Effect of tides on mouth bar morphology and...

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Effect of tides on mouth bar morphology and hydrodynamics Nicoletta Leonardi, 1 Alberto Canestrelli, 1 Tao Sun, 2 and Sergio Fagherazzi 1 Received 1 November 2012 ; revised 28 June 2013 ; accepted 1 July 2013. [1] Mouth bars are morphological units important for deltas, estuaries, or rivers debouching into the sea. Several processes affect the formation of these deposits. This paper focuses on the role of tides on shaping mouth bars, presenting both hydrodynamic and morphodynamic results. The effect of tides is analyzed in two end-member configurations: a river with a small tidal discharge compared to the fluvial discharge (fluvial dominated) and a river with a very large tidal discharge (tidal dominated). Mouth bar formation is analyzed using the coupled hydrodynamic and morphodynamic model Delft3D. The presence of tides influences the hydrodynamics of the jet exiting the river mouth and causes an increase in the averaged jet spreading. At low tide the lower water depth in the basin promotes a drawdown water profile in the river and an accelerated flow near the mouth. The resulting velocity field is characterized by residual currents affecting growth and final shape of the mouth bar. Simulations indicate that mouth deposits are characterized by the presence of two channels for negligible tidal discharge, whereas three principal channels are present in the tidal-dominated case, with a central channel typical of tidal inlets. On the basis of our numerical analyses, we present a robust criterion for the occurrence of mouth deposits with three channels. Trifurcations form when the tidal discharge is large with respect to the fluvial one and the tidal amplitude is small compared to the water depth. Finally, predicted mouth bar morphologies are compared with good agreement to river mouths in the Gulf of Mexico, USA. Citation : Leonardi, N., A. Canestrelli, T. Sun, and S. Fagherazzi (2013), Effect of tides on mouth bar morphology and hydrodynamics, J. Geophys. Res. Oceans, 118, doi:10.1002/jgrc.20302. 1. Introduction [2] Deltas result from the interaction between rivers and marine or lacustrine systems, giving rise to complex depo- sitional patterns. Deltas are vulnerable to both anthropo- genic and natural changes, such as sea level rise, variations in sediment supply, increase in storm activity and hurricane frequency, urbanization, and changes in land-use practices [e.g., Day et al., 2007; Edmonds, 2012a; Paola et al., 2011; Syvitski et al., 2009]. Human activities continuously threaten these valuable environments, and new efforts are required to improve their management and restoration strat- egies. A vast literature on the overall morphology of deltas is already available; however, little work has been done on the effects of tides on delta morphology, and, in particular, on the effect of tides on mouth bars development. [3] Researchers have analyzed both large-scale structure of deltaic systems [Edmonds, 2012b ; Edmonds et al., 2009, 2011a, 2011b; Edmonds and Slingerland, 2010; Canes- trelli et al., 2010, Geleynse et al., 2010, 2011; Jerolmack, 2009; Jerolmack and Paola, 2007; Fagherazzi, 2008; Jer- olmack and Swenson, 2007; Fagherazzi and Overeem, 2007] and their morphological units, such as mouth bars [Esposito et al., 2013; Nardin et al., 2013; Nardin and Fagherazzi, 2012; Edmonds and Slingerland, 2007; Wang, 1984; Wright, 1977 ; Bates, 1953]. [4] As indicated by the conceptual model of Edmonds and Slingerland [2007], when a channelized flow enters a body of water the sediment transport rate decreases and a mouth bar evolves through initial deposition, progradation, and stagnation, finally leading to channels formation and bifurcation. Esposito et al. [2013] successfully tested Edmonds and Slingerland [2007] model for mouth bar evo- lution by means of field data near the mouth of the Missis- sippi River. [5] Deltaic bifurcations occur at the fossilized location of mouth bars, which are crucial to delta progradation and often constitute much of the deltaic system [Edmonds and Slingerland, 2009]. With increasing channel bifurcation order, there is a systematic reduction in channels length, width, and depth, due to a lower jet momentum flux and consequent lower transport distance basinward [Edmonds and Slingerland, 2007, 2009]. [6] Marine processes might play a considerable role in sediment deposition, and their influence is reflected in the diversity of planar configurations and internal stratigraphy of coastal deposits. Among others, wave energy, tidal range, and the degree to which tidal currents determine the flow within the lower reaches of a river have been indicated as important geomorphic agents for delta morphodynamics 1 Department of Earth and Environment, Boston University, Boston, Massachusetts, USA. 2 ExxonMobil Exploration Company, Houston, Texas, USA. Corresponding author: N. Leonardi, Department of Earth and Environ- ment, Boston University, Rm. 141I, 675 Commonwealth Ave., Boston, MA 02215, USA. ([email protected]) ©2013. American Geophysical Union. All Rights Reserved. 2169-9275/13/10.1002/jgrc.20302 1 JOURNAL OF GEOPHYSICAL RESEARCH : OCEANS, VOL. 118, 1–15, doi :10.1002/jgrc.20302, 2013

Transcript of Effect of tides on mouth bar morphology and...

Effect of tides on mouth bar morphology and hydrodynamics

Nicoletta Leonardi,1 Alberto Canestrelli,1 Tao Sun,2 and Sergio Fagherazzi1

Received 1 November 2012; revised 28 June 2013; accepted 1 July 2013.

[1] Mouth bars are morphological units important for deltas, estuaries, or rivers debouchinginto the sea. Several processes affect the formation of these deposits. This paper focuses on therole of tides on shaping mouth bars, presenting both hydrodynamic and morphodynamicresults. The effect of tides is analyzed in two end-member configurations: a river with a smalltidal discharge compared to the fluvial discharge (fluvial dominated) and a river with a verylarge tidal discharge (tidal dominated). Mouth bar formation is analyzed using the coupledhydrodynamic and morphodynamic model Delft3D. The presence of tides influences thehydrodynamics of the jet exiting the river mouth and causes an increase in the averaged jetspreading. At low tide the lower water depth in the basin promotes a drawdown water profile inthe river and an accelerated flow near the mouth. The resulting velocity field is characterized byresidual currents affecting growth and final shape of the mouth bar. Simulations indicate thatmouth deposits are characterized by the presence of two channels for negligible tidal discharge,whereas three principal channels are present in the tidal-dominated case, with a central channeltypical of tidal inlets. On the basis of our numerical analyses, we present a robust criterion forthe occurrence of mouth deposits with three channels. Trifurcations form when the tidaldischarge is large with respect to the fluvial one and the tidal amplitude is small compared to thewater depth. Finally, predicted mouth bar morphologies are compared with good agreement toriver mouths in the Gulf of Mexico, USA.

Citation: Leonardi, N., A. Canestrelli, T. Sun, and S. Fagherazzi (2013), Effect of tides on mouth bar morphology andhydrodynamics, J. Geophys. Res. Oceans, 118, doi:10.1002/jgrc.20302.

