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Wave-Induced Advective Transport Below a Rippled Water-Sediment Interface
Abstract
The total exchange across the water-sediment interface, averaged over one wave period, is significantly higher across a rippled interface than across a flat bed. This difference increases with increasing ripple slope and the strength of the wave motion, and it decreases with increasing thickness of the sediment layer relative to the length of the gravity wave. Since rippled bed forms are commonly found in coastal waters, the increase in the total exchange across a rippled water-sediment boundary can enhance the exchange of solutes due to "wave pumping'. Immediately below the water-sediment interface, circulation cells with net advective transport over a wave period are found. -from Author
... where C is the solute concentration, t is time, z is depth below the sediment-water interface, De is the effective diffusion coefficient, and r is a degradation coefficient, which includes the effect of biodegradation and irreversible adsorption as reported in the literature (Gr€ utzmacher et al. 2010;Song et al. 2014). This one-dimensional approach does not represent heterogeneities in transport that are known to occur beneath bedform crests and troughs under the influence of waves (i.e., Shum 1992;Rocha 2008). Nevertheless, one-dimensional approaches are a computationally efficient and widely used way to estimate average transport and reaction rates over large areas (Boudreau 2000;O'Connor and Harvey 2008). ...
... Benthic exchange rapidly flushed the sediment with dye (see Supporting Information Fig. S3). Because bedform crests are zones of low pressure, dye downwelled at bedform troughs and upwelled at bedform crests (Shum 1992;Precht and Huettel 2003). Dye was transported to an approximate depth of 2 cm within 10 min, 4 cm within 30 min, and 5 cm within 3 h. ...
... It treats wave pumping as a one-dimensional diffusive transport process, even though wave pumping is in fact multi-dimensional and advective. Wave pumping causes complex solute concentration patterns and reaction rates beneath bedforms (Shum 1992;. However, the one-dimensional simplification is frequently used (Higashino 2013;Boano et al. 2014) and is advantageous for reducing mathematical complexity and computation requirements. ...
Microcystin is one of the most common toxins associated with freshwater harmful algal blooms, but little is known about microcystin fate in the aquatic environment. Laboratory wave tank experiments were performed to determine whether exchange of surface water and pore water (benthic exchange) removes and dilutes microcystin-LR (MC-LR) at environmentally relevant concentrations in coastal waters overlying permeable sediments. Over the 100 h experiment, 60% of MC-LR mass was removed due to interaction with sediment (via adsorption and/or biodegradation), while only 20% was removed in an experiment without sediment. The observed fate and transport of MC-LR in sediments was adequately described with a one-dimensional reactive transport model that uses an enhanced diffusion coefficient to represent benthic exchange of solutes. Numerical sensitivity studies showed that MC-LR removal increases with hydraulic conductivity of sediment and wave height and decreases with water depth. For MC-LR concentration at the WHO recreational guideline (20 ppb), sandy sediments can remove the equivalent MC-LR mass in 1 m of surface water under typical nearshore wave conditions within tens of hours. In open water at large depths above a silty bed, removal times are much longer (on the order of weeks). Wave-driven benthic exchange is therefore an important control on MC-LR fate in energetic coastal areas but not in deep or calm settings where sediment–water interactions are greatly reduced. The nearshore fate of algal toxins is important to human health and socioeconomic vitality, since recreational activities and direct human exposures are concentrated along coasts.
... On both the stream and sediment side of the SWI, advection is associated with both steady and unsteady processes. In the water column hydrostatic pressure gradients are induced by streambed geometry (Elliott and Brooks, 1997a), changes in the velocity head (Shum, 1992) (known as Bernoulli pumping"), stream gradients (Bottacin-Busolin and Marion, 2010) and rapid streamwise variation in the free surface (Endreny et al., 2011). ...
... basin (Stewardson et al., 2011) scales. While downwelling and upwelling are significantly influenced by bedforms (Elliott and Brooks, 1997b;Packman et al., 2004), heterogeneity (Cardenas et al., 2004;Aubeneau et al., 2014), and variations in velocity field in the water column (Shum, 1992) over a scale of cm to m, interactions with groundwater occur over a scale of many hundreds of kilometres. ...
... is the depth averaged stream velocity. h m is attributed to the pressure gradients induced by both geometry of bedforms and an increase in the velocity head at the crest of a dune (Shum, 1992). The latter is often referred to as Bernoulli pumping. ...
Mixing between water from free surface flow and subsurface pore-water in the sediment bed is known as hyporheic exchange. At local scales, flushing through porous sediments purifies streamborne water and biogeochemical cycling of oxygen and nutrients supports organisms in the benthic region of the sediment bed. At larger scales, hyporheic exchange provides the connectivity between streams, adjacent aquifers and floodplain networks, providing a critical link for the distribution and retention of nutrients and pollutants throughout the environment. This thesis proposes a framework to upscale advective hyporheic exchange processes using mass transfer coefficients, assuming a thin-film model and is presented in four key contributions: (1) an explicit derivation of the mass transfer coefficient for generic downwelling-upwelling cells based on the geometric addition of regional fluxes with periodic flushing of the hyporheic zone; (2) an examination of steady-state and turbulent mass transfer, demonstrating that steady and unsteady processes can each be represented by a mass transfer coefficient; (3) experiments indicate downwelling and upwelling cells are associated with steady and unsteady mass transfer coefficients; and (4) the analogy between the thin-film model and Ohm’s Law is used to shown that resistors representing steady and unsteady mass transfer are best aligned in parallel, suggesting mass transfer coefficients are additive. This provides a framework to model hyporheic exchange at different spatial and temporal scales, in which no contributing scale is rate limiting. It is anticipated that this will enhance existing predictive hyporheic exchange models, making them more applicable to the study and management of natural water resources at any scale.
... The advection in wave-impacted environments predomi-Miniature thermistor chain for determining surficial sediment porewater advection nantly derives from wave-driven flow over seafloor sand ripples, resulting in lower pressures over sand-ripple crests than over troughs (Webb and Theodor 1968); this pressure difference infuses water into the sediment at troughs and draws water out at the crests. It can be inferred from Shum (1992), , and Hebert et al. (2007) that, in nearshore sands in which surface waves and currents generate clearly defined ripples, the advectively dominated layer extends to a sediment depth equal to ca. 0.5-1 sand-ripple wavelength. There are pronounced opposing gradients in dissolved oxygen and other important biogeochemical constituents at these depths (e.g., Falter and Sansone 2000;Sørensen et al. 2007;Pawlak et al. 2009), and vertical oscillations of these gradients can vary rapidly at a given site in response to changes in the physical environment (Sansone et al. 2008a;Fogaren 2010, Fogaren et al. 2013). ...
... Precht and Huettel used dye to characterize this advective mechanism in the lab (2003) and in the field (2004), and Hebert et al. (2007) measured transport from this mechanism by injecting fluorescent dye in the field at one depth over a range of surface wave conditions. However, when Shum (1992) modeled this mechanism, he showed that transport decreased rapidly with depth within this advectively dominated layer; thus, to validate a porewater transport model of surficial permeable sediments, it is necessary to simultaneously measure transport at several depths while also accurately measuring the location of the SWI, two non-trivial tasks that are the center of interest for the work described here. ...
... Fig. 11 collects all 70 days of data in the Figs. 7d and 8d time series to show that lag between adjacent thermistors increases with depth below the SWI and is negatively correlated with near-bed velocity magnitudes from waves, as expected from porewater advection models (e.g., Webb and Theodor 1968;Shum 1992). Lag data are grouped into top (1 to 3), middle (4 to 5), and bottom (6 to 7) thermistors. ...
A miniature thermistor chain (mTc) was developed to measure the subdiurnal variability of temperature in the upper layers of subtidal coastal permeable (sandy) sediments and across the sediment-water interface (SWI). The mTc has 15 precision thermistors (0.002°C accuracy) attached by narrow tines to a stainless steel backbone that connects to an electronics module, all of which is buried in the top 20 cm of the sediment. Instrument performance was tested by deploying the mTc in nearshore permeable sediment at the Kilo Nalu Observatory, Oahu, Hawaii over an 80-d period. The mTc reached thermal equilibrium with the adjoining sediment within a few days after deployment and then recorded the advective propagation of the sub-daily water-column temperature variation into the sediment. The data produced are consistent with predicted effects of surface waves on advective porewater transport: transport rate increased with wave height and decreased with depth below the SWI, and temperature time lag increased with depth below the SWI. Data from an independent, more deeply buried thermistor are in good agreement with the mTc time-series data, showing attenuated temperature variability and similar (but longer, as expected) thermal time lags. Because thermal variations in surficial sediments is dominated by advection in wavy environments, mTc subdiurnal temperature propagation data can be used to calculate advective transport across the SWI and as deep as 20 cm into the sediment (i.e., over depths where advection dominates over thermal diffusion).
... [2] Physical forcing of porewater circulation occurs through a variety of processes ( Burnett et al. 2003), including the generation of pressure gradients along the sediment-water interface (SWI) and within the sediment. The drivers are typically tides, waves, and currents acting on flat or rough surfaces (Shum 1992;Huettel et al. 1996;Cardenas et al. 2008). These forcing factors occur over the majority of the areas comprising continental shelves (Moore and Shaw 1998;Moore et al. 2002;Reimers et al. 2004). ...
... That is, the sediment is assumed to be a low-pass filter, such that high-frequency oscillations in pressure, occurring above the frequency of waves, are ignored. A steady or steadily varying pressure field, and therefore a steady flow field, is assumed in most previous models (Shum 1992(Shum , 1993). The pioneering study by Riedl et al. (1972) showed that the total flux across the ripple surface increases with frequency of a progressive gravity wave over a flat surface. ...
... The pioneering study by Riedl et al. (1972) showed that the total flux across the ripple surface increases with frequency of a progressive gravity wave over a flat surface. Shum (1992) revisited this problem while explicitly considering ripple geometry. He found an even stronger dependence of the flux on wave frequency that compared to Riedl et al. (1972). ...
Waves induce porewater flow and solute transport through permeable marine sediment. However, past studies have ignored high-frequency pressure pulses, under the assumption that the porewater flow field is adequately represented by a time-averaged one or that the saturated sediment is incompressible. We modeled porewater flow and solute transport inside ripples, forced by instantaneous pressure profiles along the sediment-water interface (SWI) with 0.1-s temporal resolution. The transient pressure profiles were taken from a field data–driven large-eddy simulation model of wave-driven oscillatory flow. The simulations suggest that in elastic, permeable, and saturated sediment, a time-averaged representation of the flow field may be inadequate and that this also leads to shortcomings in how transport is modeled. Bursts in fluid flushing occur when high-frequency pressure fluctuations were considered, leading to larger long-term average fluid fluxes compared to a steady flow field driven by a time-averaged pressure profile. The pressure perturbations along the SWI propagate within a few milliseconds to meter depths within the sediment leading to strongly transient porewater velocity fields. This leads to enhanced dispersion of solutes and larger time-averaged solute fluxes. However, enhanced solute flux across the SWI diminished through time with increasing permeability. The high-frequency transient pressures and sediment elastic properties we considered have been largely ignored and unrecognized. Future observational and modeling studies should consider these processes, especially since they mediate timing-sensitive biogeochemical reactions.
