance, m s = s = s = s = s = 0.02 s = 0.04 s = 0.06 s = 0.08 s = 0.0 s = s = s = s = s = 0.02 s = 0.04 s = 0.06 s = 0.08 Figure 4. Infiltration rate obtained through the phase-resolving approach (symbols) and fitting curves, F, (lines) for the wave-only experiment (T s and H cm). The results reflect the increase of the infiltration with the general hydraulic gradient (positive) in the beach. FðxÞ5max 11 s s 0 f F 0 ðxþ; 0 (4) where F(x) is the net inflow magnitude due to waves in the swash zone at location x for a given large-scale hydraulic gradient s (i.e., the hydraulic gradient between the inland GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1416

9 Infiltration rate, m 3 /(m day) water table and the SWL), and s 0 represents the slope of the beach (taken as positive herein for simplicity). The parameter F 0 (x) is the inflow rate at zero large-scale beach hydraulic gradient (i.e., when the landward water table elevation is equal to the SWL elevation). The max represents the maximum value to ensure that the equation is restricted to infiltration (i.e., no exfiltration). The quantity f is a dimensionless quantity that is expected to depend on wave and beach properties. The fit gave values of f equal to 1.1 and 1.35 in Figures 4 and 5, respectively. Thus, the value of f alters the direct dependence on the beach slope by only 10% and 30% for the waves in Figures 4 and 5, respectively. The high value of determination coefficient, R 2, in both figures suggests that the proposed relation (equation (4)) captures closely the behavior of all the plots in Figures 4 and 5. The physical basis of equation (4) is illustrated in Figure 6. The dotted area (i.e., A 5 d 3 h) denotes the area that could be filled up by wave-induced seawater infiltration during each upwash. Notice that, the dotted area started at the top edge of the capillary fringe, as the capillary fringe is essentially saturated with water. For a rise in the landward water table by Dh, the shaded area decreased proportionally. Thus, the shaded area is proportional to 2 Dh d. This is consistent to the expression of equation (4) where the inflow at one gradient can be related to that of another gradient by a multiplicative constant. In equation (4), the parameter f is added to consider capillary effects as the infiltration into the beach depends not only on the water table location (i.e., the value of s) but also on the height of the capillary fringe above the water table [Boufadel et al., 1998; Naba et al., 2002]. For this beach, the height of the (static) capillary fringe was about 0.07 m [Boufadel et al., 2011b; Geng et al., 2014b]. Therefore, F (equation (4)) and subsequently the quantity ð11 s s 0 f Þ would approach zero when the height of the capillary fringe at the landward edge of the swash zone reaches the beach surface. In other words, F approaches zero when the water table is still below the beach surface. Indeed, this was noted in this study, the simulation results for a gradient equal to (i.e., water table at the maximum runup is 1 and 0.4 cm below the beach surface for the cases of f equal to 1.1 and 1.35, respectively), gave values of F that are essentially equal to zero (Figures 4 and 5). Further evaluation of the functional relation of f with wave and beach properties is being conducted by our team. In summary, equation (4) is a major (fortunate) finding relating the infiltration into the beach at various hydraulic gradients. It clearly establishes that if one evaluates the infiltration into the beach from one hydraulic gradient, one can predict the infiltration into the beach at a broad range of hydraulic gradients. It was expected that the largescale hydraulic gradient and Beach face Capillary fringe Water table h Distance, m s = s = s = s = s = 0.02 s = 0.04 s = 0.06 s = 0.08 s = 0.0 s = s = s = s = s = 0.02 s = 0.04 s = 0.06 s = 0.08 d Wave run-up F/F 0 =1+13.5s R 2 =0.97 Figure 5. Infiltration rate obtained through the phase-resolving approach (symbols) and fitting curves, F, (lines) for the wave-only experiment (T s and H cm). The results reflect the increase of the infiltration with the general hydraulic gradient (positive) in the beach. Water level Figure 6. Simplified geometry of the water table illustrating how beach infiltration decreases with a rise in the landward water table. associated inland groundwater recharge affect seawater infiltration along the swash zone. Indeed this was pointed out in numerous studies [see, for example, Li et al., 2002; Robinson et al., 2014]. However, equation (4) provides a GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1417

