Understanding Morphodynamic Changes of a Tidal River Conﬂuence Through Field Measurements and Numerical Modeling

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Article Understanding Morphodynamic Changes of a Tidal River Conﬂuence through Field Measurements and Numerical Modeling

Qiancheng Xie 1,* , James Yang 2,3 , Staffan Lundström 1 and Wenhong Dai 4

1 Division of Fluid and Experimental Mechanics, Luleå University of Technology (LTU), 97187 Luleå, Sweden; [email protected] 2 Division of Resources, Energy and Infrastructure, Royal Institute of Technology (KTH), 10044 Stockholm, Sweden; [email protected] 3 Vattenfall AB, Research and Development (R & D), Älvkarleby Laboratory, 81426 Älvkarleby, Sweden 4 College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China; [email protected] * Correspondence: [email protected]; Tel.: +46-72-2870-381

Received: 20 August 2018; Accepted: 8 October 2018; Published: 11 October 2018

Abstract: A confluence is a natural component in river and channel networks. This study deals, through field and numerical studies, with alluvial behaviors of a confluence affected by both river run-off and strong tides. Field measurements were conducted along the rivers including the confluence. Field data show that the changes in flow velocity and sediment concentration are not always in phase with each other. The concentration shows a general trend of decrease from the river mouth to the confluence. For a given location, the tides affect both the sediment concentration and transport. A two-dimensional hydrodynamic model of suspended load was set up to illustrate the combined effects of run-off and tidal flows. Modeled cases included the flood and ebb tides in a wet season. Typical features examined included tidal flow fields, bed shear stress, and scour evolution in the confluence. The confluence migration pattern of scour is dependent on the interaction between the river currents and tidal flows. The flood tides are attributable to the suspended load deposition in the confluence, while the ebb tides in combination with run-offs lead to erosion. The flood tides play a dominant role in the morphodynamic changes of the confluence.

Keywords: tidal river confluence; flow features; morphological changes; field measurements; numerical simulations

1. Background A river confluence is a key feature of a drainage basin in terms of hydrology and geomorphology, for geological records, as well as from a habitat point of view [1]. In the confluence, two merging run-off streams often result in enhanced turbulent mixing. This has a bearing on transported sediment and its amount delivered downstream. In a long-term perspective, the flow patterns govern the morphology changes of the confluence, e.g., the scouring and sediment deposition [2]. Many studies focused on hydrodynamic patterns and morphology changes in run-off confluences. Mosley [3] was a pioneer in the research, which was further developed by Best who defined six distinct hydraulic regions in a confluence [2,4]. Those included areas of flow stagnation, flow deflection, flow separation, maximum velocity, gradual flow recovery, and shear layers. With advanced instrumentation and novel experimental design, research of river confluences evolved and focused on the separation zone and the shear layer [5–8]. Yuan et al. [9] made a review of the state of the art in hydraulic research of run-off confluences. Best [2] examined principal morphological features