... This circulation may occur by pumping mechanisms, such as wave action and bio-irrigation (e.g. Emerson et al. 1984, Shum 1992, Li et al. 1999. The need to identify and understand this additional source of water is critical in order to accurately assess the hydrologic and nutrient budgets of the lagoon. ...
... The concept of mixing in shallow marine sediments has been the focus of discussion for over two decades. A number of theories have been proposed that may cause this mixing, for example, bioirrigation and bioturbation (Korosec 1979, Emerson et al.1984, wave action and tidal pumping (Shum 1992, 1993, Li et al. 2000, and fluiddensity fluctuations (Rasmussen et al. 2003). Regardless of the process or processes that may cause this mixing, each one may be an important transport mechanism that can carry substantial amount of dissolved solutes from the sediments to the overlying water column. ...
... This may mean that a different regime exists between 110-230 cm depth, one which may still cause mixing, but not as enhanced as the type seen between 0-110 cm depth. This could probably be due to the fact that wave action and tidal pumping do not influence mixing processes at depths greater than 110 cm below the sediment-water interface (Shum 1992). Model solutions for the depth distribution of silicate for enhanced mixing (K = 10 -3 cm 2 s -1 ) with no non-local transport (α = 0), and molecular diffusion (K = 10 -5 cm 2 s -1 ) and non-local transport (α = 4 × 10 -7 s -1 ): December 2000. ...
... The results from these laboratory, nearshore, and small-scale modeling studies imply that realistic regional models of the nitrogen conversions in inner shelf sands require reliable information on in situ advective transport for calculating reaction rates. When hydrodynamic regime and physical sediment characteristics are known, models can provide some of the pore-water transport information (Shum 1992;Cardenas et al. 2008). However, existing models have so far only been tested at small scales (on the scale of sand ripples, i.e., meters) and therefore represent idealized cases. ...
... While these models work well for clays and muds, they do not appropriately represent permeable sediments because they neglect advective flow, which is fundamental to the latter's biogeochemical functioning. Building on pioneering contributions by Shum (1992Shum ( , 1993Shum ( , 1995, novel modeling work on permeable sediments Continued Box 2. Biogeochemical models and permeable sediments.-cont'd by Cardenas et al. (2008), Cardenas and Wilson (2007a,b), and Meysman et al. (2007) showed the importance of turbulence and oscillatory flows for diagenetic modeling of sands. ...
The marine nitrogen cycle is a main driver of ocean productivity and affects global climate. Despite decades of study, we still have an incomplete understanding of the role of the marine nitrogen cycle in the Earth system. While marine sediments play a major role in nitrogen cycling in the ocean, magnitudes and mechanisms are largely unconstrained. Recent research suggests that permeable sandy sediments on the highly energetic and dynamic continental shelf are key components of the marine nitrogen cycle, but data to quantify their contribution are lacking. Here, we use insights from measurements and modeling studies to substantiate the hypothesis that shelf sediments are an overlooked driver of the marine nitrogen cycle. Specifically, we propose that permeable shelf sediments are sites for intense nitrogen conversions and suggest a three‐pronged approach to address unresolved controversies.
... However, such sophisticated models have the potential to make quantitative predictions of sediment transport and erosion/accretion around partly buried objects in the bottom, an important problem in scour around and burial of pipelines (e.g., Brørs, 1999;Liang and Cheng, 2005), cobblestones (e.g., Voropayev et al., 2003), short cylinders (e.g., Voropayev et al., 2007;Testik et al., 2005Testik et al., , 2006Cataño-Lopera and García, 2006;Bower et al., 2007;Hatton et al., 2007;Trembanis et al., 2007), and bottom sea mines (e.g., Inman and Jenkins, 2002;Guyonic et al., 2007). Moreover, most bed morphology models proposed to date have been limited to 2-D problems (e.g., Jensen and Fredsøe, 2001;Soulis, 2002), and only a few models have recently been proposed which attempt to simulate 3-D scour (e.g., Smith and Foster, 2005). Once fully validated, the coupled FNPF-3-D-LES model used here could be applied on a larger scale to these problems, while accounting for fully nonlinear and shoaling effects in incident wave fields, as opposed to only considering uniform oscillatory flows or linear waves, as in work published to date. ...
... In many of the early theoretical solutions or models of flow over ripples (e.g., Benjamin, 1959;Lyne, 1971;Longuet-Higgins, 1981;Tanaka, 1986), the ripple geometry was transformed into a flat bed through a conformal mapping. In such an approach, a complex series expansion such as used by Shum (1992) can provide a reasonably accurate representation of any measured ripple geometry: ...
Wave-induced boundary layer (BL) flows over sandy rippled bottoms
are studied using a numerical model that applies a one-way coupling
of a "far-field" inviscid flow model to a "near-field" large
eddy simulation (LES) Navier–Stokes (NS) model. The incident
inviscid velocity and pressure fields force the LES, in which
near-field, wave-induced, turbulent bottom BL flows are simulated.
A sediment suspension and transport model is embedded within the
coupled flow model. The numerical implementation of the various
models has been reported elsewhere, where we showed that the LES was
able to accurately simulate both mean flow and turbulent statistics
for oscillatory BL flows over a flat, rough bed. Here we show that
the model accurately predicts the mean velocity fields and suspended
sediment concentration for oscillatory flows over full-scale vortex
ripples. Tests show that surface roughness has a significant effect
on the results. Beyond increasing our insight into wave-induced
oscillatory bottom BL physics, sophisticated coupled models of
sediment transport such as that presented have the potential to make
quantitative predictions of sediment transport and erosion/accretion
around partly buried objects in the bottom, which is important for a
vast array of bottom deployed instrumentation and other practical
ocean engineering problems.
... Downstream of the lee face, a zone of low pressure forms and creates a zone of upwelling. 142 If the current oscillates due to wave action, the zone of low pressure and upwelling is located at the ripple crest 143 (Figure 6(a)). The depths of surface water-pore water exchange are typically on the order of the bedform wavelength. ...
... Exchange rates increase with current or wave height, bedform steepness, and permeability of the sediment. 142,143 Residence times can range from seconds to weeks. 144 If currents are sufficient to mobilize sediment, bedform migration rapidly exchanges surface water and pore water. ...
Near coasts, surface water–groundwater interactions control many biogeochemical processes associated with the critical zone, which extends from shallow aquifer to vegetative canopy. For example, submarine groundwater discharge delivers a significant fraction of weathering products such as silica and calcium to the world's oceans. Owing to changing fertilizer and land use practices, submarine groundwater discharge is also responsible for high nitrogen loads that drive eutrophication in marine waters. Submarine groundwater discharge is generally unmonitored due to its heterogeneous and diffuse spatial patterns and complex temporal dynamics. Here, we review the physical processes that drive submarine groundwater discharge at various spatial and temporal scales and highlight examples of interdependent critical zone processes. Like the inland critical zone, the coastal critical zone is undergoing rapid change in the Anthropocene. Disturbances include warming air and sea temperatures, sea‐level rise, increasing storm severity, increasing nutrient and contaminant inputs, and ocean acidification. In a changing world, it is more important than ever to understand complex feedbacks between dynamic surface water‐groundwater interaction, rocks, and life through long‐term monitoring efforts that extend beyond inland rivers to coastal groundwater. WIREs Water 2016, 3:706–726. doi: 10.1002/wat2.1157
This article is categorized under: Water and Life > Nature of Freshwater Ecosystems
Science of Water > Water and Environmental Change
Science of Water > Water Quality
... In the context of permeable sediments, a variety of interesting phenomena exists in the field of marine microbiology which can benefit from the knowledge available in porous media. Examples include but are not limited to topography effects in nutrient transport into deeper sediment layers (Huettel and Gust, 1992b), enhanced bottom transport by gravity waves (Shum, 1992a), reactive solute transport below rippled beds (Shum, 1992b), and tide-driven deep pore-water flow in intertidal sands flats (Røy and Lee, 2008). ...
... The oxygen concentration in the middle of this DBL oscillated in time with a magnitude of more that 10% of its mean value and at the frequency of the prevalent surface gravity wave. Gundersen and Jørgensen (1990) attributed the oscillations to the 'numerous eddies which approach the sediment surface from the bulk of the following sea water and hit the viscous and diffusive sublayers', but details of the physical mechanism involved had yet not been explored However, mathematical models for quantifying fluxes across permeable seabeds in the presence of oscillatory flows are, in comparison, not numerous, and limited to the studies of Shum (1992aShum ( ,b, 1995; Hara et al. (1992). Although these models provide a good insight into solute distribution below the sediment-water interface, all of them are based on assuming linearized potential flows, and hence, of limited applications. ...
... Advective flow of porewater in marine sediments can be caused by a number of mechanisms [40], including (1) deeply sourced buoyancy causing the upward flow observed at hydrothermal vents or cold seeps (e.g. [4,6]), (2) flow over topographic features, such as sand ripples [41] or (3) the activity of benthic macrofauna [50]. Termed bioirrigation, biologically induced flow can be a major influence on solute exchange between sediment and overlying water [29], organic matter cycling or sediment cracking [49]. ...
Flow fields are determined from image sequences obtained in an experiment in which benthic macrofauna, Arenicola marina , causes water flow and the images depict the distribution of a tracer that is carried with the flow. The experimental setup is such that flow is largely two-dimensional, with a localised region where the Arenicola resides, from which flow originates. Here, we propose a novel parametric framework that quantifies such flow that is dominant along the image plane. We adopt a Bayesian framework so that we can impart certain physical constraints on parameters into the estimation process via prior distribution. The primary aim is to approximate the mean of the posterior distribution to present the parameter estimate via Markov Chain Monte Carlo. We demonstrate that the results obtained from the proposed method provide more realistic flows (in terms of divergence magnitude) than those computed from classical approaches such as the multi-resolution Horn–Schunk method. This highlights the usefulness of our approach if motion is largely constrained to the image plane with localised fluid sources.
... It has been proven to play a critical role in biogeochemical processes in marine benthic sediments, including carbon mineralization, nutrient recycling, and recycled primary production (Janssen et al., 2005a;Geng et al., 2021b). Tracer studies illustrated that ripple-flow interactions generate groundwater recirculation cells in marine sediments with flows infiltrating in the ripple troughs and exfiltrating from crests ( Fig. 1B) (Webb and Theodor, 1968;Shum, 1992). Such seawater-groundwater recirculation brings organic matter and oxygen into the sediment, creates horizontal concentration gradients that can be as strong as the vertical gradients, and provides an important mechanism for enhancing mineralization of organic matter in marine sediments (Huettel et al., 1998). ...