10 quantification that has not been done before, and such quantification is crucial for evaluating the impact of waves on solute transport in tidally influenced beaches, as addressed in the next section. For completeness, Figure S1 reports the distribution of simulated exfiltration rates along the swash zone of the beach under different beach hydraulic gradient for the waves with the period of 1.11 s and height of 4.8 cm. The variation of the exfiltration rates for the waves with period T s and height H cm revealed a similar trend to that of Figure S1, and thus is not presented for brevity. Figure S1 shows that the exfiltration rates increased as the landward water table became higher (i.e., the beach hydraulic gradient became more negative). In particular, for the case of s , the groundwater exfiltration covered the whole swash zone at a relatively higher rate in comparison to other hydraulic gradient cases. It is because that enhancing inland water table would induce a large hydraulic gradient between landside and seaside and lead to a large groundwater exfiltration along the beach face. The simulation results also indicate that even for situations where the landward water table was much lower than the SWL (e.g., 0.20 m below SWL for s ), a considerable amount of water continued to exit the beach (during rundown) due to the high frequency of waves. The exchange flux (infiltration and exfiltration) from a beach is of importance for geochemical processes occurring in the swash zone, such as nonconservative behavior of dissolved Fe concentrations [Rouxel et al., 2008], cation exchange [Zghibi et al., 2012], ph and dissolved oxygen distribution [Robinson et al., 2007], and nutrient recycle [Slomp and Van Cappellen, 2004; Rocha et al., 2009; Charbonnier et al., 2013]. However, the biochemical signature of such a flux is worth investigating in future works to assess whether this water has sufficient time to interact with pore water. For example, the exfiltration at s is considerable, but it is worth knowing if that water has any signature of interaction with the pore water or it is simply the water that enters the beach from the sea in the previous uprush. If the latter is true, then using exchange fluxes alone might overestimate the extent of waves on biochemical reactions in the beach Comparison With Combined Wave and Tide Experiment The net inflow approach is applied herein to simulate the experiments reported by Boufadel et al. [2007] where waves with the properties T s and H cm were superimposed on tide. The tide varied linearly from 0.70 to 1.10 m, and the tidal period was approximately 37.5 min. Boufadel et al. [2007] applied 100 L of tracer onto the beach surface at low tide as discussed earlier. To implement the net inflow approach, equation (4) was used to estimate the flow rate F based on the flow rate F 0 estimated in Figure 5. The value of F was obtained at each time step based on the value of the hydraulic gradient. The estimated infiltration rate was then assigned along the swash zone as Neumann boundary condition in MARUN to represent wave effects on the beach. The modeling results were obtained using the parameter values in Table 1 and equation (4) with f Figures S2a and S2b show the simulated and observed water table at PT3 and PT4 along with the boundary condition assigned at landward (PT1) and seaward (WG). The abrupt increase in the water head in the first hour was due to the application of the 100 L solution. Before and after the tracer application, the groundwater table fluctuated with tide, and the model was able to reproduce the observed water table, especially at PT3. At PT4, a maximum difference of 5.0 cm was noted during falling tides, which could be due to variety of reasons but we suspect the main one being the accretion of sand seaward of the sensor, which would have caused the water table to remain higher than that obtained assuming the perfect geometry of Figure 1. For more detailed discussions on the modeling of the water table in the tank, the reader is urged to consult the studies of Boufadel et al. [1998], Boufadel [2000], and Boufadel et al. [2011b]. Figures 7a 7c show time series of the observed and simulated concentration at eight conductivity meters (CM). Note that the initial concentration in the beach and open water was 0.15 g/l. Modeling results overall captured the concentration variation at CMs with exceptions at the lower sensors CM3 and CM5, where the simulated results rose and dropped slower than the observed data. The discrepancy between the modeling results and observations may be due to the following: (1) the CMs were encased in screened plexiglass boxes to avoid direct contacts with sand. The boxes were 10 cm 3 10 cm 3 10 cm in dimension. Therefore, the observations depict an average value of the sample volume, while the simulation results represent the concentration at a single point location of CM; (2) the measurement accuracy of the sensors was 610% [Boufadel et al., 2007]; (3) local heterogeneity may exist in the tank, which could create different three- GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1418