Water 2018, 10, 1424; doi:10.3390/w10101424 www.mdpi.com/journal/water Water 2018, 10, 1424 2 of 21 such as deep scour holes, bank-attached lateral bars, tributary-mouth bars, and a region of sediment accumulation in a river confluence. Other similar studies looked at the sediment and morphological aspects at non-tidal alluvial confluences [10–12]. They contributed to the understanding of the confluence scouring. A literature review shows that limited attention is drawn to tidal confluences with bi-directional flows [4]. In tidal environments, the confluence is also affected by tidal currents. As a result, the alluvial process in terms of erosion and deposition is different, which is an issue of concern for many practical applications, especially if the confluence is in an urban development area. Pittaluga et al. [13] investigated the morphodynamic equilibrium of alluvial estuaries, where river flows and tides meet. The complexity in a tidal confluence does not draw much attention [4,14,15]. In bi-directional flows, the shift of the dominant processes between river run-off and tides, featuring periodical changes in both magnitude and direction, induces more degrees of complexity in terms of flow patterns, sediment transport, and bed morphology change in the confluence. Ferrarin et al. [16] identified 29 scour holes at tidal channel confluences by examining their geomorphological characteristics and comparing them with scours in rivers. As a consequence of changes in the flow regime, their findings revealed, on a century scale, the morphological dynamics of scouring. Field studies [10–12] and laboratory experiments [17–20] are major tools for studying sediment transport and the hydromorphic process in a confluence. In some studies, field measurements were made with tides; their purpose was to examine transport of the bed load [21–23]. The study of suspended load in tidal confluences is limited. One reason is attributable to the fact that it is not easy to, in a controlled manner in the laboratory, produce flow conditions of suspended load in combination with tides. Due to the complexity of the process, erosion and deposition are still not well understood [18]. Hypotheses are usually made that the origin of mid-stream scour is related to high flow velocity, strong turbulence, and the effect of shear layer or curvature-induced helical circulation [2,18–20]. Numerical modeling allows duplications of complex boundary conditions and prediction of different scenarios in a short time [24–29], which is also true for the study of tidal river confluences. Previous attempts were made with three-dimensional (3D) models for simulations of secondary circulations and flow variations in the vertical direction [30,31]. For a shallow confluence with a large width-to-depth ratio, a depth-averaged model is an acceptable compromise if necessary corrections of cross-circulatory motion are made [32–35]. In this research, field measurements of flow and sediment were made in the study area including the confluence. A two-dimensional (2D) morpho-dynamic model was set up, in which the cohesive suspended sediment transport was simulated. The objective was, by means of field measurements and simulations, to provide insight into the physical phenomenon that governs flow features of the tidal confluence, to describe circulatory patterns of suspended load transport, and to predict the scour-hole evolution. This study reveals the relationship between the velocity and suspended sediment movement influenced by both the run-off and the tides. The results provide reference to behaviors of tidal currents, sediment transport patterns, and fluvial process in similar situations. The paper includes a description of the study area, field measurements of flow and sediment and data analyses, numerical formulation, model set-up with calibration and validation, major flow features, and morphological changes of the confluence.

2. Study Area The confluence in question is called Sanjiangkou, formed by the Fenghua and the Yao River in southeast China. The stream after the confluence is called the Yong River. It is approximately 26 km upstream from the mouth into the Pacific Ocean (Figure1). The Yao River runs into the junction roughly at a 90◦ angle with the other two rivers. The confluence is significantly affected by combined actions of river run-off and tidal currents. The bed load is negligibly small; the sediment transport in the rivers is mainly in form of suspended load, a common feature of many fluvial rivers [36]. WaterWater 20182018,, 1010,, 1424x FOR PEER REVIEW 33 of of 2120

Measured at the normal water surface, the width of the Fenghua River ranges from 90 to 180 m, and itsMeasured average at bed the normalslope is water 0.81%. surface, The reach the width near ofthe the confluence Fenghua River is almost ranges straight; from 90 its to 180cross-section m, and its averageis nearly bed U-shaped. slope is The 0.81%. yearly The averaged reach near run-off the confluence is 53.6 m3 is/s; almost the annual straight; sediment its cross-section discharge isis nearly4.35 × U-shaped.104 tons [36]. The yearly averaged run-off is 53.6 m3/s; the annual sediment discharge is 4.35 × 104 tons [36]. The normal width of the Yao River ranges from 180180 to 230 m. About 500 m m before before the the confluence, confluence, a local constriction exists, with it itss water-surface width expanding from 140 to 180 m at at the the confluence. confluence. The dailydaily run-off,run-off, as wellwell asas sedimentsediment transport,transport, is controlled by the sluicesluice gates located 3.3 km upstream ofof thethe confluence;confluence; thethe annualannual sedimentsediment dischargedischarge isis comparativelycomparatively small.small.

Figure 1. The water system, locations of the river confluence, conﬂuence, and hydrological stations of water levels (WL)(WL) andand ofof ﬂowflow andand sedimentsediment (FS).(FS).