Oil spills have been recognized as among the worst kinds of environmental disasters, causing severe coastal ecological and economic damages. Although benthic flow and solute fluxes are known to have strong impacts on fate and transport of oil deposited within marine sediments, their endogenous mechanisms still remain to be uncovered. In this paper, simulations of flow and solute transport processes along with hydrocarbon biodegradation were conducted in a cylindrical benthic chamber system to investigate influences of benthic hydrodynamics on oil biodegradation in permeable marine sediments. Results show that ripple-flow interactions create subsurface recirculation cells whereby seawater infiltrates into the benthic sediments at ripple troughs while groundwater discharges near the crests. It results in a spatially varied oil biodegradation rate in marine sediments. Significant oil biodegradation occurs near sediment ripple troughs due to direct oxygen recharge, while biodegradation of oil deposited uphill becomes slow due to limited oxygen replenishment. Oil biodegradation decreases subsurface oxygen content, and consequently impedes discharge of oxygen from benthic sediments. Our results reveal a dynamic interaction between oil biodegradation and benthic flow and solute transport processes, which has strong implications for predicting oil persistence and biodegradation within marine sediments and its associated impacts on benthic biogeochemical processes.
... The total flux exchange across the watersediment interface has been identified to be higher across a rippled interface than across a flat bed. The water exchange increases with increasing ripple slope and the strength of the ocean current (Shum, 1992;Shum, 1993). Tracer studies suggest that ripple-flow interactions generate groundwater circulation cells in marine sediments with flows infiltrating in the ripple troughs and exfiltrating from crests (Webb and Theodor, 1968) (Fig. 6). ...
Coastal beach aquifers are biogeochemically active systems that mediate chemical and material fluxes across the land-sea interface. This paper provides a review of major physical stressors and geologic features that influence flow and solute fate and transport in coastal beach aquifers. We outline current understanding of the interactions between these factors and their associated impacts on water and geochemical fluxes within and across these aquifers. The physical processes that control flow, transport, and the formation and distribution of reactive zones in beach aquifers (e.g., tides, waves, density gradients, precipitation, episodic ocean events, and evaporation) operate across overlapping temporal and spatial scales, and present challenges for measuring and modeling physical flow and biogeochemical processes in coastal groundwater systems. Geologic heterogeneity introduces further complexity by modifying flowpaths, mixing patterns, and rates of biotransformation. Interactions between these physical stressors and geological controls are likely to evolve with changes in sea level, climate variability, human settlement, coastal erosion, and other natural and anthropogenic stresses, providing avenues for scientific exploration into the future role of beach aquifers as chemical mediators between the land and ocean.
... In general, a gradual decrease in the influence of advective transport is expected as a function of sediment depth (Shum 1992;Santos et al. 2012;Drupp et al. 2016), yielding a lower spatial and temporal variability at greater depths. The temporal variability of carbonate parameters in Mangrove Bay largely followed this pattern, with a deviation at 8 cm depth, where variability was higher than at neighboring sediment depths. ...
Seagrass systems are integral components of both local and global carbon cycles and can substantially modify seawater biogeochemistry, which has ecological ramifications. However, the influence of seagrass on porewater biogeochemistry has not been fully described, and the exact role of this marine macrophyte and associated microbial communities in the modification of porewater chemistry remains equivocal. In the present study, carbonate chemistry in the water column and porewater was investigated over diel timescales in contrasting, tidally influenced seagrass systems in Southern California and Bermuda, including vegetated (Zostera marina) and unvegetated biomes (0–16 cm) in Mission Bay, San Diego, USA and a vegetated system (Thallasia testudinium) in Mangrove Bay, Ferry Reach, Bermuda. In Mission Bay, dissolved inorganic carbon (DIC) and total alkalinity (TA) exhibited strong increasing gradients with sediment depth. Vertical porewater profiles differed between the sites, with almost twice as high concentrations of DIC and TA observed in the vegetated compared to the unvegetated sediments. In Mangrove Bay, both the range and vertical profiles of porewater carbonate parameters such as DIC and TA were much lower and, in contrast to Mission Bay where no distinct temporal signal was observed, biogeochemical parameters followed the semi-diurnal tidal signal in the water column. The observed differences between the study sites most likely reflect a differential influence of biological (biomass, detritus and infauna) and physical processes (e.g., sediment permeability, residence time and mixing) on porewater carbonate chemistry in the different settings.
... The total flux exchange across the watersediment interface has been identified to be higher across a rippled interface than across a flat bed. The water exchange increases with increasing ripple slope and the strength of the ocean current (Shum, 1992;Shum, 1993). Tracer studies suggest that ripple-flow interactions generate groundwater circulation cells in marine sediments with flows infiltrating in the ripple troughs and exfiltrating from crests (Webb and Theodor, 1968) (Fig. 6). ...
Extreme storms can cause rapid morphological changes that pose high risk to society (Sallenger 2000). Semiempirical and process-based models often are used to simulate storm-induced coastal processes (Roelvink et al. 2009, Palmsten & Holman 2012, Stockdon et al. 2014, Overbeck et al. 2017). However, there are few observations of surfzone waves and currents during extreme storms. Therefore, parameterizations often are calibrated by minimizing model-data errors for pre- to post-storm bathymetric and topographic changes, and the accuracy of the simulated processes during the storm is unknown. Here, surf, swash, and dune observations collected near Duck, NC, USA, will be used to investigate wave processes and dune erosion during the passage of recent (2015-2017) Hurricanes.
... For bare, permeable, sandy sediment substrates, several studies have shown high rates of water exchange between the water column above the substrate and the pore water within it, which may cause biological and chemical modifications of the pore water via advection of suspended or dissolved matter (Huettel and Gust, 1992;Huettel and Rusch, 2000). Such fluxes are generally caused by pressure gradients, which may be due to wave propagation causing pressure oscillations at the sediment surface (Webb and Theodor, 1972;Shum, 1992;Precht and Huettel, 2004) or to currents' interactions with seabed topography (Huettel and Webster, 2001). For example, a local vertical pressure gradient of 100 Pa m 21 , caused by flow encountering a small rise in the bed, is enough to force water several centimeters into the sediment and draw pore water from more than 0.1 m beneath the sediment surface into the water column (Huettel et al. 1998). ...
Seagrasses need dissolved nutrients to maintain their productivity through uptake processes, from substrate pore-water via their roots and/or from the water column via their leaves. Here, we present the first study of exchanges of dissolved nutrients between pore water and the water column in the vicinity of seagrass canopies. We address the following research questions, using a laboratory flume experiment: (1) How does solute exchange between the water column and substrate pore water vary spatially within seagrass patches? (2) How does seagrass leaf length affect this solute exchange? (3) How does the measured rate of solute exchange compare with seagrasses' rates of uptake of dissolved nutrients? Our results indicate that solute intrusion from the water column into the substrate pore water is highest in the area around seagrass patches' leading edges, where flow deceleration is strongest, and decreases approximately linearly with downstream distance into the patch. The decrease in measured flow speed in the canopy fits well the predictions of previously reported models of arrays of rigid obstacles. The length of the region in which the concentration of solute that has infiltrated into the substrate at the upstream end of the seagrass patches is similar to the length scale predicted from model estimates of infiltration rate (based on the substrate permeability) and the length of time over 24-h runs. We conclude that the mechanism we identify only pertains near canopy edges, and therefore that other mechanisms must govern nutrient supply in the interior of seagrass meadows.
... The enhanced dispersion formulation has been useful for characterizing porewater solute properties and reaction rates in seafloor (Berg et al. 1998) and hyporheic (Bhaskar et al. 2012) settings. The model explicitly assumes only that the strength of the external forcing declines exponentially with depth (e.g., Shum 1992;Jahnke et al. 2005;Fram et al. 2014). As described below, application of the model to a sediment temperature time series indicates that the intensity and timing of mixing events on the mid-shelf of Georgia USA are related to both local tidal boundary layer processes and thermal gradients across the interface generated by shelf-scale upwelling and downwelling episodes. ...
Fluid exchange across the sediment–water interface in a sandy open continental shelf setting was studied using heat as a tracer. Summertime tidal oscillation of cross-shelf thermal fronts on the South Atlantic Bight provided a sufficient signal at the sediment–water interface to trace the advective and conductive transport of heat into and out of the seabed, indicating rapid flushing of ocean water through the upper 10–40 cm of the sandy seafloor. A newly developed transport model was applied to the in situ temperature data set to estimate the extent to which heat was transported by advection rather than conduction. Heat transported by shallow 3-D porewater flow processes was accounted for in the model by using a dispersion term, the depth and intensity of which reflected the depth and intensity of shallow flushing. Similar to the results of past studies in shallower and more energetic nearshore settings, transport of heat was greater when higher near-bed velocities and shear stresses occurred over a rippled bed. However, boundary layer processes by themselves were insufficient to promote non-conductive heat transport. Advective heat transport only occurred when both larger boundary layer stresses and thermal instabilities within the porespace were present. The latter process is dependent on shelf-scale heating and cooling of bottom water associated with upwelling events that are not coupled to local-scale boundary layer processes.
... For more complex geometries, such as boundaries of variable ("wavy") elevation (e.g., a field furrowed by plowing, or a seafloor rippled by wave action) in which flow occurs in the fluid medium along the interface, Bernoulli's principle dictates that differences in pressure will exist between high and low points on the boundary (Vogel, 1994). Assuming that the solid medium is permeable, the result will be pressure-induced advection in the porous medium (Shum, 1992(Shum, , 1993Boudreau, 1997) (Fig. 3.24). This "ventilation" may be beneficial to resident organisms in the sediment or soil (see next section). ...
In this chapter we consider several aspects of passive diffusion in the environment. In this book, passive diffusion is defined to be the diffusion of chiefly abiotic objects that are not capable of performing random motion without the help of environmental turbulence. Likewise, active diffusion is defined to be the diffusion of objects, chiefly animals, that perform motion by themselves.
... We found that DOU values were always smaller than TOU values for all stations throughout the North Sea. In general, the total oxygen uptake can be decomposed as TOU = DOU + BMU + AMU (Glud, 2008), where BMU represents benthos mediated O 2 uptake resulting from burrow irrigation and the respiration of infauna, and AMU represents the advection mediated O 2 uptake by purely physical transport processes, such as pore-water advection induced by currents over bottom topography (Huettel and Rusch, 2000;Meysman et al., 2007) and oscillatory pore-water mixing induced by waves (Shum, 1992). ...
It has been previously proposed that alkalinity release
from sediments can play an important role in the carbonate
dynamics on continental shelves, lowering the pCO2
of seawater and hence increasing the CO2 uptake from the
atmosphere. To test this hypothesis, sedimentary alkalinity
generation was quantified within cohesive and permeable
sediments across the North Sea during two cruises in
September 2011 (basin-wide) and June 2012 (Dutch coastal
zone). Benthic fluxes of oxygen (O2), alkalinity (AT) and dissolved
inorganic carbon (DIC) were determined using shipboard
closed sediment incubations. Our results show that
sediments can form an important source of alkalinity for the
overlying water, particularly in the shallow southern North
Sea, where high AT and DIC fluxes were recorded in nearshore
sediments of the Belgian, Dutch and German coastal
zone. In contrast, fluxes of AT and DIC are substantially
lower in the deeper, seasonally stratified, northern part of
the North Sea. Based on the data collected, we performed
a model analysis to constrain the main pathways of alkalinity
generation in the sediment, and to quantify how sedimentary
alkalinity drives atmospheric CO2 uptake in the southern
North Sea. Overall, our results show that sedimentary alkalinity
generation should be regarded as a key component in
the CO2 dynamics of shallow coastal systems.