1. Introduction

[2] Deltas result from the interaction between rivers andmarine or lacustrine systems, giving rise to complex depo-sitional patterns. Deltas are vulnerable to both anthropo-genic and natural changes, such as sea level rise, variationsin sediment supply, increase in storm activity and hurricanefrequency, urbanization, and changes in land-use practices[e.g., Day et al., 2007; Edmonds, 2012a; Paola et al.,2011; Syvitski et al., 2009]. Human activities continuouslythreaten these valuable environments, and new efforts arerequired to improve their management and restoration strat-egies. A vast literature on the overall morphology of deltasis already available; however, little work has been done onthe effects of tides on delta morphology, and, in particular,on the effect of tides on mouth bars development.

[3] Researchers have analyzed both large-scale structureof deltaic systems [Edmonds, 2012b; Edmonds et al., 2009,2011a, 2011b; Edmonds and Slingerland, 2010; Canes-trelli et al., 2010, Geleynse et al., 2010, 2011; Jerolmack,

2009; Jerolmack and Paola, 2007; Fagherazzi, 2008; Jer-olmack and Swenson, 2007; Fagherazzi and Overeem,2007] and their morphological units, such as mouth bars[Esposito et al., 2013; Nardin et al., 2013; Nardin andFagherazzi, 2012; Edmonds and Slingerland, 2007; Wang,1984; Wright, 1977; Bates, 1953].

[4] As indicated by the conceptual model of Edmondsand Slingerland [2007], when a channelized flow enters abody of water the sediment transport rate decreases and amouth bar evolves through initial deposition, progradation,and stagnation, finally leading to channels formation andbifurcation. Esposito et al. [2013] successfully testedEdmonds and Slingerland [2007] model for mouth bar evo-lution by means of field data near the mouth of the Missis-sippi River.

[5] Deltaic bifurcations occur at the fossilized locationof mouth bars, which are crucial to delta progradation andoften constitute much of the deltaic system [Edmonds andSlingerland, 2009]. With increasing channel bifurcationorder, there is a systematic reduction in channels length,width, and depth, due to a lower jet momentum flux andconsequent lower transport distance basinward [Edmondsand Slingerland, 2007, 2009].

[6] Marine processes might play a considerable role insediment deposition, and their influence is reflected in thediversity of planar configurations and internal stratigraphyof coastal deposits. Among others, wave energy, tidalrange, and the degree to which tidal currents determine theflow within the lower reaches of a river have been indicatedas important geomorphic agents for delta morphodynamics

1Department of Earth and Environment, Boston University, Boston,Massachusetts, USA.

2ExxonMobil Exploration Company, Houston, Texas, USA.

Corresponding author: N. Leonardi, Department of Earth and Environ-ment, Boston University, Rm. 141I, 675 Commonwealth Ave., Boston,MA 02215, USA. ([email protected])

©2013. American Geophysical Union. All Rights Reserved.2169-9275/13/10.1002/jgrc.20302

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JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 118, 1–15, doi:10.1002/jgrc.20302, 2013

and, in particular, for mouth bar evolution [e.g., Wright andColeman, 1974; Jerolmack, 2009; Ashton and Giosan,2011; Geleynse et al., 2010; Nardin and Fagherazzi,2012; Nardin et al., 2013]. As an example, the mouth barsof the Danube Delta change repeatedly, switching from acondition in which fluvial factors are predominant to a con-figuration in which marine processes are more relevant[Dolgopolova and Mikhailova, 2008].

[7] Nardin and Fagerazzi [2012] showed how the pres-ence of waves leads to different bar morphologies depend-ing on the relative importance of wave angle and wave-induced bottom shear stress. Large waves do not allow theformation of mouth bars either because of deflection of theriver mouth jet, in case of oblique waves, or jet destabiliza-tion, in case of frontal waves. Wave angles between 45�

and 60� have been identified as the most unfavorable forbar deposition. Nardin et al. [2013] found that waves canreduce the time of mouth bar formation and their distancefrom the river mouth leading to wave-induced deltas beingshorter with respect to deltas experiencing no-waves condi-tions. According to Edmonds [2012], during the 2011 floodin Louisiana, USA, the Atchafalaya and Mississippi Riverscontributed to the same amount of land building, despite ofthe Mississippi River carrying a volume of sediments twiceas large. This outcome was mainly due to the influence ofcoastal currents that can keep the sediment near the shore-line or disperse it in the ocean.

[8] Few studies have focused on the morphodynamicrole of tides near river mouths; on the contrary, a rich liter-ature is available on tidal inlets and their deposits. Sinceseveral tidal processes acting on river mouths are also pres-ent in tidal inlets, a comparison between the two systems isdeemed necessary.

[9] Tidal inlets are channels maintained by tidal flowthat connect the ocean with bays, lagoons, or salt marshes[e.g., FitzGerald et al., 2006]. The classical tidal inlet sys-tem consists of an ebb delta at the ocean side built around adeep central channel and two lateral shallower channels[Hayes, 1975; Fitzgerald, 1976]. The main channel is ebbdominated while the other two are flood dominated. A flooddelta is also present in the bay, resulting from the combina-tion of flood channels and tidal flats [Hayes, 1975; FitzGer-ald, 1976, 1996, 2006; De Swart and Zimmerman, 2008].

[10] Tidal prism and reversing tidal currents are, to alarge extent, the governing forces for inlet dimensions andsediment transport dynamics. River mouths present similardynamics but only when the tidal discharge is considerablylarger than the river discharge [FitzGerald, 1996]. Accord-ing to Lanzoni and Seminara [2002], even if the tidal rangeis small, it is still possible to have a tide dominance situa-tion in case of large tidal prism or limited wave action.

[11] Tidal inlets are also strongly affected by externaldrivers, in the same way that mouth bars are. Waves, along-shore currents, and sea-level rise can have a nonnegligibleinfluence on inlet morphology [Dissanayake et al., 2008,2009; Lanzoni and Seminara, 2002]. It has been shownthat, during periods of increasing tidal prism, the inlets ofthe barrier islands in the Mississippi delta evolve from awave-dominated configuration, with broad flood deltas, totransitional forms, with sand shoals choking the mouththroat, and finally to a river mouth, with a deep main chan-nel and a well-developed ebb delta resembling a mouth bar

[Levin, 1993]. Dissanayake et al. [2009] used the numericalmodel Delft3D to illustrate how shore-parallel tidal cur-rents and their time lag with respect to inlet currents haveinfluenced the evolution of the Ameland inlet in the DutchWadden Sea.

[12] Numerical models are particularly suitable to under-stand the behavior of fluvial and deltaic systems at mediumto long time scales. Among others, numerical results ondelta formation by Geleynse et al. [2010, 2011] show no-ticeable agreement with natural systems. Their simulationsinclude deltaic mouth bars, distributary formation, andmeander-bend evolution. Numerical results from Edmondsand Slingerland [2010] suggest that deltas without vegeta-tion, as those that formed antecedent to the Devonian pe-riod, should show more fan-like characteristics, with fewerchannels and delta plain lakes. This is mainly due to thefact that vegetation operates as a cohesive agent. In fact,they show that highly cohesive sediments favor formationof bird’s-foot deltas with complex floodplains and rugoseshorelines. On the contrary, less cohesive sediments morelikely form fan-like deltas.