11 Figure 7. Observed (symbols) and simulated (black lines) tracer concentrations (a) at the top portion of the beach (CM9 and CM10), (b) at the middle portion of the beach (CM 4, CM6, and CM7), and (c) at the lower (CM3 and CM5) and landward (CM2) portions of the beach. The sensor locations are shown in Table S1. dimensional pathways for solute transport that are not accounted for in the two-dimensional model MARUN; and (4) the morphologic change of the beach profile due to wave and tide and seepage face is not considered in the simulation, which may cause the differences between modeling results and observations. In addition, the discrepancy could be due to shortcomings in the net inflow method, which suggests that further investigation should be conducted to evaluate this method. Nevertheless, considering that the net inflow method upscaled the effects of waves from a time step of s to a time step of 10.0 s for subsurface flow and solute transport simulation, a major time savings (a reduction in the computation time by 2000-folds), the scale of discrepancy with data is acceptable. To our knowledge, with the exception of Geng et al. [2014b], no one compared solute transport due to waves to actual data. Thus, matching the observations of solute transport due to the combined effects of waves and tides as done in this work is a first step in a long series of belated validations of numerical models of solute transport due to waves (and tide). Figure 8 shows the infiltration (negative) and exfiltration (positive) flow rates per unit width along the beach face at different tide level under tide-only and tide 1 wave forcing. The simulation results for the tide-only were validated in Boufadel et al. [2011b]. The following is noted in Figure 9: at high tide, waves significantly increased seawater infiltration and shifted the recharge zone landward; at midtide falling, waves shifted the exfiltration seaward and the infiltration landward and both values were larger in magnitude than those from tide-only. At low tide, the waves extended the infiltration zone landward, and increased the magnitude of the exfiltration. However, the location of the maximum exfiltration was the same as that due to tide-only. At midtide rising, waves engendered a considerable exfiltration in comparison to tide-only, which is understandable as the rising tide in the absence of waves has the consequences of increasing infiltration into the beach even if the SWL is lower than the landward water table [Boufadel and Peridier, 2002, and GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1419

12 Figure 8. Infiltration (negative) and exfiltration (positive) rates per unit width along the beach face at high tide, falling mid tide, low tide, and rising mid tide. publications therein], and thus exfiltration would be essentially zero. At midtide rising, waves increased the magnitude of infiltration and stretched its spatial extent landward. Therefore, the results indicate that waves superimposed on tide tend to increase the exchange flux (infiltration and exfiltration), and to engender a wider exchange flux zone along the beach surface. Figure 9 shows concentration contours at different time for the tide 1 wave case along with the tide-only case (dashed lines). The 2 h contours (i.e., approximately after three tidal cycles) show that the unsaturated zone in the tide-only case still contained a considerable amount of the applied solute (note the 0.2 g/l contour in the landward portion of the beach), while it was devoid of the applied solute in the tide- 1 wave case. The tide 1 wave plume was deeper than the tide-only plume at t h, and this discrepancy increased with time as one could deduce from noticing the distance from the bottom of the tank to the lower edge of the plumes. For t h, a landward tail of the tide-only plume is noted and it almost reached the water table, while the landward edge of the tide- 1 wave plume was lower by approximately 0.30 m and was more seaward. Notice that, the tidal range was 0.40 m, a vertical difference of 0.30 m due to waves suggests that the impact of waves extends deep into the beach which is consistent with studies on the impact of waves on the submarine groundwater discharge [Xin et al., 2010; Robinson et al., 2014]. Figure 10a shows the trajectory of the plume centroid as a function of time for the tide-only and tide- 1 wave cases. The plumes moved downward initially until t h (recall the tracer application was between t 5 22 min and t 5 42 min). Then the centroid s trajectories split, and the movement of both centroids (tide only and tide 1 wave) became jagged due to tidal effects. Although both plumes moved seaward, the tide-only centroid was consistently above the tide 1 wave centroid, which agrees with the contours in Figure 10 (t h in particular). The effect of waves (i.e., tide 1 wave) increased the centroid s trajectory reaching further seaward than the tide-only