... Mixing occurs above and below discharging fresh groundwater (Fig. 1). Shallow mixing near the sedimentwater interface is driven by wave pumping (Shum 1992), current-bedform interactions (Thibodeaux and Boyle 1987), density-driven convection , bioirrigation and bioturbation (Cable et al. 2006), and sediment resuspension. Deep mixing is driven by density gradients (Cooper 1959) and influenced by tides and inland water table fluctuations (Michael et al. 2005). ...
Shallow stratigraphic features, such as infilled paleovalleys, modify fresh groundwater discharge to coastal waters and fluxes of saltwater and nutrients across the sediment–water interface. We quantify the spatial distribution of shallow surface water–groundwater exchange and nitrogen fluxes near a paleovalley in Indian River Bay, Delaware, using a hand resistivity probe, conventional seepage meters, and pore-water samples. In the interfluve (region outside the paleovalley) most nitrate-rich fresh groundwater discharges rapidly near the coast with little mixing of saline pore water, and nitrogen transport is largely conservative. In the peat-filled paleovalley, fresh groundwater discharge is negligible, and saltwater exchange is deep (,1 m). Long pore-water residence times and abundant sulfate and organic matter promote sulfate reduction and ammonium production in shallow sediment. Reducing, iron-rich fresh groundwater beneath paleovalley peat discharges diffusely around paleovalley margins offshore. In this zone of diffuse fresh groundwater discharge, saltwater exchange and dispersion are enhanced, ammonium is produced in shallow sediments, and fluxes of ammonium to surface water are large. By modifying patterns of groundwater discharge and the nature of saltwater exchange in shallow sediments, paleovalleys and other stratigraphic features influence the geochemistry of discharging groundwater. Redox reactions near the sediment–water interface affect rates and patterns of geochemical fluxes to coastal surface waters. For example, at this site, more than 99% of the groundwater-borne nitrate flux to the Delaware Inland Bays occurs within the interfluve portion of the coastline, and more than 50% of the ammonium flux occurs at the paleovalley margin.
... Driving forces for pore water mixing in the shallow (< ~70 cmbsf) sediments may include a combination of bioirrigation, wave and tidal pumping, and density-driven convection (e.g. Emerson et al., 1984;Shum, 1992). Wave pumping and convection are likely to be minor due to a small tidal range, limited fetch within the lagoon, and lack of strong density contrasts between lagoon and pore waters (Martin et al., 2006). ...
... This is in agreement with Precht et al. (2004), who demonstrated that advective porewater exchange can be strongly correlated with fine scale sediment topography. Interaction of orbital and tidal boundary layer flows with topography generates pressure gradients that drive a net flux of water into the sediment within troughs and out of the sediment beneath crests (Webb and Theodor 1972;Shum 1992Shum , 1993Huettel and Webster 2001;Precht and Huettel 2003;Precht et al 2004). To further understand the nature of the system, each data parameter had its long-term trend removed through linear detrending then another multilinear regression was performed. ...
An underwater membrane introduction mass spectrometer was deployed in permeable sandy sediment on the Georgia continental shelf (depth = 27 m) to measure in situ dissolved gas concentrations in sediment porewaters. Over a 54-h period, 30 profiles (up to 18 cm deep) were sampled using an automated sediment probe coupled with an underwater positive displacement syringe pump. Porewater was analyzed with a flow-through membrane assembly at constant sample flow rate (0.35 mL/min) and membrane temperature (45°C). Calibration was performed on-site using ambient seawater equilibrated with gas standards. Measurements of methane, nitrogen, argon, oxygen, and carbon dioxide concentrations were used to produce depth-time contours and demonstrate the dynamics of dissolved gases in the porewater. Profiles indicated a well-oxygenated surface layer (1 to 2 cm depth) and anoxia below -3 to -5 cm. Elevated concentrations of methane below the oxycline reveal active methanogenesis in shelf sands despite low (0.05%) organic carbon content. Chemocline depth and sediment ripple height were correlated, suggesting that the porewater environment is controlled by advection-driven interactions between boundary-layer flow and bottom topography. By coupling in situ concentration profiles to independent estimates of sediment-water exchange, it was estimated that maximal oxygen consumption at this site occurs > 2 cm below the interface. Oxygen consumption at this site is estimated as 2.3 mmol m-2 d-1 based on combined dissolved profiles and advection estimates. Raw data and data analysis scripts (Matlab) are available electronically in a Web Appendix. © 2012, by the American Society of Limnology and Oceanography, Inc.
... Other important mechanisms causing hyporheic flow that are less commonly studied in streams and rivers include turbulence, wave pumping, and biological processes that transport water and materials across the sediment interface. For example, currents and wave oscillations cause flow through permeable sediments which may be the dominant form of hyporheic exchange in shallow areas of lakes, estuaries, and nearshore ocean waters [Riedl et al., 1972;Harrison et al., 1983;Webster and Taylor, 1992;Shum, 1992Shum, , 1993Habel et al., 2002;Habel and Bagtzoglou, 2005;King et al., 2009]. Tides also drive periodic surface-subsurface exchange along the intertidal banks of coastal rivers [Harvey et al., 1987]. ...
... Other important mechanisms causing hyporheic flow that are less commonly studied in streams and rivers include turbulence, wave pumping, and biological processes that transport water and materials across the sediment interface. For example, currents and wave oscillations cause flow through permeable sediments which may be the dominant form of hyporheic exchange in shallow areas of lakes, estuaries, and nearshore ocean waters [Riedl et al., 1972;Harrison et al., 1983;Webster and Taylor, 1992;Shum, 1992Shum, , 1993Habel et al., 2002;Habel and Bagtzoglou, 2005;King et al., 2009]. Tides also drive periodic surface-subsurface exchange along the intertidal banks of coastal rivers [Harvey et al., 1987]. ...
... Variables that may influence circulation of water into and out of sediments include hydraulic gradient, sediment permeability, burrow mound height, ripple length and amplitude, and the wavelength, height, and period of water waves. Shum (1992Shum ( , 1993) demonstrated that water movement over a seabed can provide significant penetration of water into sediments if bedforms, such as ripples, are present. Recent work demonstrates that penetration of water into the sediments results from development of a pressure gradient into the sediment as water flows across the top of the bedforms (Huettel and Gust 1992;Huettel et al. 1996;Huettel and Webster 2001). ...
Seepage meters, like most benthic flux chamber techniques, come with inherent concerns about how their presence may alter the environment and flow regimen of the benthic boundary layer and underlying sediments. Flow due to wave and current movement across topographic features induces a downward and upward flow field within the sediments surrounding the feature. We found this Bernoulli-induced flow is a real, but maybe minor, component of measured advection using seepage meters. This study was conducted in a Florida coastal lagoon to test the physical forcing mechanisms that may influence seepage measurements from sediments. Calculated Bernoulli seepage was within the measured background (∼1 to 2 cm day-1) expected from seepage meters when a plastic barrier beneath the device is used to inhibit natural seepage contributions. Nearby seepage measurements made with Lee-type seepage meters placed directly in the sediments ranged from 1 to 12 cm day -1. Thus, when seepage flow is very slow from sediments, Bernoulli-induced seepage may obscure the measurement. However, this study demonstrates that seepage in the Indian River Lagoon must be driven by forces other than Bernoulli-induced (pumped) flow. Suggestions for these forcing mechanisms highlight the uncertainty of the water source(s) in seepage measurements. In these Florida lagoon sediments, bioirrigation and terrestrial groundwater inputs are the most likely drivers, depending on distance from shore, benthic community composition, and continental recharge. Seepage measurements can be an excellent measure of advection in shallow-water marine sediments if Bernoulli-induced seepage is taken into account either experimentally or calculated based on local hydrographic and meteorological data. © 2006, by the American Society of Limnology and Oceanography, Inc.
... Mixing occurs above and below discharging fresh groundwater ( Fig. 1). Shallow mixing near the sedimentwater interface is driven by wave pumping (Shum 1992), current-bedform interactions (Thibodeaux and Boyle 1987), density-driven convection ( Konikow et al. 2013), bioirrigation and bioturbation (Cable et al. 2006), and sediment resuspension. Deep mixing is driven by density gradients (Cooper 1959) and influenced by tides and inland water table fluctuations ( Michael et al. 2005). ...
Shallow stratigraphic features, such as infilled paleovalleys, modify fresh groundwater discharge to coastal waters and fluxes of saltwater and nutrients across the sediment—water interface. We quantify the spatial distribution of shallow surface water—groundwater exchange and nitrogen fluxes near a paleovalley in Indian River Bay, Delaware, using a hand resistivity probe, conventional seepage meters, and pore-water samples. In the interfluve (region outside the paleovalley) most nitrate-rich fresh groundwater discharges rapidly near the coast with little mixing of saline pore water, and nitrogen transport is largely conservative. In the peat-filled paleovalley, fresh groundwater discharge is negligible, and saltwater exchange is deep (∼1 m). Long pore-water residence times and abundant sulfate and organic matter promote sulfate reduction and ammonium production in shallow sediment. Reducing, iron-rich fresh groundwater beneath paleovalley peat discharges diffusely around paleovalley margins offshore. In this zone of diffuse fresh groundwater discharge, saltwater exchange and dispersion are enhanced, ammonium is produced in shallow sediments, and fluxes of ammonium to surface water are large. By modifying patterns of groundwater discharge and the nature of saltwater exchange in shallow sediments, paleovalleys and other stratigraphic features influence the geochemistry of discharging groundwater. Redox reactions near the sediment—water interface affect rates and patterns of geochemical fluxes to coastal surface waters. For example, at this site, more than 99% of the groundwater-borne nitrate flux to the Delaware Inland Bays occurs within the interfluve portion of the coastline, and more than 50% of the ammonium flux occurs at the paleovalley margin.
... Other important mechanisms causing hyporheic flow that are less commonly studied in streams and rivers include turbulence, wave pumping, and biological processes that transport water and materials across the sediment interface. For example, currents and wave oscillations cause flow through permeable sediments which may be the dominant form of hyporheic exchange in shallow areas of lakes, estuaries, and nearshore ocean waters [Riedl et al., 1972;Harrison et al., 1983;Webster and Taylor, 1992;Shum, 1992Shum, , 1993Habel et al., 2002;Habel and Bagtzoglou, 2005;King et al., 2009]. Tides also drive periodic surface-subsurface exchange along the intertidal banks of coastal rivers [Harvey et al., 1987]. ...
Fifty years of hyporheic zone research have shown the important role played by the hyporheic zone as an interface between groundwater and surface waters. However, it is only in the last two decades that what began as an empirical science has become a mechanistic science devoted to modeling studies of the complex fluid dynamical and biogeochemical mechanisms occurring in the hyporheic zone. These efforts have led to the picture of surface-subsurface water interactions as regulators of the form and function of fluvial ecosystems. Rather than being isolated systems, surface water bodies continuously interact with the subsurface. Exploration of hyporheic zone processes has led to a new appreciation of their wide reaching consequences for water quality and stream ecology. Modern research aims toward a unified approach, in which processes occurring in the hyporheic zone are key elements for the appreciation, management, and restoration of the whole river environment. In this unifying context, this review summarizes results from modeling studies and field observations about flow and transport processes in the hyporheic zone and describes the theories proposed in hydrology and fluid dynamics developed to quantitatively model and predict the hyporheic transport of water, heat, and dissolved and suspended compounds from sediment grain scale up to the watershed scale. The implications of these processes for stream biogeochemistry and ecology are also discussed.