[13] This work aims at analyzing concurrent effects oftides and fluvial discharge on the evolution of river mouthbars with the numerical model Delft3D. Our investigationis limited to a simple geometry and a homopycnal effluent(i.e., with negligible buoyancy); wind waves and Coriolisforces are also neglected. Two extreme cases are taken intoaccount and discussed: (1) a river mouth with a fluvial dis-charge much larger than the tidal discharge and thereforecharacterized by unidirectional flow; (2) a river mouthwith a tidal discharge much larger than the fluvial dis-charge, allowing the flow to reverse direction.

[14] As we are going to show, different morphologiescorrespond to the two aforementioned cases. Therefore, aseries of additional numerical experiments with intermedi-ate ratios of river discharge to tidal discharge are also pre-sented in order to identify the transition from one conditionto the other. The manuscript is organized as follows: insection 2 we describe the model, the model geometry, andthe boundary conditions utilized in the simulations. In sec-tion 3 we present key hydrodynamic results derived fromthe simulations. These results are divided into (i) effect oftides on jet spreading, (ii) effect of tides on the velocityfield, and (iii) residual tidal currents. Section 4 deals withthe implication of the hydrodynamic results for mouth barformation and evolution. In section 5 we qualitatively com-pare our results to the morphology of river mouths in theGulf of Mexico, USA. A set of conclusions is finally pre-sented in section 6.

2. Model Description and Setup

[15] The formation of river mouth bars is studied usingthe computational fluid dynamics package Delft3D [Roel-vink and Van Banning, 1994; Lesser et al., 2004]. Delft3Dis a numerical model composed of a number of integratedmodules. Together, they allow the simulation of hydrody-namic flow, sediment transport and related bed evolution,short-wave generation and propagation, and the modelingof ecological processes and water quality parameters[Lesser, 2004]. The Delft3D-FLOW module is able to solvethe unsteady shallow-water equations in two (depth-

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averaged) dimensions. These equations consist of the hori-zontal momentum equations, the continuity equation, thesediment transport equation, and a turbulence closuremodel. The vertical momentum equation is reduced to thehydrostatic pressure relation because vertical accelerationsare assumed to be small compared to gravitational accelera-tion and are not taken into account [Lesser et al., 2004].The sediment transport and morphology modules accountfor bed and suspended load transport of cohesive and non-cohesive sediments and for the exchange of sedimentbetween the bed and the flow. The suspended load is calcu-lated using the advection-diffusion equation for sediments.The bed-load transport on a horizontal bed is calculatedusing an empirical transport formula. In the present work,the formulation proposed by Van Rijn [1993] is used. Themodel mesh is rectangular with rectangular cells, whoselong axis is parallel to the flow (Figure 1). The simulationsare designed to investigate the hydrodynamic and morpho-logical conditions of a river discharging into a body ofwater with flat bottom and in the presence of tides of vary-ing amplitude. The simulated river length (400 m) is neces-sarily limited in order to ensure a reasonable computationaleffort. Hence, a suitable landward flow discharge needs tobe specified to describe the two end-member cases.

[16] In the first, river-dominated case, a constant riverdischarge is assumed, such that the tidal-induced fluxes aresmaller than the fluvial fluxes. In the second, tidal-dominated case, an oscillating discharge is superposed on aconstant discharge, of fluvial origin, to mimic the overalldischarge typical of a tidal-dominated river reach.

[17] Tidal motion in channels as well the interaction oftides with a riverine discharge is complex and difficult tobe properly modeled. Factors like channel slope and shape,and bed friction can affect the velocity field [Lanzoni andSeminara, 1998; Savenije et al., 2008]. According to Lan-zoni and Seminara [1998], river discharge can significantlyalter tidal dynamics. For example, with an increase in river-ine discharge, both the tidal wavelength and celeritydecrease, while the tidal amplitude shows a more rapidupstream decay. The relationship between tidal elevationand maximum discharge depends on the nonlinear propaga-tion of the tide in the lower reaches of the river and itsfloodplains. In river mouths, the tidal propagation fallssomewhere between a progressive (0� of phase differencebetween tidal level and tidal velocity fluctuations) andstanding wave (90� of phase difference). The main factorsaffecting the phase difference are the mouth topography

and the river currents [Son and Hsu, 2011]. Savenije et al.[2008] considers the phase lag between high water andslack water as one of the main parameters for the classifica-tion of estuaries, and proposes explicit analytical andgraphical solutions to determine it. Lanzoni and Seminara[1998] show how the phase lag increases with estuary con-vergence. Approaching the convergent limit for the estuary,the phase lag reaches 90�. Son and Hsu [2011] indicate thephase difference as a key process for the flux of sedimentsin the river. Accordingly, the flux of sediment is larger inthe progressive wave condition.

[18] Here we assume that the tidal wave mimics a stand-ing wave at the river mouth, so that the phase lag betweenhigh water and high water slack is zero. This assumption isvalid for strongly convergent estuaries [Lanzoni and Semi-nara, 1998; Savenije et al., 2008], tidal inlets [Bruun et al.,1978], or for rivers with a length much smaller than thetidal wavelength. A standing wave is also the standardassumption of tidal channel hydrodynamics [Boon, 1975;Fagherazzi et al., 1999; Fagherazzi, 2008]. Thus, weneglect further elaborations connected to the contributionof both landforming discharges and propagation of the tidalsignal in the fluvial reaches.

[19] In the tidal-dominated case, a constant river dis-charge is superimposed to an oscillating tidal dischargehaving a frequency of 30 deg/h (thus approximating a tidalfrequency) and out of phase of 90� with respect to the waterlevel. To impose the phase delay of 90� between dischargeand water level at the river mouth we need to account forthe propagation of the tide in the domain. In fact, we pre-scribe the water level at the seaward boundary, while the si-nusoidal discharge is prescribed at the landward boundary.Since the two boundaries are distant in space a small phaselag is present.

[20] According to Lanzoni and Seminara [2002], in caseof tide dominance, the volume of water exchanged in eachtidal cycle is at least 1 order of magnitude larger than riverdischarge. Therefore, we use a discharge equal to 10% ofthe maximum tidal discharge in order to simulate a relativesmall and constant riverine flow in the tide-dominatedcondition.

[21] In fluvial-dominated conditions the discharge Q is1500 m3/s. In the tidal-dominated case, the amplitude ofthe sinusoidal discharge is 570 m3/s. The choice of the dis-charge is based on the tidal inlet cross-sectional area A(m2) and tidal prism P (m3), further referred as A-P rela-tionship. In fact, for tidal inlets field observations suggestthat equilibrium exists, of the form of

A ¼ CPq ð1Þ

[22] where C and q are empirical parameters [O’Brien,1931; Jarrett, 1976; Tambroni et al., 2005; D’Alpaos etal., 2009, 2010].