case (3 m for tide 1 wave in comparison with 2.68 m for tide-only). The vertical downward acceleration of the centroids around t 5 15 h is artificial as by then, most of the mass of the plume near the beach face discharged to sea, and most of the remaining solute was in the lower part of the beach. The average speed of the plume centroid was calculated based on the trajectory length and travel time for the first 6 h, as most of the solute discharged from the beach within 6 h. We found a speed of 7.96 m/d for the tide-only case and 8.58 m/d for the tide 1 wave case. The calculation indicates that besides modifying the solute s pathway, wave forcing accelerates the speed of the solute within the beach. Figure 10b shows the variation of the normalized mass (mass at time t divided by that at the end of the application period, i.e., at t 5 42 min) of the solute in the unsaturated zone of the beach. The amount of GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1420

13 solute in the unsaturated zone in the tide-only case was almost double that of the tide 1 wave case at t h (the first high tide after application). The decrease of mass in the unsaturated zone was much faster for the tide 1 wave than that for the tide-only case. At t h, the mass of solute in the unsaturated zone for the tide-only case was around 4 times larger than that for the tide 1 wave. This indicates that the flushing of solutes from the unsaturated zone by waves is much more rapid than the flushing due to tide. This could be because the tide rises slowly giving sufficient time for the beach water table to rise in response to it, and thus little water enters the beach. Waves have high frequency and percolate through the unsaturated zone flushing all solute in their way. The role of solute in the unsaturated zone is paramount for biochemical reactions due to the abundance of oxygen there, which engenders a plethora of aerobic reactions whose rates are usually much larger than those of anaerobic reactions [Tchobanoglous et al., 2002]. Figure 9. Concentration (in g/l) contours at different time for the tide 1 wave case along with the tide-only case (dashed lines). Water table under tide 1 wave forcing is shown with white dashed line. Compared to the tide-only case, the plume moved more downward and seaward Effects of Waves and Tides on Flow Pathway and Travel Time In order to identify the impact of waves on groundwater flow pathways and exclude dispersion-caused random movement, particle tracking simulations were conducted using NEMO3D where only advection transport was considered. The particles were released just 0.10 m below the beach surface at the location x 5 1.0, 1.2, 1.4, and 1.6 m. Figure 11a shows the flow paths of the particles for the tide-only and tide 1 wave cases. In comparison to tide-only, the path lines of the tide 1 wave dipped, and intersected the beach face more seaward. The wave-induced downward movement was more apparent on particles released further landward (i.e., x and 1.2 m). Figure 11b presents the travel time of the particles shown in Figure 11a. It shows that the travel time of particles in the tide 1 wave case was larger than that in the tide-only case. However, the difference was small, and became negligible for particles released at seaward locations (1.4 and 1.6 m). The results indicate that besides elongating the particle pathways, waves also increase the movement speed of the particles, especially those in the landward portion of the beach (x and 1.2 m). Therefore, to evaluate the combined wave and tide forcing affecting the travel time of particles in the beach, both the length of the trajectories and the particle speeds need to be considered. The net inflow method developed herein, and the relation between wave-induced infiltration rates at various hydraulic gradient are not only useful for simulating the superimposition of waves on tide, but could be used to better understand the wave-induced infiltration during the tidal cycle. In the experiments that we simulated earlier, the water table measured at PT1 (fluctuated with tide) was used as landward boundary; GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1421