... In many of the early theoretical solutions or models of flow over ripples (e.g., Benjamin, 1959;Lyne, 1971;Longuet-Higgins, 1981;Tanaka, 1986), the ripple geometry was trans-20 formed into a flat bed through a conformal mapping. In such an approach, a complex series expansion such as used by Shum (1992) can provide a reasonably accurate representation of any measured ripple geometry: 25 where z = x 1 + i x 3 , and ζ = ξ + i χ . The series coefficients (α n = a n + i b n ) needed to reproduce the measured ripple shape (Fig. 3) were computed by van der Werf et al. ...
Wave-induced Boundary Layer (BL) flows over sandy rippled bottoms are studied using a numerical model that applies a one-way coupling of a "far-field" inviscid flow model to a "near-field" Large Eddy Simulation (LES) Navier-Stokes (NS) model. The incident inviscid velocity and pressure fields force the LES, in which near-field, wave-induced, turbulent bottom BL flows are simulated. A sediment suspension and transport model is embedded within the coupled flow model. The numerical implementation of the various models has been reported elsewhere, where we showed that the LES was able to accurately simulate both mean flow and turbulent statistics for oscillatory BL flows over a flat, rough bed. Here, we show that the model accurately predicts the mean velocity fields and suspended sediment concentration for oscillatory flows over full-scale vortex ripples. Tests show that surface roughness has a significant effect on the results. Beyond increasing our insight into wave-induced oscillatory bottom BL physics, models of sediment transport as sophisticated as the present coupled model have the potential to make quantitative predictions of sediment transport and erosion/accretion around partly buried objects in the bottom, which is important for a vast array of bottom deployed instrumentation and other practical ocean engineering problems.
... Enhancement of transport by tide-induced advection has been detected in some North Sea sediments by [5] (purely diffusive transport was measured in other areas). The ripple-induced enhancement that has been measured in the laboratory by [6] and analysed by [7,8]. It probably pertains in some locations and is clearly related to the detailed investigations carried out by [9][10][11] and [12,13] on the solute flux between a stream and migrating sediment bedforms. ...
The issue of the transport of dissolved nutrients and contaminants between the sediment in the bottom of a lake or reservoir and the body of water above it is an important one for many reasons. In particular the biological and chemical condition of the body of water is intricately linked to these mass transport processes. As the review by Boudreau (Rev Geophys 38(3):389–416, 2000) clearly demonstrates those transport processes are very complex involving mechanisms as diverse as the wave-induced flux between the sediment and the overlying water and the effect of burrowing animals on the transport within the sediment as well as basic diffusion mechanisms. The present paper focuses on one facet of these transport processes; we re-examine the balance of diffusion and wave-induced advection and demonstrate that the wave-induced flux of a solute from submerged sediment is not necessarily purely diffusive as suggested by Harrison et al. (J Geophys Res 88:7617–7622, 1983) but can be dominated by a mean or time-averaged flux induced by the advective fluid motion into and out of the sediment caused by the fluctuating pressure waves associated with wave motion. Indeed along the subtidal shoreline where the fluctuating bottom pressures are greatest, wave-induced advection will dominate the mean, time-averaged transport of solute into or out of the sediment as suggested in the work of Riedl et al. (Mar Biol 13:210–221, 1972). However, the present calculations also indicate that this advective flux decreases rapidly with increasing depth so that further away from the shoreline the advective flux becomes negligible relative to the diffusive flux and therefore the latter dominates in deeper water.
... The processes that drive the large observed saline exchange flux density gradients (Cooper et al., 1964;Kohout, 1960;Smith, 2004), waves (King et al., 2009;Shum, 1992), tides (Taniguchi, 2002), density-topography interactions (Konikow et al., 2013), currents over bedforms (Precht and Huettel, 2003;Cardenas and Wilson, 2006) and bioirrigation (Martin et al., 2007). The sum of these smallerscale processes may produce enough saline SGD to explain our measurements, but is expected to be zero on the temporal (tide, wave) and spatial (wavelength or bedform width) scales of exchange; flow of saline baywater into sediments should balance outflow. ...
Submarine groundwater discharge (SGD) can be an important pathway for transport of nutrients and contaminants to estuaries. A better understanding of the geologic and hydrologic controls on these fluxes is critical for their estimation and management. We examined geologic features, porewater salinity, and SGD rates and patterns at an estuarine study site. Seismic data showed the existence of paleovalleys infilled with estuarine mud and peat that extend hundreds of meters offshore. A low-salinity groundwater plume beneath this low-permeability fill was mapped with continuous resistivity profiling. Extensive direct SGD measurements with seepage meters (n = 551) showed fresh groundwater discharge patterns that correlated well with shallow porewater salinity and the hydrogeophysical framework. Small-scale variability in fresh and saline discharge indicates influence of meter-scale geologic heterogeneity, while site-scale discharge patterns are evidence of the influence of the paleovalley feature. Beneath the paleovalley fill, fresh groundwater flows offshore and mixes with saltwater before discharging along paleovalley flanks. On the adjacent drowned interfluve where low-permeability fill is absent, fresh groundwater discharge is focused at the shoreline. Shallow saltwater exchange was greatest across sandy sediments and where fresh SGD was low. The geologic control of groundwater flowpaths and discharge salinity demonstrated in this work are likely to affect geochemical reactions and the chemical loads delivered by SGD to coastal surface waters. Because similar processes are likely to exist in other estuaries where drowned paleovalleys commonly cross modern shorelines, the existence and implications of complex hydrogeology are important considerations for studies of groundwater fluxes and related management decisions.
... [3] Several mechanisms have been proposed to drive the circulation of seawater into and out of the sea bed [Huettel and Webster, 2001; Santos et al., 2012] and explain the very large proportion of saline SGD relative to fresh SGD that is commonly observed [e.g., Michael et al., 2003; Martin et al., 2007; Santos et al., 2009] . These mechanisms include dispersion-induced density gradients (and mixing) along the freshwater-saltwater interface [Cooper, 1959], seasonal changes in the upland water-table elevation [Michael et al., 2005], tide-and wave-induced hydraulic gradients in the nearshore zone [Robinson et al., 2007; Xin et al., 2011], tidal pumping [Taniguchi, 2002; Li et al., 2009], wave-induced pressure variations [Riedl et al., 1972; Shum, 1992; Shum and Sundby, 1996; King et al., 2009; Cardenas and Jiang, 2011], bedform migration [Elliott and Brooks, 1997; Pilditch and Miller, 2006], and current-induced pressure variations as a result of flow over bedforms (a Bernoulli effect) [Thibodeaux and Boyle, 1987; Elliott and Brooks, 1997; Cardenas and Wilson, 2007]. But it is not clear that these mechanisms are sufficient to explain what some consider to be anomalously large saline SGD relative to the fresh SGD derived directly from hydraulic gradients on land. ...
Measurements of submarine groundwater discharge (SGD) in coastal areas
often show that the saltwater discharge component is substantially
greater than the freshwater discharge. Several mechanisms have been
proposed to explain these high saltwater discharge values, including
saltwater circulation driven by wave and tidal pumping, wave and tidal
setup in intertidal areas, currents over bedforms, and density gradients
resulting from mixing along the freshwater-saltwater interface. In this
study, a new mechanism for saltwater circulation and discharge is
proposed and evaluated. The process results from interaction between
bedform topography and buoyancy forces, even without flow or current
over the bedform. In this mechanism, an inverted salinity (and density)
profile in the presence of both a bedform on the seafloor and an upward
flow of fresher groundwater from depth induces a downward flow of saline
pore water under the troughs and upward flow under the adjacent crest of
the bedform. The magnitude and occurrence of the mechanism were tested
using numerical methods. The results indicate that this mechanism could
drive seawater circulation under a limited range of conditions and
contribute 20%-30% of local SGD when and where the process is operative.
Bedform shape, hydraulic conductivity, hydraulic head, and salinity at
depth in the porous media, aquifer thickness, effective porosity, and
hydrodynamic dispersion are among the factors that control the
occurrence and magnitude of the circulation of seawater by this
mechanism.
... Notably, equation (9) assumes a flat bed, while equation (4) assumes a rippled bed. Ripple topography can significantly enhance wave pumping [Shum, 1992, Figure 6], but in the absence of a purely analytical solution, we retain the flat bed solution as a conservative estimate. ...
In shallow, fetch-limited estuaries, variations in current and wave
energy promote heterogeneous surface water-groundwater mixing (benthic
exchange), which influences biogeochemical activity. Here, we
characterize heterogeneity in benthic exchange within the subtidal zone
of the Delaware Inland Bays by linking hydrodynamic circulation models
with mathematical solutions for benthic exchange forced by
current-bedform interactions, tides, and waves. Benthic fluxes oscillate
over tidal cycles as fluctuating water depths alter fluid interactions
with the bed. Maximum current-driven fluxes (~1-10 cm/d) occur in
channels with strong tidal currents. Maximum wave-driven fluxes (~1-10
cm/d) occur in downwind shoals. During high-energy storms, simulated
wave pumping rates increase by orders of magnitude, demonstrating the
importance of storms in solute transfer through the benthic layer. Under
moderate wind conditions (~5 m/s), integrated benthic exchange rates due
to wave, current, and tidal pumping are each ~1-10 m3/s, on
the order of fluid contributions from runoff and fresh groundwater
discharge to the estuary. Benthic exchange is thus a significant and
dynamic component of an estuary's fluid budget that may influence
estuarine geochemistry and ecology.
... 10,11 In permeable sediments, transport of solutes is dominated by advection − transport by the bulk flow of pore water through the sediment. 12 On the continental shelf this advection is mainly caused by pressure gradients over ripples or mounds generated by interaction of flow of the overlying water column with topographic features; the direction of this flow is upward at ripple peaks or mounds, while at ripple troughs downward flow is observed. 13 This advection results in a two-or threedimensional distribution of solutes − and biogeochemical processes − throughout the sediment. ...
Measurement of biogeochemical processes in permeable sediments (including the hyporheic zone) is difficult because of complex multi-dimensional advective transport. This is especially the case for nitrogen cycling, which involves several coupled redox-sensitive reactions. To provide detailed insight into the coupling between ammonification, nitrification and denitrification in stationary sand ripples, we combined the diffusion equilibrium thin layer (DET) gel technique with a computational reactive transport biogeochemical model. The former approach provided high-resolution two-dimensional distributions of NO3- and 15N-N2 gas. The measured two-dimensional profiles correlate with computational model simulations, showing a deep pool of N2 gas forming, and being advected to the surface below ripple peaks. Further isotope pairing calculations on these data indicate that coupled nitrification-denitrification is severely limited in permeable sediments because the flow and transport field limits interaction between oxic and anoxic pore water. The approach allowed for new detailed insight into sub-surface denitrification zones in complex permeable sediments.