[23] Specifically, Tran et al. [2012] determined the A-Prelationship for a series of hypothetical inlets using theprocess-based model Delft3D. Based on their results, weuse the values of C¼ 2.14 � 10�4 m2–3q and q¼ 0.96 inorder to evaluate the tidal prism in equilibrium with thecross-sectional area of the tidal-dominated case.

[24] In the fluvial-dominated case the sediment concen-tration at the inflow boundary is constant, while in thetidal-dominated case we impose an equilibrium sand

Figure 1. Computational domain and boundaryconditions.

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concentration profile. This condition means that the sedi-ment load entering through the boundary is adapted to thelocal flow conditions so that neither erosion nor depositionoccurs at the river mouth.

[25] For the upper and lower boundaries, we impose azero-flux boundary condition, consisting in imposing thegradient of the alongshore water level equal to zero (Figure1). As shown by Roelvink and Walstra [2004], in case ofunknown lateral boundary conditions it is preferable toimpose the water level gradient and allow the model todetermine water levels and current velocities.

[26] Finally, in order to make the solution well posed,we prescribe an oscillating water level at the seawardboundary. The water level varies with a semidiurnal tidalfrequency (30 deg/h) and has an amplitude ranging from0.25 to 2.5 m. Therefore our simulations represent bothmicrotidal and mesotidal environments.

[27] The initial condition for each simulation consists ofa constant bathymetric depth (3.5 or 4.5 m) and a waterlevel equal to mean sea level. Both sediments in the basinand sediments delivered by the river and possibly enteringfrom the seaward boundary are noncohesive and have aspecific density of 2650 kg/m3, a dry bed density of 1600kg/m3, and a median sediment diameter D50 of 200 �m.

[28] A sensitivity analysis was performed in order tochoose the proper grid size, and the results presented in thiswork are a good compromise between small computationaltime and accuracy of the solution. The grid size varies from60 � 60 m at the margins of the basin to 20 � 60 m in thecentral part. The time step is set to 0.25 min. Every simula-tion runs for 12 model hours before starting the morpholog-ical evolution. This period is sufficient for a completeadaptation of the hydrodynamic simulation to the dynamicboundary conditions.

[29] In Delft3D, horizontal viscosity coefficients can bedetermined by means of two different closure models. Thefirst is by specifying a constant or space-varying value ofeddy viscosity. The second is by using a large eddy simula-tion model (HLES) that is added to a background value ofeddy viscosity [Van Vossen, 2000; Uittenbogaard and VanVossen, 2001]. In our simulations, we used the HLESmodel with a background eddy viscosity equal to 10�4 m2/s. Before adopting this value, we tested different values ofbackground eddy viscosity, from 10�5 to 10�1 m2/s, with-out finding any substantial influence on the simulationsresults from a qualitative point of view. Moreover, we com-pared the results from the HLES method with those for aconstant value of eddy viscosity. We used 0.1 m2/s [Vander Wegen and Roelvink, 2008], 1 m2/s [Battjes, 1975], 2m2/s, and 5 m2/s. Also in these cases we did not find anysignificant qualitative difference.

[30] Bed slope affects sediment transport as indicated byIkeda [1982]. Two coefficients are used in Delft3D in orderto adjust the bed load transport in the direction of the aver-age bed stress (longitudinal slope factor) and in the direc-tion perpendicular to it (transverse slope factor). In thesimulations, we use default values of 1 and 1.5 for longitu-dinal and transverse slope factors, as suggested by Ikeda[1982]. However, these parameters are uncertain and theirestimates are based on small-scale experiments. For exam-ple, Van der Wegen and Roelvink [2008] suggest a value of5 for the transverse slope factor, while Dissanayake et al.

[2009] use a value of 50. According to our sensitivity anal-ysis, the fluvial-dominated case is slightly affected by vari-ation of either longitudinal or transverse slope factor forvalues up to 50. The tidal-dominated case is influenced byvariations in transverse slope factor, but significant changesonly occur for values larger than 20, as the central channelgradually becomes shallower and wider. These findingsconfirm previous results by Dissanayake et al. [2009], forwhich a smaller transverse slope factor leads to a narrowand deep central channel, whereas the effect of the longitu-dinal slope factor is negligible.

[31] In order to account for the difference in time scalesbetween hydrodynamics and morphological evolution, bot-tom changes per time step are scaled up by a morphologicalfactor [Roelvink, 2006]. The morphological factor is 15 forthe fluvial-dominated case and 450 for the tidal-dominatedcase.

3. Hydrodynamic Results

[32] At river mouths, the width generally exceeds thedepth by a factor of at least 4, and width to depth ratiosgreater than 50 are common [Edmonds and Slingerland,2007]. Vertical motions of the water are usually less signifi-cant than horizontal ones and therefore the flow can beapproximated with the shallow water equations [€Ozsoy and€Unl€uata, 1982]. Note that the numerical model used in thiscontribution is in agreement with the shallow water approx-imation. As rivers empty into oceans or lakes, they expandas a confined jet, experiencing mixing, diffusion with theambient fluid and decrease in sediment concentration andmomentum. The jet is divided into two regions: the zone offlow establishment (ZOFE), having a core of constant ve-locity, and the zone of established flow (ZOEF), where asimilarity function can be assumed for the transverse veloc-ity profile. The transition from ZOFE to ZOEF marks thedownstream location at which the turbulence generated byshearing along the margins of the jet affects the entire jet[Bates, 1953]. Jet theory has been largely used to describerivers and inlets discharging into a standing water body[Bates, 1953; Wright and Coleman, 1974; €Ozsoy and€Unl€uata, 1982; Wright, 1977; Rowland et al., 2010; Fal-cini and Jerolmack, 2010; Nardin and Fagherazzi 2012;Nardin et al., 2013].

[33] The presence of tides influences the hydrodynamicof the jet and the velocity field producing residual currentsthat affect the growth and the final shape of mouth bars. Tostudy these currents, we first focus on the jet width and cen-terline velocity in the case of fixed bed. The self-similarityof the lateral velocity profile is assumed and the jet spread-ing is represented by the half width, defined as the lateraldistance at which the velocity decreases to 5% of its center-line value [€Ozsoy, 1986]. According to Tee [1976], residualcurrents are the velocity field after the removal of all the si-nusoidal components of tidal motion. They are time inde-pendent and can be obtained by the average over a tidalcycle. From a mathematical point of view, residual currentscan be described through the fundamental equations offluid mechanics simplified with the no-time dependenceassumption [De Swart and Zimmerman, 2008; Nihoul andRonday, 1975]. Tides can generate residual currents by sev-eral mechanisms such as nonlinear bottom friction,

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nonlinear terms in the continuity equation, and the nonlin-ear advective term in the momentum equation. Residualcurrents can be studied using vorticity balance, as shownby Zimmerman [1981]: in order to create residual circula-tions in a tidal cycle, both the production of residual tidalvorticity and a net flux of vorticity through a closed curveare necessary. Residual currents account for part of thesediment transport [Van der Vegt et al., 2006] and thereforeare considered as important indicators for mouth bar mor-phodynamics in our study.