14 Elevation, m Tide forcing Tide+wave forcing (a) Distance, m Normalized mass of the plume in unsaturated zone (b) Tide forcing Tide+wave forcing Tide level Time, hours Water level, m Figure 10. (a) Trajectory of the plume centroid in the beach for tide-only and tide 1 wave experiments. The locations of the plume centroid at specific time are shown as symbols; (b) variation of normalized mass (current divided by that at 42 min) of the solute in the unsaturated zone of the beach as a function of time. the average water table elevation at PT1 was 1.0 m. However, to better illustrate seasonal variation of inland water table affecting wave-induced infiltration, we adopted different average groundwater table at PT1. For simplicity, the tidal effects on PT1 was ignored (i.e., the groundwater table at PT1 was fixed with time). The infiltration fraction of F/F 0 (spatial invariant) was computed within a tidal cycle using net inflow approach (i.e., equation (4)). This was repeated for various values of the landward water table, and the results are reported in Figure 12. The value of F 0 was obtained for a SWL m, which is reported in Figure 5. The results in Figure 12 demonstrate that the highest infiltration rate occurred at the high tide and lowest infiltration rate occurred at low tide, which is to be expected. In addition, for higher inland water table cases (1.0, 1.05 and 1.1 m), the infiltration rate reached zero at low tide. It is consistent to physical basis as higher inland water table would saturate a larger portion of the beach surface along the intertidal zone and prohibit seawater infiltration from there. Also, the duration of small infiltration flow rates tended to be longer at higher inland water tables; the flat portion of the curves occurred over a long duration, as one notes for example the case of water level equal to 1.1 m (the lowest curve in Figure 12). The results indicate that the large-scale beach hydraulic gradient significantly impacts wave effects on the beach. During the tidal cycle, when the tide level rose, the difference in elevation increased linearly with time (as the tide level in this particular case was linear as function of time). In addition, the distance between the SWL and the location of the water table (i.e., at PT1) decreased due to the slopped beach surface. This means that the hydraulic gradient s changes nonlinearly with time. Direct application of equation (4) thus implies that F will also vary nonlinearly as function of time, which is indeed noted in Figure 12. For a natural variation of tide with time, one can simply use the observed tide time series and obtain F based on equation (4), and then one can deduce the variation of infiltration with time. We could venture to state that the exfiltration flux could be also obtained using an approach similar to equation (4), Figure 12, and the approach proposed for a field observation of tide. But such a task is left for future endeavors. GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1422

15 Elevation, m Distance, m Time, h Tide forcing Tide+wave forcing (a) Tide forcing Tide+wave forcing (b) Distance, m Figure 11. (a) Simulated flow paths of the particles released along the beach inland (0.1 m below the beach face) for tide only and tide 1 wave experiments; (b) transit time of the particles in the beach for the two experiments. Notice that the wiggles shown in the flow paths are due to the tidal fluctuation of water level Impact on Beach Geochemistry Processes and Bioremediation of Oil Spills Microorganism-mediated geochemical reactions tend to occur near the beach surface as seawater has a high concentration of oxygen and the beach sediments provide a favorable environment for the attachment and proliferation of microorganisms. Figure 12 suggests that such reactions could be slowed down for a high water table. Actually, based on the seaward flushing due to tide and wave hydraulics, the zone near the beach surface in the mid to low intertidal zone could become anoxic. This could have adverse consequences when discharged into receiving water bodies (e.g., Chesapeake Bay). This is very important in terms of managing coastal aquifers, as a higher inland water table tends to minimize saltwater intrusion, and is viewed as a positive trait. However, Figure 12 suggests that having a high inland water table might have adverse effects on chemical transformation in the beach, and subsequently receiving water bodies. The residence time of solute and its relation to beach properties and oceanic conditions have important implications on geochemical reactions within the pore space of the beach. To have a better understanding, the persistence of the plume at each portion of the domain, the residence time map (RTM) was delineated based on the simulation results at each computation node as follows: RTðx; zþ5 ð1 s50 ð1 s50 sc t ðx; z; sþds C t ðx; z; sþds (5) where the integration time of infinity is used for generality, but a time of 20 h is used herein. The term C t (x, z, t) represents a threshold concentration of relevance to delineate the edge of the plume. Thus, concentrations lower than C t (x, z, t) would not be used in the evaluation of the residence time at a particular location (x, z). This is because if the concentration at a location is small, associating it with a large value of time s could bias the results suggesting that the plume was at that location for a long time, while in reality the plume had barely passed by that location. It is common to use the 10% of the maximum to delineate the edge of the plume [Boufadel and Bobo, 2011, and