... Seepage meters have been used to quantify SGD under a variety of conditions in many nearshore coastal environments and lakes over the years (Lee 1977;Bokuniewicz 1992;Cable et al. 1997). However, these devices have also drawn concerns with regard to the Bernoulli-type flow induced around the seepmeters (Shum 1992;1993). Such flow was suggested to be an important source of artifacts in a study conducted in the Florida Keys . ...
Submarine groundwater discharge (SGD) assessments conducted both in the laboratory and at a field site in the northeastern Gulf of Mexico, using a continuous-heat type automated seepage meter (seepmeter) have shown that the device has the potential of providing long-term, high-resolution measurements of SGD. The improvements on the device using a simple inexpensive laboratory set up, have shown that: (1) connecting an extension cable to the seepmeter has a negligible effect on its measuring capability and, (2) influence of very low temperature (≤ 3 ºC) on seepmeter measurements can be accounted for by conducting calibrations at such temperatures prior to field deployments and, (3) salinity had no significant effect on the performance of the seepmeter. Calibration results from fresh water and sea water showed close agreement at a 95% confidence level significance between the data sets from the two media (R2 = 0.98).
The observed artifacts on seepmeter measurements associated with Bernoulli-induced flow, the vertically directed flow arising due to water movement across topographic features can significantly be reduced by burying (or submerging) the seepmeter to nearly the same level as the sediment topography. While the study revealed that in general wind speeds > 6 m/s were associated with enhanced SGD measurements in seepmeters with buried and unburied benthic chambers, the influence was greater in the unburied meters, and more pronounced for SGD rates < 2 cm/day. Comparatively, the seepmeter SGD measurements provided data that are comparable to manually-operated seepage meters, the radon geochemical tracer approach, and an electromagnetic (EM) seepage meter.
Study of the Sarasota Bay (SB) system revealed SGD advection rates ranging from 0.7 to 24.0 cm/day, except for rare isolated hot spot occurrences where higher rates were observed. In general, SGD estimates were relatively higher in the middle and south regions (5.9 – 24.0 cm/day) compared to the north region (0.7 – 5.9 cm/day). Although no obvious seawater nutrient concentration trend was revealed, the average N/P ratio was higher in the north compared to the middle and south regions of the SB system. The importance of SGD was evident in that about 40% of the regional nutrient fluxes were observed in the north while ~ 60% occurred in the middle and south regions combined. The latter two regions also had the highest overall nutrient flux per water volume ratio, compared to the north region, thus making them potentially more vulnerable to eutrophic conditions. On average, we estimate about 27% of total dissolved N in the SB system was derived via SGD.
Most existing studies do not consider the effect that the deformability of submarine sediments may have on solute transport under the action of ocean waves. In this study a two-dimensional numerical model based on Biot’s poro-elastic consolidation theory and an advection-dispersion equation is established to investigate the transport of non-reactive solute into a deformable porous seabed under the influence of ocean waves. The numerical model is then validated against experimental and analytical results in order to demonstrate its accuracy and robustness. The simulation results indicate that ignoring the deformability of seabed soil and associated vertical seepage force due to ocean waves may lead to a significant underestimation of the rate of solute transport in shallow layers of marine sediment, particularly fine sand or silt. The effects of parameters such as the shear modulus, non-dimensional mechanical dispersion coefficient (related to particle size and permeability), dimensionless sediment thickness, wave steepness and the relative water depth has on solute transport into deformable sediment were investigated. The results indicate that the ratio of the longitudinal coefficient of mechanical dispersion between deformable and non-deformable sediments that can represent the enhancement of solute migration due to soil deformation may reach up to 85. This becomes more pronounced as the shear modulus and permeability of sediments decrease and the depth of water increases when the sediment thickness is less than 0.8 times the wavelength. The rate of solute transport in deformable sediment reaches its maximum when the sediment thickness is about 0.2 times the wavelength. In fact, as the relative water depth increases from 0.1 to 0.3, the enhancement of solute migration due to wave-induced soil deformation increases by about 60%-80%. In comparison to linear waves, shallow water waves, e.g., the first-order cnoidal waves, can increase the transport of solute more due to its strong non-linear behaviour, particularly in deformable seabed.
Both tide and wave are significant coastal driving forces of submarine groundwater discharge (SGD). The hydrodynamic process of tidal SGD is well studied while wave induced part is still challenging to quantify. In this paper, an analytical study was performed to investigate wave-induced SGD in a subtidal aquifer extending horizontally infinitely with impermeable horizontal bottom. The loading effect of seawater weight overlying the seabed was taken into account. The analytical solution was validated by two-dimensional numerical simulations with modeling domains of finite horizontal extension length. Sensitivity analyses of the analytical solution showed that the amplitude of groundwater head fluctuations generally decayed exponentially with the aquifer thickness, and the decay rate decreased with increasing loading efficiency. Loading effect can decrease the head gradients between seawater and porewater. Wave-induced SGD generally increased with the aquifer’s thickness, permeability, wavenumber, wave period, and decreased with the loading efficiency and specific storage of the aquifer. The analytical and simulated results may provide guidance for assessing the wave-induced SGD and shed light on modeling the biogeochemistry process in wave dominated porous seabed environment.
Solute exchange between the pore water of a streambed and overlying flowing surface water can have important effects on the chemical mass balance and biological productivity in the aquatic environment. The base mechanism for driving this hyporheic exchange in a moving current is turbulence at the water- sediment interface and the water surface slope. Many previous studies have shown that the nature of the exchange can be significantly modified when spatial pressure variations, induced by standing surface waves or bed forms, are present in the system. In contrast to these studies, we consider how transient pressure variations induced by moving waves modify hypothetic exchange. This is achieved experimentally by using a vertical array of electrical conductivity probes to track the movement of a conservative solute tracer in the gravel bed of a recirculating laboratory flume under a variety of flow conditions. Our experimental observations indicate that the addition of traveling waves greatly increases the initial rate and depth of solute penetration into the bed. When the analytical solution of a one-dimensional (vertical) advection–dispersion model is fit to the experimental measurements it appears that the presence of traveling surface waves results in a more dispersive hyporheic transport. Through experimental observation, model fitting, and direct simulation we demonstrate that this apparent dispersion dominated transport is due to the vertical “pumping” of interstitial fluid in the presence of traveling surface waves. From these simulations we develop a relation that for a given set of flow and wave characteristics allows us to estimate the apparent dispersion due to traveling waves.
Seagrass communities form highly productive multispecific meadows, which cover on global scale an estimated area of about 0.6 × 106 km2 (Charpy-Roubaud and Sournia 1990) developing a global biomass of about 9.2 Tmol C(460 g dry wt m−2 on average, Duarte and Chiscano 1999), which results in a net primary production of about 20 Tmol Ca−1 (92 mmol C m−2 d−1 on average, Duarte and Chiscano 1999). Despite the importance and high productivity of seagrass meadows in nutrient-poor waters, present understanding of their nutrient dynamics is still poor.
Seagrass meadows affect sedimentary dynamics by promoting sedimentation and preventing resuspension (Gacia et al. 1999; Terrados and Duarte, 1999; Ward et al. 1984). Resuspension is prevented by the network of rhizomes and roots that bind the sediments (e.g. Fonseca 1996; Fonseca and Fisher 1989), and by the wave attenuation by the plant canopies. Together, these are the main mechanisms responsible for increased deposition within seagrass beds (Fonseca and Fisher 1986; Verduin and Backhaus 2000).
Canopy trapping has been demonstrated in temperate areas (Koch 1999, Koch and Gust 1999, Terrados and Duarte 2000, Gacia and Duarte 2001, Granata et al. 2001, Gacia et al. 2002) as well as in tropical ones (Agawin and Duarte 2002, Gacia et al. 2003). In a seagrass meadow dominated by Thalassia hemprichii, Agamin and Duarte 2002 showed that particle loss is 4 times higher than in unvegetated areas, suggesting an important transfer of planktonic production to the seagrass meadow. Sediment trap and sediment data suggest that material of planktonic origin was the dominant source of sedimentary planktonic organic matter in seagrass beds (Kennedy et al. 2004 and Gacia et al. 2002). About a third of the total organic C in seawater may be colloidal and smaller than 1 μm (Sharp 1973; McCave 1984). Up to 60% of the particles in surface waters are between 1 and 10 μm, and only 10% may be bigger than 100 μm (Mullin 1965).
Recently, a large body of work has convincingly shown that there can be efficient exchange of particles (e.g. phytodetritus) between the sediment pore water and the above laying water column, especially in coarse sediments (e.g. Huettel & Gust 1992a,b, Huettel & Rusch 2000, Rusch & Huettel 2000 and Cornelisen and Thomas 2006).Two field studies reveal that once phytodetritus are trapped in the sediment, there is a rapid transfer of nutrients from the degradation product to seagrass plants, via uptake by the roots (Evrard et al. 2005; Barrón et al. 2006). A flume study by Frade et al. 2004 (student report NIOO) demonstrated that the exchange between the sediment pore water and the above laying water column is strongly depending on the location within a seagrass meadow. When exposed to a unidirectional flow, water infiltration is the largest at the leading edge of the vegetation.
We showed an exchange of fluorescent particles across the seawater – sediment interface in a tropical seagrass meadow. The infiltration efficiency of fluorescent particles across the seawater – sediment interface into the sediment of dense seagrass meadows was 6.36%. The infiltration efficiency at dense seagrass locations (6.36%) is 1.75 times higher compared to the infiltration rate at bare sediment locations (3.63%). This higher infiltration rate is possibly caused by the combination of the occurrence of seagrass leaves which generates advective transport and decreasing water depth at locations of dense seagrass meadows which generally increases wave-induced sediment filtering. The smaller infiltration depth of fluorescent particles is possibly induced by the presence of finer soil texture and lower permeability of the sediment at dense seagrass locations.
Conventional methods determining solute fluxes across the sediment–water interface have limitations in terms of the reproducibility of hydrodynamic forcing and the representativeness of spatially-heterogeneous biological processes. The newly developed eddy-covariance technique overcomes these limitations. The eddy-covariance technique is based on the principle that vertical flux is expressed by an average of the product of fluctuating vertical velocity and passive scalar, such as dissolved oxygen. Here I review previous studies using the eddy-covariance technique and two case studies on in-situ measurement of benthic oxygen exchange rates.
Benthic flux is the rate of flow across the bed of a water body, per unit area of bed. It is forced by component mechanisms, which interact. For example, pressure gradients across the bed, forced by tide, surface gravity waves, density gradients, bed-current interaction, turbulence, and terrestrial hydraulic gradients, drive an advective benthic flux of water and constituents between estuarine and coastal waters, and surficial aquifers. Other mechanisms also force benthic flux, such as chemical gradients, bioturbation, and dispersion. A suite of component mechanisms force a total benthic flux at any given location, where each member of the suite contributes a component benthic flux. Currently, the types and characteristics of component interactions are not fully understood. For example, components may interact linearly or nonlinearly, and the interaction may be constructive or referred to, in some literature, as submarine groundwater discharge. Benthic flux is important in characterizing water and constituent budgets of estuarine and coastal systems. Analytical models to characterize selective benthic flux components are reviewed. Specifically, these mechanisms are for the component associated with the groundwater tidal prism, and forced by surface gravity wave setup, surface gravity waves on a plane bed, and the terrestrial hydraulic gradient. Analytical models are applied to the Indian River Lagoon, Florida; Great South Bay, New York; and the South Atlantic Bight in South Carolina and portions of North Carolina.