[34] We compute residual tidal currents by calculatingthe difference between the velocity field with tides, aver-aged in a tidal cycle, and the velocity field in the absenceof tides. Thus, we depurate the flow field from the influenceof the riverine discharge, and we can focus our attention onnonlinear residual currents produced by tidal motion only.Two purely hydrodynamic simulations have been run forthe calculation of each residual velocity field: one withtides and the other without tides, using the same bar mor-phology and a nonmoving bottom.

3.1. Jet Spreading

[35] The hydrodynamics of the problem is investigatedfor a flat and fixed horizontal bathymetry. According to€Ozsoy and €Unl€uata [1982], a turbulent jet in the presenceof flat bottom with friction is characterized by an exponen-tially growth of the jet width and a decay of the centerlinevelocity. For large width to depth ratios, as those here con-sidered, the ZOFE is small relatively to the ZOEF [€Ozsoyand €Unl€uata, 1982] and, thereafter, the analysis will be re-stricted to the latter.

[36] To compute the velocity and jet half width in thecase of flat bottom with friction, the following nondimenso-nal parameters are defined (Figure 2):

� ¼ x

b0; � ¼ y

b xð Þ ; � ¼fb0

8h0;H �ð Þ ¼ h

h0;

B �ð Þ ¼ b

b0;U �ð Þ ¼ uc

u0; �s ¼

xs

b0ð2Þ

[37] where b0is the inlet half width, b xð Þ is the jet halfwidth, h0 is the inlet depth, h is the water depth, u is thevelocity, u0 is the jet velocity at the inlet, and f is theDarcy-Weisbach friction coefficient. The parameter xs isthe end coordinate for the core region and marks the pas-

sage between ZOFE and ZOEF. The solution for theunknown centerline velocity and jet half width in case offlat bottom with friction is [€Ozsoy and €Unl€uata, 1982]

U ¼ e���

e�2��s þ 2�I2

�I1e���s � e���ð Þ

h i1=2ð3Þ

B ¼ e��

I2e�2��s þ 2�I2

�I1e���s � e���� �� �

ð4Þ

[38] where � ¼ 0:05 in the ZOEF and I1 and I2 are twoconstant values equal to 0.450 and 0.316, respectively.According to these equations, as the water depth decreases,the jet spreading increases, and the jet half width has an ex-ponential dependence on the distance from the river mouth.For simplicity, in this work the jet half width has beenapproximated using a simple exponential curve of theform:

B �ð Þ ¼ a � e�� ð5Þ

[39] where � is the nondimensional e-folding length rep-resenting the spreading of the jet.

[40] The jet spreading for the river-dominated case isevaluated at different instants of the tidal cycle. The largestspreading occurs at low tide, whereas the smallest spread-ing corresponds to high tide (Figure 3). The mean

Figure 2. Sketch of a turbulent jet exiting a river mouth.

Figure 3. Jet half width for different tidal conditions. Thepoints represent locations having an along � velocity equalto the 5% of the centerline value and have been fitted withequation (4) to obtain the solid lines. Black line: jet spread-ing at low tide (ht ¼2.5 m). Green line: jet spreading athigh tide (ht¼2.5 m). Blue line: averaged jet spreading intime with a tidal amplitude ht ¼2.5 m. Red line: jet spread-ing without tide.

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spreading computed by averaging the spreading over sev-eral tidal cycles is larger than the spreading in the casewithout tides (Figure 3). This effect is present in all testedtidal amplitudes (ranging from 0.25 to 2.5 m). Moreover,the higher is the tidal range, the more evident is theincrease in average spreading. This result can be explainedby a nonlinear relationship between water depth and jetspreading (Figure 4a). To further investigate this aspect,the jet half width has been computed for a series of addi-tional numerical experiments, in which a constant dis-charge is prescribed at the landward boundary and aconstant mean water level is prescribed at the seawardboundary. The water depth varies among the experimentsand Figure 4a highlights the nonlinear relationship betweenwater depth and �, representative of jet spreading. The e-folding length �, calculated for different depths, is com-pared with the analytical solution of €Ozsoy and €Unl€uata

[1982, equation (3)], after fitting it with the simple expo-nential formulation adopted in equation (4).

[41] We also explore the effect of friction on jet spread-ing. We increase friction by reducing the Chezy coefficientfrom 45 m1/2/s to 30 m1/2/s (Figure 4). Larger friction leadsto more jet spreading, with the e-folding length � maintain-ing the same trend (i.e., hyperbolic decay as a function ofwater depth and constant value as a function of velocity).Morphological and hydrodynamic considerations are there-fore similar for different friction coefficients.

[42] The water depth in the numerical simulations rangesfrom 2 to 7 m, with a mean sea level at 4.5 m of depth anda maximum tidal amplitude of 2.5 m. Because the e-foldinglength � does not decrease linearly with water depth (Fig-ure 4a), it follows that

Z hþDh

h� hð Þ dh <

Z h�Dh

h� hð Þ dh ð6Þ

[43] being h the water depth for a generic instant of thetidal cycle, Dh a finite positive variation of depth in time,and h the basin depth for a fixed instant. Therefore, througha tidal cycle, the jet spreading increment during periods oflow water level is more relevant than its decrease during aperiod of high water. As a consequence, on average, tidestend to increase jet spreading. Note also that this is true notonly for our particular value of mean sea level (4.5 m) butalso for any other value. In fact, � becomes constant as htends to infinite, and the curve is always concave upward(Figure 4a). Clearly, this effect is more relevant for largertidal ranges and smaller depths, for which the concavity ismaximum.

[44] The solution of €Ozsoy and €Unl€uata [1982] for thenormalized jet half width does not depend on jet velocity,but it is mainly affected by water depth. Figure 4b showsthe jet spreading for different velocities of the river andconstant water depth (i.e., in the absence of tides). Asexpected, the influence of velocity on jet spreading is negli-gible. Also in this case the analysis has been done for twodifferent friction coefficients.

3.2. Velocity

[45] For river-dominated conditions, velocities are meas-ured at different locations along the centerline and at differ-ent distances from the river mouth (points A–E in Figure1). It is possible to notice a shift from a standing wave cur-rent to a progressive wave current moving from the sea-ward boundary toward the mouth (Figure 5). At theseaward boundary, where we impose the varying waterlevel, the velocity is negligible at high and low tide (slackwater), a typical condition of a standing wave. On the con-trary, near the river mouth, the maximum flood and ebbvelocities occur at high and low tide, with slack water tak-ing place near mean sea level (progressive tidal wave) (Fig-ures 5a and 5b).