The Yong RiverRiver runsruns roughlyroughly inin thethe west–east direction,direction, withwith its normal width ranging from 150 3 toto 250250 m.m. TheThe averageaverage river-bedriver-bed slopeslope isis 0.117%.0.117%. ItsIts annualannual meanmean run-offrun-off is is approximately approximately 92 92 m m/s3/s × 9 3 (annual(annual averageaverage run-offrun-off 2.9122.912 × 109 m3).). The The peak peak discharge discharge of of run-off run-off and tides occurs normallynormally 3 during the secondsecond halfhalf ofof June,June, amountingamounting toto aboutabout 18001800 mm3/s./s. The The field field recording stations for river waterwater levels (WL) (WL) and and of of flow flow and and sediment sediment (FS) (FS) are are also also marked marked in Figure in Figure 1. At1. the At theriver river mouth, mouth, e.g., e.g.,at station at station WL6, WL6, the theannual annual mean mean tidal tidal range range is 1. is91 1.91 m; m; the the flood flood and and ebb ebb durations durations are are almost the same, approximatelyapproximately 6 6 h. h. The The tidal tidal asymmetry asymmetry aggregates aggregates from from the the river river mouth mouth to theto the upstream. upstream. In the In confluence,the confluence, the ebbthe durationebb duration is 40 minis 40 longer min longer than the than flood the duration. flood duration. At station At WL7, station the WL7, duration the differenceduration difference becomes 60becomes min [36 60]. min On the[36]. Yao On River,the Yao the River, sluice the gates sluice stop gates the stop tidal the propagation tidal propagation further upstream.further upstream. As for theAs for location the location of the upstreamof the upst limitream of limit current of current reversals reversals along thealong Fenghua the Fenghua River, theRiver, tides the affect tides approximatelyaffect approximately 15 km 15 upstream km upstream of WL7/FS7; of WL7/FS7; no records no records are availableare available to show to show the run-offthe run-off influence. influence. The The sediment sediment in the in riverthe river is mainly is ma frominly from the coastal the coastal area andarea is and carried is carried by the by tides. the tides.Local scouring is a typical morphological feature of the river confluence. Our concern of the bed morphologyLocal scouring is is its a scour-holetypical morphological evolution (Figure feature1 ).of the Previous river confluence. field measurements Our concern show of the that bed a scourmorphology hole, like is its a narrowscour-hole and evolution deep crater (Figure along 1) the. Previous Fenghua–Yong field measurements River, exists show in the that confluence a scour andhole, its like deepest a narrow point and is moredeep thancrater 10 along m below the theFenghua–Yong confluence bed River, elevation. exists in During the confluence the earlier and years, its scouringdeepest point dominated is more the than river 10 sedimentation m below the process. confluence Since bed the 1980s,elevation. the studyDuring area the was earlier affected years, by ascouring number dominated of factors, the such river as the sedimentation construction process. of the sluice Since gatesthe 1980s, on the the Yao study River area and was other affected human by activities.a number Theseof factors, changes such modified as the construction the hydraulic of the conditions sluice gates and affectedon the Yao the River erosion and potential other human in the wateractivities. system, These including changes modified the confluence. the hydraulic Bathymetric conditions surveys, and althoughaffected the irregular erosion and potential fragmental, in the show that the morphology tends to shift from erosion to deposition.

Water 2018, 10, x FOR PEER REVIEW 4 of 20

Water 2018, 10, 1424 4 of 21 water system, including the confluence. Bathymetric surveys, although irregular and fragmental, show that the morphology tends to shift from erosion to deposition. 3. Field Measurements 3. Field Measurements 3.1. Data Collection 3.1. Data Collection To map the river and confluence topography and to record the tidal hydrological data, field surveysTo map were the carried river out and during confluence two major topography periods, i.e.,and Juneto record 2015 andthe Januarytidal hydrological 2016. The formerdata, field was surveysused for were this study. carried The out river during bathymetry two major used periods, in the simulationsi.e., June 2015 was and mapped January from 2016. June The 2015–January former was used2016, for which this wasstudy. achieved The river using bathymetry an HY1600 used bathymetric in the simulations profiler (SunNavwas mapped Technology from June Co., 2015 Ltd.,‒ Tianjin,January China).2016, which The hydrologicalwas achieved data using included an HY1600 water bathymetric level, flow velocity,profiler (SunNav flow discharge, Technology sediment Co., Ltd.,concentration, Tianjin, China). grain-size The distribution, hydrological water data quality, included and water salinity. level, flow velocity, flow discharge, sedimentThe waterconcentration, levels were grain-size monitored distribution, at seven cross-sectionswater quality, (WL1–WL7),and salinity. five of which were along the YongThe River.water Tolevels measure were flowmonitored velocity at andseven suspended cross-sections sediment, (WL1 seven‒WL7), corresponding five of which cross-sections were along (FS1–FS7)the Yong River. were arranged, To measure each flow with velocity three plumb and suspended lines (Figure sediment,2). Their seven distances corresponding to the confluence cross- (measuredsections (FS1 along‒FS7) the were river arranged, centerline) each are with given three in Table plumb1. FS5 lines and (Figure FS6 are 2). a fewTheir meters distances apart to from the confluenceeach other and(measured are treated along as the sameriver centerline) section. Along are given each line, in Table the sampling 1. FS5 and was FS6 made are a at few six depthsmeters apartfrom thefrom water each surface,other and i.e., areh =treated 0, 0.2H as0, the 0.4 Hsame0, 0.6 section.H0, 0.8H Along0, and each 1.0H line,0, where the samplingH0 (m) is was the watermade atdepth six depths at each from line. Allthe thewater data surface, were recordedi.e., h = 0, in 0.2 one-hourH0, 0.4H intervals.0, 0.6H0, 0.8H0, and 1.0H0, where H0 (m) is the water depth at each line. All the data were recorded in one-hour intervals. Table 1. Distance of field measurement stations to the confluence. Table 1. Distance of field measurement stations to the confluence. Water Level Station WL1 WL2 WL3 WL4 WL5 WL6 WL7 DistanceWater to confluenceLevel Station (km) 2.20 WL1 0.25WL2 6.00WL3 14.80WL4 20.30WL5 25.20WL6 WL7 2.80 FlowDistance and Sedimentto confluence Station (km) FS1 2.20 FS2 0.25 FS3 6.00 FS4 14.80 20.30 FS5 (FS6) 25.20 2.80FS7 Flow and Sediment Station FS1 FS2 FS3 FS4 FS5 (FS6) FS7 Distance to confluence (km) 2.20 0.25 9.70 18.10 24.70 3.20 Distance to confluence (km) 2.20 0.25 9.70 18.10 24.70 3.20