Continental shelf sediments on the South Atlantic Bight (SAB) consist of relict sands that, at depths ranging from 14–45 m, fall within the photic zone and are sites in which significant rates of benthic primary production are observed. Thus, SAB seafloor sediments are a source of organic matter to the shelf system and are possibly a sink for nutrients regenerated within the sediments. We have investigated the nutrient dynamics in SAB shelf sediments along two transects (off the coasts of Georgia and Florida) as part of a study that addresses the significance of benthic primary production in terms of overall shelf biogeochemistry. Sandy sediments were sampled with a newly designed corer that permits retention of pore water in highly permeable sands and thus avoids commonly encountered “washout” problems. Nutrient (ammonium, silicate, nitrate + nitrite, and phosphate) distributions from sediments along both transects show substantial variation in concentration magnitudes and profile shapes over short horizontal spatial scales (meters). Laboratory experiments and numerical models of diagenetic processes in these sediments suggest that (1) pore-water advection, driven by current flows over wave ripples and bioturbational features, is likely an important transport process in promoting nutrient exchange in these porous sands (more so than irrigation), and (2) reaction rates in SAB sediments are rapid and are comparable to those in nearshore muddy habitats. In spite of this variation and the apparently high rates of advective transport, time series measurements show a gradual increase in depth-integrated nutrient concentrations at one station along the Georgia transect from the spring through the fall. This increase is probably related to elevations in temperature and metabolic rates in sediments during the warmer summer months.
Bedform celerity, the migration rate of ripples along a sediment bed, has previously been shown to have dramatic effects on oxygen distribution and transport within the hyporheic zone of permeable sediments. This has the potential to influence denitrification rates – in particular by increasing the coupling of nitrification and denitrification. To further understand this, we numerically modelled nitrogen cycling under migrating ripples. While the simulated oxygen profiles match with expected behaviour, almost no effect on denitrification or coupled nitrification-denitrification was observed with increasing celerity. Instead, denitrification rates were dominantly controlled by the flow velocity of water overlying the sediment.
After the pollutant discharged into the river or lake has been reduced, the release of the contaminant from the sediment to the overlying water may cause the river and lake be contaminated again. On the condition that the overlying water flow does not lead to sediment suspension, numerical researches are carried out for the mechanism of contaminant release through the sediment-overlying water interface. The overlying water flow is calculated as turbulence. The sediment is regarded as isotropic homogeneous porous medium, therefore the seepage field in the porous sediment layer is obtained by solving Darcy's equations. Coupled two dimensional steady flows of the overlying water and the pore water in the sediment are calculated. Based on the flow fields obtained, the unsteady contaminant solute transportation process in the pore water in the sediment and the overlying water is numerically simulated, as the shapes of the sediment-overlying water interface are flat or periodic triangular respectively. Numerical results show that the exchange of the pore water and the overlying water is an important factor which decides the release flux of the contaminant from the sediment to the overlying water. The pressure distribution produced by the overlying water flow along the sediment-overlying water interface, as it is not flat, may induce the seepage of the pore water in the sediment and through the sediment-overlying water interface, which may increase the release flux of the contaminant from the sediment to the overlying water.
Spatially periodic solute boundaries force symmetry across a model domain by ensuring that concentrations and concentration gradients are identical at the same location on opposite boundaries. They have been used in multiple publications on a hyporheic zone model of a single ripple or dune style bedform, including variable density flow and reactive transport variants. We evaluate simulations of multi-bedform models without imposing spatially periodic transport to demonstrate that non-physical solute distributions arise from the periodic solute transport assumption. That is, the flow field within the single bedform model leads to a transport scenario that violates the forced symmetry of periodic solute boundary conditions, culminating in a physically unrealistic solute distribution. Our results show that lack of symmetry between boundaries is a function of the vertical concentration gradient and two dimensionless parameters characterizing the hyporheic and underflow flow regimes, and the solute exchange between them. We assess the error associated with the spatially periodic assumption based on an analysis of solute fluxes across the lateral bedform model boundaries. While the focus is on steady-state concentration distributions, the implications for transient solute transport models are also discussed. We conclude that periodic solute transport boundary conditions should be applied only to bedform models that have minimal vertical dispersive and diffusive solute transfer. This includes gaining systems and tracers such as temperature, for which a temporally-periodic flux reversal occurs across the top boundary.
The primary objective of this work is to synthesize components of
benthic flux in the Patos Lagoon coastal zone, Rio Grande do Sul,
Brazil. Specifically, the component of benthic discharge flux forced by
the terrestrial hydraulic gradient is 0.8 m3 d-1;
components of benthic discharge and recharge flux associated with the
groundwater tidal prism are both 2.1 m3 d-1;
components of benthic discharge and recharge flux forced by
surface-gravity wave setup are both 6.3 m3 d-1;
the component of benthic discharge flux that transports radium-228 is
350 m3 d-1; and components of benthic discharge
and recharge flux forced by surface-gravity waves propagating over a
porous medium are both 1400 m3 d-1. (All models
are normalized per meter shoreline.) Benthic flux is a function of
components forced by individual mechanisms and nonlinear interactions
that exist between components. Constructive and destructive interference
may enhance or diminish the contribution of benthic flux components. It
may not be possible to model benthic flux by summing component
magnitudes. Geochemical tracer techniques may not accurately model
benthic discharge flux or submarine groundwater discharge (SGD). A
conceptual model provides a framework on which to quantitatively
characterize benthic discharge flux and SGD with a multifaceted
approach.
The effects of surface gravity waves on pore-water release from permeable sediment (k = 1.3-1.8 × $10^{-11}\ \text{m}^{2}$ ) in shallow water were studied in a wave tank. Our tracer experiments demonstrated that shallow-water waves can increase fluid exchange between sandy sediment and overlying water 50-fold, relative to the exchange by molecular diffusion. The main driving force for this increased exchange are the pressure gradients generated by the interaction of oscillating boundary flows and sediment wave ripples. These gradients produce a pore-water flow field, with a regular pattern of intrusion and release zones, that migrates with ripple propagation. The ensuing topography-related filtering rates in the wave tank ranged from 60 to 590 $\text{L m}^{-2}\ \text{d}^{-1}$ and exceeded the solute exchange rates caused by hydrostatic wave pumping (38 L m<sup>-2</sup> d<sup>-1</sup> and initial molecular diffusion (corresponding to 10-12 L m<sup>-2</sup> d<sup>-1</sup>). Wave-induced filtration is ecologically relevant because permeable sandy sediments are very abundant on the continental margins and can be converted into effective filter systems, which suggests that these sediments are sites for rapid mineralization and recycling. We propose that the wave influenced continental shelf may be subdivided into two zones: a shallow zone (water depth < wavelength/2), where wave orbital motion at the sea floor creates ripples and causes topography related advective filtering; and a deeper zone (wavelength/2 < water depth < wavelength), where wave pumping enhances interfacial exchange by hydrostatic pressure oscillations.
Ripples are generated and modified by wind-generated waves and their profiles are controlled by the nature of the near-bottom wave motion and by the size of the bed material. Wave-formed ripples develop under a definable set of conditions called the ripple regime. The ripple regime is bounded by those conditions that initiate grain motion, low-wave intensity, and by those that cause the disappearance of ripples, onset of sheet flow. Sheet flow occurs when intense wave motion causes several grain layers to be in motion. Three distinct ripple types occur in nearshbre areas of fine sand - relict ripples, vortex ripples, and transition ripples. Vortex and transition ripples lie within the active ripple regime, whereas relict ripples do not. Ripples in fine sand were studied in the field at La Jolla, California, where profiles were obtained using a newly developed high-resolution sonar capable of vertical resolution of the order of one millimeter. Simultaneous profile and wave-pressure measurements permit correlation of the ripple profiles with individual waves and with the wave spectrum. The sonar, with its rapid scan capability (^ one meter per second), gives instantaneous measurement of the actively changing bed features in nearshore waters. The combination of bottom scans and wavepressure measurements extends previous wave-ripple studies to include all of the nearshore ripple regime. The relation between the wave and ripple data from this study is best shown by plotting ripple steepness n/A against the wave form of the Shields relative stress criterion 0. Vortex ripples (n /\ ^_ 0.15) occur for 0 values less than 40 but greater than the minimum value which is determined by the onset of grain motion.
Measurements were made of the sand transport (solid discharge) caused by waves and currents traveling over a horizontal sand bed in water 50 cm deep. The waves had heights of 15 cm, and periods of 1.4 and 2.0 sec. The sand transport was measured first in the presence of waves only, then in the presence of waves superimposed on currents. The currents flowed in the direction of wave travel, with steady uniform velocities of 2, 4, and 6 cm/sec. Since sand moves to and fro under the influence of waves, sand traps were placed flush with the surface at either end of the bed. The net sand transport was determined by subtracting the amount of sand trapped at the upwave end of the bed, from that trapped at the downwave end. The total amount of sand caught in both traps was greatest with waves of 2.0 sec period, while the net sand transport was greatest with waves of 1.4 sec period. Super position of waves on currents of 2 cm/sec produced a two-fold increase in the sand transport for both wave types. Surprisingly, faster currents of 4 and 6 cm/sec caused the discharge to decrease somewhat. Estimates of the power expended by waves was obtained from the decrement in wave height as the wave traveled over the sand bed. The decrement in wave height was found to be about I0--5 per unit of distance traveled. Certain calculations show that about one tenth of the total power expended by the waves was used in transporting sediment.
This book is based on the author's experience with calculations involving polynomial splines. It presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines. After two chapters summarizing polynomial approximation, a rigorous discussion of elementary spline theory is given involving linear, cubic and parabolic splines. The computational handling of piecewise polynomial functions (of one variable) of arbitrary order is the subject of chapters VII and VIII, while chapters IX, X, and XI are devoted to B-splines. The distances from splines with fixed and with variable knots is discussed in chapter XII. The remaining five chapters concern specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting. The present text version differs from the original in several respects. The book is now typeset (in plain TeX), the Fortran programs now make use of Fortran 77 features. The figures have been redrawn with the aid of Matlab, various errors have been corrected, and many more formal statements have been provided with proofs. Further, all formal statements and equations have been numbered by the same numbering system, to make it easier to find any particular item. A major change has occured in Chapters IX-XI where the B-spline theory is now developed directly from the recurrence relations without recourse to divided differences. This has brought in knot insertion as a powerful tool for providing simple proofs concerning the shape-preserving properties of the B-spline series.
A theory is developed for the loss in wave energy as a result of currents induced in a permeable sea bottom by wave action. This loss in energy is reflected as a reduction in the wave height as the waves move shoreward. It is shown by numerical examples that this reduction may be on the order of ten per cent on very flat beaches for wave periods and bottom materials commonly found in the ocean.