[46] The transitional region between the standing waveand the progressive wave conditions can be detectedthrough the cross correlation in time between water leveland depth-averaged velocity, which determines the delay(Figure 5c). The discontinuity point indicates the transitionbetween the two conditions.

Figure 4. (a) The � coefficient as a function of waterdepth; (b) � coefficient as a function of the centerline ve-locity at the inlet boundary condition. Colored dots (Fig-ures 4a and 4b) have been obtained with additionalnumerical experiments with constant discharge and vari-able depths (Figure 4a), or with constant depth (4.5 m) andvariable discharge (Figure 4b). Continuous lines are repre-sentative of the analytical solution of €Ozsoy. Red dots referto a Chezy coefficient of 45 m1/2/s, while blue dots refer toa Chezy coefficient of 30 m1/2/s. Gray arrows indicate therange of depth and velocity of the present work.

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[47] This transition is caused by the interaction betweenriverine discharge and seaward water level. At low tide thewater depth in the basin is low, thus promoting a drawdownwater profile in the river with accelerated flow near themouth [Lamb et al., 2012]. On the contrary, as the seawarddepth rises, a backwater profile establishes, with milderwater gradients and limited flow acceleration near themouth. Figure 6c shows the relationship between velocitygradient and water level in time. The velocity gradient ismaximum when the water level is minimum, demonstratingthe presence of an accelerated flow during periods of lowwater level. The velocity is therefore in phase with tidalelevation, peaking at low tide.

3.3. Tidal Residual Velocities

[48] To determine the effect of tides on mouth hydrody-namics and bar formation we compute the tidal residualvelocities by integrating the velocity field in a tidal cycleand subtracting the flow field due to the river discharge inthe absence of tides [Zimmerman, 1981].

[49] In the fluvial-dominated case, the residual velocitiesform two lateral bands that bifurcate within a short distancefrom the river mouth (Figure 7). These bands are producedby an increase in spreading at low tide, which is only partlycompensated by a decrease in spreading at high tide (Figure3). A residual current is also present in the river, and it iscaused by high velocities during low tide. In fact a draw-down water surface gradient establishes at low tide thataccelerates the flow (Figure 6). Again this acceleration isonly partly compensated by a deceleration due to the back-

water effect at high tide, yielding a net residual currentexiting the river.

[50] In the tidal-dominated case, the residual velocity isassociated with the difference between the confined flow ofthe turbulent jet during the ebb phase and the sink flow dur-ing the flood phase, which is radially distributed across theentire domain [Chao, 1990; Tambroni et al., 2005]. The re-sidual velocity field displays two counterrotating vorticesexiting the river mouth (Figure 8), which agrees with previ-ous results in tidal inlets [Chao, 1990; Van der Vegt et al.,2006].

4. Bar Morphology

[51] According to Edmonds and Slingerland [2007],mouth bar formation is due to the reduction of the sedimenttransport rate when the turbulent jet expands into a standingbody of water. More specifically, the decrease in the jetmomentum flux is responsible for the formation of mouthbars. After initial deposition of sediments, the mouth barprogrades and aggrades until the depth over the bar is shal-low enough to create an upstream fluid pressure that is ca-pable of forcing the fluid around the bar rather than overthe bar. The mouth bar then widens, creating a classic trian-gular deposit in planar view.

[52] Following the notation used by Edmonds and Sling-erland [2007], h and h0 are defined as the water depthabove the peak of the river mouth bar and the channeldepth at the landward boundary (the water depths beingreferred to the mean sea level). In order to explore changesin residual currents during bar evolution, additional numer-ical experiments have been conducted during the growth ofa bar, for ratio h/h0 equal to 0.8, 0.6, and 0.4. Successively,the morphology of the bottom was frozen, i.e., maintainedconstant in time, preventing the bar from growing or beingdemolished, and two purely hydrodynamic simulationswere run, one with tides and one without them. The resid-ual velocities are computed from the difference betweenthe velocity averaged over a tidal cycle and the velocity

Figure 5. (a) Water level and (b) depth-averaged velocityin time. Different colors correspond to different distancesfrom the inlet along the centerline. The location of thepoints is indicated in Figure 1 (A is the closest to the rivermouth, E the farthest). (c) Phase shift between velocity andwater level oscillations for points along the centerline.

Figure 6. Water surface profile along the domain center-line at (a) low tide and (b) high tide; (c) water level in time(blue line) and difference between the velocities in twopoints within the channel (red line), representative of thespatial velocity gradient.

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without tide (Figures 7b–7d and 8b–8d). Residual veloc-ities are found to increase when the mouth bar grows.Under dominant fluvial conditions, for example, for a tidalamplitude of 0.75 m, the maximum residual velocity isaround 0.05 m/s for h/h0¼ 1, and 0.15 m/s for h/h0¼ 0.4.

[53] The presence of tides also promotes variations inbottom morphology. Even though fluvial conditions domi-nate, tides increase bar widening (Figure 9). At the begin-ning of bar formation, the greater is the tidal range, thehigher are the residual velocities, which in turn increasesediment transport rates. Figure 10 shows longitudinal pro-files of the bar for increasing tidal amplitudes. Same colorscorrespond to same intervals of time. It is possible to noticethat the part in gray, representative of the initial stage ofmouth bar formation, is higher in the presence of tides. Thetwo lateral bands of residual velocity spread the sediments

at the two sides of the river mouth and the bar immediatelywidens (Figure 10b). When the bar is high enough, the flowis laterally channelized during the ebb phase, when themaximum velocities occur. Hence, the bar confines theflow and favors the bifurcation process. As the magnitudeof the two lateral bands of residual velocity increases, thelateral spreading grows, as well as the tendency of the barto widen. The widening rate also starts prevailing upon theaccretion rate, producing a larger but shallower bar (Figure10). Aggradation rates therefore diminish in the final stagesof bar development for large tidal amplitudes (Figure 10).

[54] The tidal-dominated case may be regarded as thesum of the fluvial-dominated case plus the influence of thetidal discharge. In our simulations the constant river dis-charge is only 10% of the maximum tidal discharge at theriver mouth. However, it is enough to accelerate the

Figure 7. Residual currents for the fluvial-dominated case, at different stages of mouth bar formation.The tidal amplitude is 2.5 m. The isolines in each plot represent the location of the bar.

Figure 8. Residual currents for the tidal-dominated case at different stages of mouth bar formation.The tidal amplitude is 2 m. The isolines in each plot represent the location of the bar. The two blackarrows are indicative of two counterrotating eddies.

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process of bar growth, because of a larger sediment dis-charge due to the presence of the additional riverine flow,and to modify the configuration of the deposit with respectto the fluvial-dominated case. Similar to what happens intidal inlets, the oscillating flow triggered by the tidal prism

leads to the formation of a central channel (Figures 8 and11) due to strong ebbing currents in the central part of thedomain. The presence of the riverine discharge leadsinstead to the formation of two lateral channels, similar tothe fluvial-dominated case. Different from the case of tidal

Figure 9. Fluvial-dominated case: cumulative erosion and sedimentation for different tidal amplitudesht after 3 days of numerical simulation and morphological factor of 15.