references herein]. The RTM (equation (5)) provides, in essence, an integrated metric for the plume persistence within the beach. Simulated residence time maps (RTM) of the released solute in the beach was calculated for the tide-only and tide 1 wave cases, and are shown in Figures 13a and 13b, respectively. For the tide-only case, the smallest RT occurred at the landward and upper parts of the plume, which is due to the tidal flushing. Compared to the tide-only case, the tide 1 wave case shifted the RT map further downward and seaward. In particular, a narrow low residence time zone was formed due to the intensified seawater infiltration induced by waves, which accelerated the plume downward movement and subsequently decreased the residence time of the plume in this zone. To further illustrate wave effects on the residence time of the plume within the beach, GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1423

16 F/F Tide Time, min Figure 12. Variation of the infiltration fraction F/F 0 (equation (4)) during a tidal cycle under different inland water table condition (0.9, 0.95, 1.0, 1.05, and 1.1 m). Note that the inland water table was fixed, which is different than the situation of tide- 1 wave experiment conducted by Boufadel et al. [2007]. The values of F/F 0 are calculated based on the beach hydraulic gradient simulated at each time step. Notice that the F/F 0 function is symmetric with respect to lowest tide time point (t min). the map obtained as RTM (tide 1 wave) 2 RTM (tide-only) was generated and plotted in Figure 13c, where the green and red color tube indicates that waves increase the residence time of the plume at the deep part of the beach and shift the solute discharge zone seaward; the dark blue region at shallow part of the beach indicates that the plume movement is accelerated in there due to wave-caused flushing. For situations where the compound of interest (e.g., nutrient) affects the biochemistry in the beach, the minimum concentration is needed but also the value above which there is no practical effect. For example, if one determines that a minimum nutrient concentration of 1.0 mg N/L is acceptable for bioremediating a beach [Venosa et al., 1996; Geng et al., 2014a; Torlapati and Boufadel, 2014], a concentration of 2.0 mg N/L would probably accelerate oil biodegradation, but a concentration of 10.0 mg N/L would probably result in no additional increase in the biodegradation rate. The same could be stated regarding the concentration of dissolved oxygen, where a concentrations above 2.0 mg/l do not increase the biodegradation rate but concentrations much below 2.0 (e.g., 0.5 mg/ L) dramatically decrease the biodegradation rate [Boufadel et al., 2010; Li and Boufadel, 2010]. Therefore, for the biochemical retention time, we propose using an upper threshold concentration, C Th, in equation (5) resulting in the following equation: Water level BRTðx; zþ5 ð1 s50 ð1 s50 smin ðc t ðx; z; sþ; C Th Þds min ðc t ðx; z; sþ; C Th Þds (6) Figure 13. Simulated residence time map of the applied solute in the beach for (a) tide-only and (b) tide 1 wave experiments. (c) RTM obtained as RTM (tide 1 wave) 2 RTM (tide-only). The area of the contour surrounded with dark blue color in Figures 13a and 13b is restricted by over 10% of the maximum solute concentration (i.e., 0.27 g/l) at that location. where C Th (threshold) is the concentration above which, no practical enhancement in biological activity takes place. Thus, if Cðx; z; sþ > C Th, then C Th would be used in equation (6). Equation (6) is more general, as equation (5) can be derived from equation (6) by assigning a threshold value C Th larger than the maximum possible concentration of solute in the pore water (i.e., C max ). GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1424

17 Figure 14. Simulated biochemical residence time map (BRTM) in the beach at C Th 5 20%, 30%, and 50% of C 0 (i.e., 0.55, 0.83, and 1.38 g/l) for (left) tide-only and (right) tide 1 wave experiments. Biochemical residence time maps (BRTM) are created in Figures 14a 14f at C Th 5 20%, 30%, and 50% of C max for the two experiments. The simulation results show that an increase in the threshold concentration (i.e., C Th ) resulted in a retreat of the BRTM when compared to the RTM. This means that concentrations higher than the C Th did not stay long enough at these locations to cause an increase in the biochemical residence time. This thinning of the BRTMs toward the low tide line reflects the fact that as one approaches the sea, the hydrodynamics (and mixing) there becomes more dominated by the sea. The figures also suggest that if one needs to increase the spatial extent of the BRTM for a given process, one would need to increase the concentration at the source, C max, as smaller values of C Th, which is a fraction of C max would result in wider (i.e., larger) BRTM. The increase of C