Ripples in fine sand were studied in the field at La Jolla, California, where profiles were obtained using a newly developed high-resolution sonar capable of vertical resolution of the order of one millimeter. A combination of bottom scans and wave-pressure measurements extends previous wave-ripple studies to include all of the nearshore ripple regime. Criteria are established for the limits of the ripple regime and a description is given of ripple geometry in the transition zone between constant steepness ripples and sheet flow. (from paper)
A conformal mapping of a finite region bounded by wavy boundaries is proposed. A modification leads to a transform function of the semi-infinite region over an asymmetric rippled bed. The technique can be extensively applied to the analysis of the two-dimensional fluid motion bounded by wavy boundaries.
The problem of damping of gravity waves over a permeable sea bed of great depth is re-examined, using a more rigorous approach than that employed by Putnam in 1949 It is found that Putnam's approximate method of analysis is justified in view of the smallness of the permeability factors commonly encountered. However, a misinterpretation error was discovered in Putnam's paper which makes his dissipation function too great by a factor of four
We show how surface wave action can increase the rate of transport of solutes into a sandy seabed by orders of magnitude via a mechanism known as mechanical dispersion. It is most effective for large sediment permeability and thickness, high surface wave amplitude, and shallow water. A method for setting up the appropriate transport equation, valid when dispersion is well developed, is given. Its dispersion term contains two mechanical dispersion parameters that can be estimated roughly from existing data when the sediments are well sorted. The dispersion can be inhomogeneous and anisotropic in homogeneous, isotropic sediments. The effect of surface wave action on transport into sediments on the eastern U.S. shelf is shown to be significant under certain conditions. The effect on thawing of subsea permafrost beneath Prudhoe Bay, Alaska, seems negligible.
A general theory for the pore pressures and effective stresses induced in a porous bed by ocean waves is developed. The pore fluid as well as the soil skeleton are considered compressible and the flow in the porous bed is assumed governed by Darcy's Law for an anisotropic medium. The general solution methods for a homogeneous bed of arbitrary thickness as well as for a horizontally layered bed are presented. Explicit solutions for pore pressures and effective stresses are given for an infinite homogeneous bed. The nature of these solutions' dependency on relative compressibility of pore fluid and soil skeleton, soil permeability and hydraulic anisotropy is examined in detail and illustrated by example calculations.
In situ diffusion coefficients in the pore waters of Lake 227 were measured by monitoring the movement of tritiated water into the pore waters. The diffusion coefficients were determined by analytical and numerical modeling of the tritium profiles. During the summer, tritiated water diffuses into the sediment by molecular diffusion and this process is well approximated by a constant diffusivity model. The summer coefficients for diffusion were 1–2 × 10−5 cm2∙s−1 at a water depth of 1.5 m (20 °C) and 0.3–0.8 × 10−6 cm2∙s−1 at 8.75 m (4 °C). During fall overturn, clear evidence was found for enhanced mixing of pore waters to a sediment depth of 10 cm at water depths of 0.75 and 3.85 m. This enhanced mixing was not accompanied by mixing of the solid phase of the sediments.Key words: sediments, pore water, diffusion coefficients, tritium, lake sediments
Sediment depth distributions and fluxes of dissolved chemical substances have been interpreted as being a result of reaction, diffusion, bioturbation and irrigation1,2. However, several studies suggest that density-driven convection3 can alter the depth distribution and increase the fluxes of dissolved substances when density decreases below the sediment surface4–7. We present here temperature–time series measurements for a freshwater lake undergoing autumn cooling. These are the first in situ observations of heat transport due to motion of interstitial waters over periods of less than 1 hour. Density, calculated from temperature, decreases with depth at the time and place that this motion occurs.
Pressure waves moving across the sand beds at 3 m depth at Le Racou caused circulation of water in the unconsolidated sand layer. The pattern of circulation apparently depended on the depth of the unconsolidated layer and the form of the sand ripples. The rate of flow was determined by the height of the surface waves and the permeability of the deposit. The physical properties of the sands at the crests and in the troughs of the ripples were in part determined by the organic component which in turn would have been governed largely by the patterns and flow rates of the interstitial currents supplying organic material and nutrients to the sand. Differences in the physical properties of the sediment at the crest and in the trough of a ripple due to the organic component were such as would have affected substantially the prevalence of Branchiostoma lanceolatum and harpacticoid copepods. Sand properties dependent on the organic component would clearly be subject to change in accordance with the prevailing weather conditions and hence the supply of organic material. The role of irrigated sands in the removal of organic material from shallow seas is discussed.
A theoretical study is made of shearing flows bounded by a simple-harmonic wavy surface, the main object being to calculate the normal and tangential stresses on the boundary. The type of flow considered is approximately parallel in the absence of the waves, being exemplified by two-dimensional boundary layers over a plane. Account is taken of viscosity; but, as the Reynolds number is assumed to be large, its effects are seen to be confined within narrow ‘friction layers’, one of which adjoins the wave and another surrounds the ‘critical point’ where the velocity of flow equals the wave velocity. The boundary conditions are made as general as possible by including the three cases where respectively the boundary is rigid, flexible yet still solid, or completely mobile as if it were the interface with a second fluid.
The theory is developed on the model of stable laminar flow, although it is proposed that the same theory may usefully be applied also to examples of turbulent flow considered as ‘pseudo-laminar’ with velocity profiles corresponding to the mean-velocity distribution. Use is made of curvilinear co-ordinates which follow the contour of the wave-train. This admits a linearized form of the problem whose validity requires only that the wave amplitude be small in comparison with the wavelength, even when large velocity gradients exist close to the boundary. The analysis is made largely without restriction to particular forms of the velocity profile; but eventually consideration is given to the example of a linear profile and the example of a boundary-layer profile approximated by a quarter-period sinusoid. In § 7 some general methods are set out for the treatment of disturbed boundary-layer proses: these apply with greatest precision to thin boundary layers, but are also useful for the initially very steep but on the whole fairly diffuse profiles which occur in most practical instances of turbulent flow over waves.
The phase relationships found between the stresses and the wave elevation are discussed for several examples, and their interest in connexion with problems of wave generation by wind is pointed out. It is shown that in most circumstances the stresses are distributed in much the same way as if the leeward slopes of the waves were sheltered. For instance, the pressure distribution often has a substantial component in phase with the wave slope, just as if a wake were formed behind each wave crest—although of course actual separation effects are outside the scope of the present theory. In this aspect, the analysis amplifies the work of Miles (1957).
The results are reported of velocity measurements in oscillatory flow over rippled beds. Velocities were measured with a laser-doppler anemometer in both an oscillating tray rig and an oscillatory flow water channel. Both self-formed and artificial ripples were examined. In addition, some measurements were made with an apparently plane bed with intense sediment motion. The experimental results were compared with the predictions of several workers. Measurements of the Eulerian drift velocities showed drift towards the adjacent ripple crest in the immediate vicinity of the bed and away from the crest further out. -Authors
Sandy subtidal sediments are part of the earth's largest filter system. Water flow through bottom sediments is driven by wave action on the sea surface. The mechanisms involved are described, including a theoretical deduction and field measurements. As an example, the total water exchange through part of the West Atlantic shelf is computed and the influence of the phenomenon is discussed from a biological point of view and with regard to its importance for the world's oceans.
A simple approximate formula is derived for the boundary map function of a conformal map which provides a remarkably good fit for mappings to regions with highly distorted boundaries. The approximation follows from the reduction of a nonlocal integral equation for the map function to a local equation based on the nature of the ‘crowding’ associated with distorted regions. Numerical examples are given.
An Introduction to Fluid Dynamics Shearing flow over a wavy boundary
- G K Batchelor
- T B Benjamin
Batchelor, G. K., An Introduction to Fluid Dynamics, chap. 6, Cambridge University Press, New York, 1967. Benjamin, T. B., Shearing flow over a wavy boundary, J. Fluid Mech., 6, 161-205, 1959. Bouchard, G., Variations des paramatres biog8ochimiques dans les s8diments du chenal Laurentien, Masters thesis, Univ. of Quebec at Rimouski, Tables 3-5, Rimouski, Canada, 1983.
A Practical Guide to Splines Wave-formed ripples in nearshore sands Velocity measurements close to rippled beds in oscillatory flow
- T Ippen
- J R Dingler
- D L Inman
- C G Toit
- J F A Sleath
T. Ippen, chap. 2, McGraw-Hill, New York, 1966. de Boor, C., A Practical Guide to Splines, 392 pp., Springer-Verlag, New York, 1978. Dingler, J. R., and D. L. Inman, Wave-formed ripples in nearshore sands, Proc. ASCE Coastal Eng. Conf., 14th, 2109-2126, 1976. Du Toit, C. G., and J. F. A. Sleath, Velocity measurements close to rippled beds in oscillatory flow, J. Fluid Mech., 112, 71-96, 1981.
An effect of permeability on sand transport by waves
- K E B Lofquist
- Lofquist
Inman, D. L., and A. J. Bowen, Flume experiments on sand transport by wave and currents, Proc. ASCE Coastal Eng. Conf., 8th, pp. 137-150, Table 1, 1962. Lofquist, K. E. B., An effect of permeability on sand transport by waves, Tech. Memor. 62, 73 pp., Fig. 7, Coastal Eng. Res. Center, U.S. Army Corps of Engineers, Washington, D.C., 1975.
Animal-Sediment Relations: The Biogenic Alteration of Sediments Density-driven interstitial water motion in sediments Loss of wave energy due to percolation in a permeable sea bottom
- P L Mccall
- M J S Tevesz
- D L Musgrave
McCall, P. L., and M. J. S. Tevesz, Animal-Sediment Relations: The Biogenic Alteration of Sediments, 336 pp., Plenum, New York, 1982. Musgrave, D. L., and W. S. Reeburgh, Density-driven interstitial water motion in sediments, Nature, 299, 331-334, 1982. Putnam, J. A., Loss of wave energy due to percolation in a permeable sea bottom, Eos. Trans., AGU, 30(3), 349-356, 1949.
The subtidal pump: A mechanism of interstitial water exchange by wave action A numerical study of vortex dynamics over rigid ripples. doctoral dissertation, 329 pp Wave-induced pressures in beds of sand
- R J Riedl
- N Huang
- R Machan
- K T Shum
Riedl, R. J., N. Huang, and R. Machan, The subtidal pump: A mechanism of interstitial water exchange by wave action, Mar. Biol., 13,210-221, 1972. Shum, K. T., A numerical study of vortex dynamics over rigid ripples. doctoral dissertation, 329 pp., Mass. Inst. of Technol., Cambridge, 1988. Sleath, J. F. A., Wave-induced pressures in beds of sand, J. Hydraul. Div. Am. Soc. Civ. Eng., 96(HY-2), 367-378, 1970.
Partial Differential Equations in Physics, Lectures on Theoretical Physics, VI, chap. 1 Academic
- Sommerfeld
Finite amplitude waves
- R G Dean
- Dean
Variations des paramètres biogêochimiques dans les sêdiments du chenal Laurentien
- Bouchard
Variations des paramètres biogêochimiques dans les sêdiments du chenal Laurentien Masters thesis Univ. of Quebec at Rimouski Tables 3-5 Rimouski Canada
- G Bouchard
An effect of permeability on sand transport by waves Tech
- K E B Lofquist