Figure 10. Morphology of river mouth bars for the fluvial-dominated case. (a) Longitudinal and (b)transverse sections of river mouth bars. Each plot corresponds to a different tidal range. Same colors cor-respond to same temporal intervals : gray from 0 to 6 h, blue from 6 to 12 h, gray blue from 12 to 18 h,light blue from 18 to 24 h, light green from 24 to 30 h, green from 30 to 36 h, yellow from 36 to 42 h,pink from 42 to 48 h, red from 48 to 54 h, dark red from 54 to 60 h.

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inlets, the two lateral channels are ebb dominated. In fact,for tidal inlets, the basic ebb delta configuration is a centralchannel, dominated by ebb currents, surrounded by a swashplatform and two lateral channels dominated by flood cur-rents [FitzGerald, 1996; Davis, 1997]. In tidal inlets, flooddominance in the lateral channels is due to the differentflow fields emerging in ebb and flood: while in flood phase,the flow radially distributes near the inlet and in ebb phasethe flow is confined in a central jet [Tambroni et al., 2005].

[55] Figure 12 shows the velocity for three tidal cycles atthe seaward mouth and at the right boundary. At the begin-ning of the simulation the system behaves as a tidal inlet.Therefore, a main central channel forms, dominated by ebbflow, and sediments are deposited at the lateral sides of thechannel. Due to the formation of these initial deposits andthe presence of river discharge, low slack water is delayednear the river mouth. As a result, a transitional period existsduring which slack water is already reached at the rightboundary, but there is still a positive flow at the rivermouth. The water flows through the main channel and it islaterally deviated because of the presence of the initialdeposits. During this period, the system behaves as in thefluvial-dominated case, where a constant discharge is pre-scribed. Moreover, since this transitional period corre-sponds to minimum water levels and maximum spreading,the flow is further constrained in the lateral channels withthe side deposits acting as a flow barrier.

[56] Figure 12b shows the depth-averaged velocity fieldaround low water slack at the right boundary for a bar ele-vation corresponding to h/h0¼ 0.6. The maximum veloc-ities occur in points where the lateral channels are going toform. Once the channels are incised, the confined flow

occupies them during ebb, leading to a velocity higher thanduring flood. To sum up, while a simple bifurcation charac-terizes fluvial-dominated conditions, the tidal-dominatedcase displays three principal channels. Finally, larger tidesaccelerate bar growth and widen the bar deposit similar towhat was observed for the fluvial-dominated case (Figures9 and 11).

[57] To determine the transition between bifurcation(river-dominated case) and the presence of a central chan-nel (trifurcation, tidal-dominated case), we performed a se-ries of additional numerical experiments for two differentinitial basin depths (h0¼ 4.5 m and h0¼ 3.5 m) and twodifferent friction coefficients (C¼ 45 m1/2/s and C¼ 30 m1/

2/s). The transition is a function of the nondimensional tidalamplitude and the relative importance of tidal velocity withrespect to river velocity (Figure 13). We find a robust crite-rion for the formation of a central channel (R2¼ 93%):

u0 � ut

u0 þ ut< 0:34� 1:3

ht

h0ð7Þ

[58] where u0 is the river velocity, ut the maximum tidalvelocity, ht the tidal amplitude, and h0 the water depth.For a given water depth and tidal velocity, the transitionfrom river-dominated to tidal-dominated conditionsrequires a small river velocity with small tides. Note thata large ratio ht/h0 maximizes the drawdown effect on riverdischarge, thus promoting fast shallow flows in the lateralchannels and bifurcation. Moreover, for u0> 2 ut (riverdischarge double the tidal discharge), the bifurcationforms independently of tidal oscillations in the basin (Fig-ure 13). In summary, oscillations in tidally generated

Figure 11. Tidal-dominated case, cumulative erosion and sedimentation for different tidal ranges, after10 days of numerical simulation and morphological factor of 450; ht is the tidal amplitude.

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discharge favor the formation of a central channel,whereas tidal oscillations in the basin favor bifurcationand fluvial mouth bars.

5. Discussion

[59] Based on the results of our numerical analysis, wepresent the following conceptual model of bar formationunder the effect of tides. In the fluvial-dominated case,tides enhance jet spreading (Figure 3), which, in turn, pro-motes lateral residual currents that facilitate the formationof bifurcating channels (Figure 7). Moreover, at low tideeven an incipient mouth bar becomes an obstacle to theflow, given the limited water depths. As a result, more sedi-ments are deposited on the mouth bar, speeding up its ini-tial development (Figure 10). Once the two bifurcatingchannels are emplaced, strong flow establishes at low tide,magnifying the residual currents (Figure 7). These fast,shallow flows transport large quantities of sediments to thesides, creating a wider mouth bar (Figure 9).

[60] In the tidal-dominated case, the remarkable asym-metry between flood and ebb flow fields creates two resid-

ual vortexes that magnify the flow along the central axis(Figure 8). As a result, a central channel forms (Figure 11).The oscillatory flow at the mouth prevents the silting of thecentral channel and two deposits form at the sides (Figure11). These deposits trigger two bifurcations and the forma-tion of two lateral channels, also facilitated by the confinedflow at low tide (Figure 12).

[61] The final bar configurations display similarities tonatural systems. Figure 14 shows the mouth morphology oftwo rivers, the Apalachicola and Suwanee rivers in Florida,USA, with fluvial discharge and tidal features similar tothose considered in this work. The Apalachicola River isfluvial dominated, with a drainage area of approximately50,000 km2 and a mean discharge near Sumatra (FL) of700 m3/s [U.S. Geological Survey, 2012]. The SuwaneeRiver is tidal dominated, with a drainage area of 26,000km2 and a mean discharge of 170 m3/s near Suwanee city(FL) [U.S. Geological Survey, 2010].

[62] The morphology of the Apalachicola mouth bars isdominated by bifurcations (Figure 14d). These landformscan thus be associated with the relatively small influence ofthe tidal discharge with respect to the fluvial discharge. Onthe contrary, in the Suwanee River, the tidal dischargeseems to have a considerable role, indicated by the strong

Figure 12. Tidal-dominated case with tidal amplitude of2.5 m. (a) Velocity variations in time at point A (greenline) and point E (red line). Water level variations at pointA (black line) and E (blue line). The location of the pointsis indicated in Figure 1 (A is the closest to the river mouth,E the farthest). Note that when the red line crosses the zerovalue (near the minimum in water level), the green line hasstill a positive value. (b) Velocity field at low water slackfor height of the bar corresponding to h/h0¼0.6. The iso-lines indicate the location of the bar. Note that peaks ofvelocities occur where the ebb-dominated channels form.