max would also enhance the residence time of solute at the threshold level in the beach. However, there are situations where C max is dictated by the solubility limit of the compound in solution, and thus the BRTM would provide the upper limit of biochemical enhancement that could be achieved. Figure 15 shows the biochemical residence time maps (BRTM) in the beach at C Th 5 20%, 30%, and 50% of C 0 (i.e., 0.55, 0.83, and 1.38 g/l) obtained as BRTM (tide 1 wave) 2 BRTM (tideonly). The subtraction map confirms that waves tend to shift BRTM downward and seaward, which is consistent with the results in Figure 9 regarding the location of the plumes. In addition, the major difference between the two situations appeared at the edge of the BRTM. Therefore, for a given beach, BRTM with smaller C Th would be impacted more by waves. In general, BRTM could provide a clear subsurface residence time distribution of solute at any given threshold concentration, which is instructive for shoreline oil-spill bioremediation. Previous studies have showed that the efficiency of shoreline oil bioremediation is more dependent on the kinetics of nutrient consumption, rather than the total mass of nutrients required to remediate the oil that is present [Venosa et al., 1996; Wrenn et al., 1997; Boufadel et al., 1999a; Venosa et al., 2010]. Therefore, providing BRTM would help spill GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1425

18 responders estimate the contact time between the hydrocarbon and a sufficiently high concentration of nutrients, which is essential for a successful bioremediation strategy. Figure 15. Biochemical residence time map (BRTM) in the beach at C Th 5 20%, 30%, and 50% of C 0 (i.e., 0.55, 0.83, and 1.38 g/l) obtained as BRTM (tide 1 wave) 2 BRTM (tide-only). 5. Conclusion Oceanic forcing is an essential factor affecting solute fate in coastal aquifers. A numerical study was conducted in this paper to investigate subsurface flow and solute transport in coastal beaches subjected to high and lowfrequency oceanic forcing, i.e., waves and tides, respectively. A new approach, labeled net inflow, was developed to upscale wave motions acting on the beach. The modeling approach was validated against experimental data of water level and tracer concentration at numerous locations of 6.0 m laboratory beach. Simulation results showed that waves superimposed on tide increased the exchange flux (infiltration and exfiltration), and extended landward the exchange flux zone along the beach surface. Compared to tide-only forcing, waves superimposed on the tide caused the plume to migrate seaward with a longer and deeper centroid trajectory. The net inflow approach confirmed that the spatial distribution of infiltration flux due to waves was dependent of the large-scale hydraulic gradient in the beach. The approach also revealed that the magnitude of the infiltration flux was almost proportional to the large-scale hydraulic gradient. This implied that the infiltration flux at one gradient can be predicted from that obtained from another large-scale gradient. In the presence of tide, it was found that the infiltration flux increased rapidly as the tide reached the high tide level. The infiltration flux also increased with a decrease in the landward water table. Our results also revealed that high landward water table would reduce wave-engendered seawater infiltration. Such a decrease might have adverse effects on chemical transformation processes (e.g., nutrient recycle and redox condition) in the beach, and subsequently on receiving water bodies. We also introduced a new concept known as the biochemical residence time maps to account for the effect of hydrodynamics on biochemical reactions in the beach, such as nutrient transformation [Slomp and Van Cappellen, 2004] and bioremediation of oil spills [Venosa et al., 1996; Geng et al., 2013, 2014a; Torlapati and Boufadel, 2014]. The BRTM revealed zones of predicted low biochemical activities that was not due to low concentration of limiting chemicals (such as oxygen), but due to the short residence time of such chemicals at certain locations within the beach. It was found that waves superimposed on tide would shift the BRTM of applied limiting chemical seaward and downward. Therefore, to establish a comprehensive bioremediation response to oil spills on coasts, wave effects need to be accounted for. This study was based on experiments in a 6 m laboratory beach. Upscaling of the wave results was partially addressed in Geng et al. [2014b] using the Iribarren number but additional work is being conducted to fully upscale the results. Further evaluation of the functional relation of f (equation (4)) with wave and beach properties is also needed for estimating wave-induced inflow under different hydraulic gradient conditions. GENG AND BOUFADEL VC American Geophysical Union. All Rights Reserved. 1426