Figure 13. Occurrence of bifurcation or trifurcation at ariver mouth as a function of nondimensional tidal ampli-tude and relative ratio between fluvial and tidal velocity.The green empty symbols represent trifurcations whilethe red-filled symbols are bifurcations. Circles C¼ 45 m1/

2/s, h0¼ 4.5 m; diamonds C¼ 30 m1/2/s, h0¼ 4.5 m; tri-angles C¼ 45 m1/2/s, h0¼ 3.5 m; squares C¼ 30 m1/2/s,h0¼ 3.5 m. The straight green line represents the transi-tion criterion.

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bidirectionality of the flow (Figure 14b). Here mouth barsare characterized by trifurcations, we also notice cases inwhich more than three channels are connected to the samenode, and we ascribe this morphology to the complexity ofthe coastal bathymetry and variability in tidal and river dis-charge that were not captured in our simulations.

[63] Trifurcations do not form only in the presence oflarge tides; Storms et al. [2007] show that a riverdebouching in a deep basin can also produce a centralchannel. However, in their Delft3D simulations the basinis much deeper than ours, as well as deeper than Apalachi-cola Bay and the Suwanee river mouth. Similarly, bifurca-tions can also exist in tidally dominated rivers, locallyfavored by the complexity of the coastal landscape. Ourresults are therefore valid in a statistical viewpoint, withtidal-dominated rivers giving rise, on average, to moretrifurcations.

[64] By modifying mouth bar morphology, tides can alsoaffect the evolution of the entire delta. Wider and shallowerbars favor vertical infilling with respect to lateral prograda-tion. We therefore expect a prevalence of thin and spatially

uniform deposits with fewer vertical discontinuities. Lackof steep gradients in mouth deposits inhibits possible avul-sions, locking the distributaries in place. Wide mouth barscan also affect nearby distributaries, and fewer distributa-ries are needed to feed the entire delta front. Spatiallyextensive deposition would also maintain the mouth barsunder water for a longer time, delaying vegetationencroachment and related sediment bioturbation.

[65] Our analysis has implications for future restorationprojects of deltaic environments. The basic scheme for del-tas restoration consists in diverting sediments from themain channel to subsiding and eroding areas where theycan eventually create new wetlands [Paola et al., 2011].According to Edmonds [2011], the success of such a resto-ration procedure is based on the rates of land growth esti-mated under different configurations of river diversion.Thus, hydrodynamic conditions of areas surrounding theriver diversion are crucial to determine whether sedimentswould deposit near the shore or would be moved into thedeep ocean. Only in the first case the diversion can effec-tively build new land.

Figure 14. (c) Locations of Apalachicola River and Suwanee River, Florida, USA. (a) Apalachicolariver discharge near Sumatra, FL (USGS station 02359170; from 9 April 2012 to 12 April 2012) and (d)satellite image of Apalachicola mouth bars (29�450N, 84�550W). (b) Suwanee river discharge near Suwa-nee, FL (USGS station 02323592; from 9 May 2012 to 11 May 2012) and (e) satellite image of Suwaneemouth bars (29�170N, 83�090W). Data have been obtained from the annual water data report by the U.S.Geological Survey. White arrows indicate channels and white dots indicate mouth bars.

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[66] For the fluvial-dominated case, the presence of tidesgives rise to residual currents causing the lateral spreadingof sediments. These residual currents could eventuallytransport very fine sediment fractions far away from theriver mouth and partially prevent land building. Addition-ally, vegetation encroachment is obstructed due to the factthat mouth bars tend to be shallower and are maintainedunder water for a longer time. Vegetation is generally rec-ognized for its role in accelerating sediment deposition bymeans of flow deceleration and sediment trapping. As veg-etation expands, detritus and fine-grained sediments mixinto the soil matrix, which gradually becomes less dense,finer, and more cohesive [e.g., Feagin et al., 2009; Mariottiand Fagherazzi, 2010; Nepf, 2012].

[67] According to Edmonds [2012a], finer-graded sedi-ments lead to the creation of new lands characterized by arough shoreline, with small bays and fewer but larger inte-rior lands, thus favoring trapping of incoming sedimentsand sheltering land from waves’ erosion. Since vegetationestablishment would be obstructed, all these positive feed-backs would be less effective. For the tidal-dominated case,due to the presence of the central channel, we expect theformation of more elongated deposits, with fewer but largerinterior sediment islands, providing advantageous condi-tions for vegetation growth, encroachment, and protectionfrom wave erosion. The aforeknown considerations suggestthat tides would make sediment diversions and restorationpractices less efficient in a river-dominated case, whilethey would favor them in the presence of a large tidalprism.

6. Conclusions

[68] Mouth bar formation is a complex phenomenon,owing to the interactions of several processes. Amongothers, tides play an important role in determining the finalconfiguration of the mouth deposits. Here, the effect oftides on mouth bars has been analyzed using the computa-tional fluid dynamics package Delft3D. The present workfocuses on two end-member cases: a river with a constantand significant fluvial discharge debouching in a basin withtides (small tidal prism) and a river in which the fluvial dis-charge is small compared to tidal fluxes (large tidal prism).

[69] In the fluvial-dominated case, tides increase, on av-erage, jet spreading, producing mouth bars that are widerwith respect to the case without tides [e.g., Edmonds andSlingerland, 2007]. Fast flows during low tide triggered bythe drawdown water surface profile [Lamb et al., 2012]transport sediments to the sides, increasing the width of thedepositional area. Tidal oscillations therefore act as a dis-persion process similarly to waves [Jerolmack and Swen-son, 2007; Nardin and Fagherazzi, 2012; Nardin et al.,2013]. Moreover, tidal oscillations favor flow bifurcationand the formation of a central mouth deposit. In fact, evenshallow deposits can become obstacles for the flow at lowtide.

[70] In the tidal-dominated case, a central channel formsgiving rise to a trifurcation that is commonly displayed intidal inlets [Hayes, 1975; Fitzgerald, 1976]. Flow reversalduring flood maintains the central channel flushed and pro-duces lateral deposits that trigger two lateral bifurcationsand the formation of side channels. The occurrence of a

bifurcation or trifurcation depends on the relative strengthof the tidal discharge with respect to the fluvial dischargeand the ratio between tidal amplitude and water depth. Ahigh fluvial discharge favors a bifurcation, which is alwayspresent for a river velocity more than twice the tidal veloc-ity. A high tidal range at the river mouth also favor bifurca-tions with respect to trifurcations. Two examples from theGulf of Mexico, USA, agree well with our findings. TheApalachicola Delta, characterized by a large fluvial dis-charge, is dominated by bifurcations, while the mouth ofthe Suwannee River, characterized by an oscillating dis-charge, displays on average more trifurcations.

[71] Acknowledgments. This research was supported by ExxonMobil Upstream Research Company award EM01830, the ACS-PRF pro-gram award 51128-ND8, by NSF award OCE-0948213 and through theVCR-LTER program award DEB 0621014.

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