With a four-beamfour-beam 600/1200-kHz600/1200-kHz RDI RDI Workhorse Workhorse acoustic acoustic Doppler Doppler current current profilers profilers (ADCPs) (Nortek group, Rud, Norway),Norway), water-flowwater-flow velocitiesvelocities andand dischargesdischarges werewere measured.measured. They were attached to the measurement vessels that werewere anchoredanchored onon land.land. The The uncertainty uncertainty of of the flow flow measurements was below ±±5%.5%. The The YJD-1-type YJD-1-type pres pressuresure sensors sensors (Tekscan, (Tekscan, Inc., Inc., South South Boston, Boston, MA, MA, USA) were used for thethe water-levelwater-level measurementsmeasurements andand theirtheir accuracyaccuracy isis ±±11 cm. Major efforts were made to sample the suspended sediment, using point point-integrative-integrative water water samplers samplers (Hoskin (Hoskin Scientific, Scientific, Ltd., Saint-Laurent, QC, Canada). Samples Samples of of the the bed load, although limited in amount, were also taken with Shipek grab samplers samplers (Envco, (Envco, Auckland Auckland,, New New Zealand) Zealand) and and their their amount amount was was calculated. calculated.

Figure 2. Sketch of measurement arra arrangementngement at a cross-section.

The grain-size distribution of the suspended lo loadad was analyzed using an automatic sieving device (SFY-D)(SFY-D) (Zhonghu (Zhonghu Scientific Scientific Ltd., Ltd., Nanjing, Nanjing, China) China) and an and automated an automated laser particle-size laser particle-size analyzer (Mastersizer2000)analyzer (Mastersizer2000) (Malvern (Malvern Panalytical Panalytical Ltd., Worcestershire, Ltd., Worcestershire, UK). Particle UK). sizes Particle falling sizes in thefalling range in thebetween range 0.0002between and 0.0002 2 mm and were 2 mm identified. were identified. The obtained The obtained data are data well aresuited well suited for calibration for calibration and validationand validation of numerical of numerical models. models. The fieldThe datafield acquireddata acquired during during the wet the season, wet season, i.e., the i.e., second the second half of Junehalf of 2015, June were 2015, analyzed were analyzed to determine to determine the sediment the sediment features in features the study in areathe study including area the including confluence. the Theyconfluence. are also They used are for also calibration used for and calibration validation. and validation.

Water 2018, 10, 1424 5 of 21

3.2. Features of Suspended Sediment For each WL and FS station, the time series of the raw measurement data were analyzed. For each time period, the average value was first obtained for each plumb line with the six points. Based on the results of the three lines, the cross-sectionally averaged value was achieved using the weighted average method. According to the grain-size distribution, the sediment is classified as sand (0.05–2 mm), silt (0.005–0.05 mm), and clay (<0.005 mm) [37]. The field measurements show that approximately 95% of the river sediment is suspended load of cohesive silt and clay, most of which is carried into the river by the tides from the coastal area, as shown later. Table2 shows their median grain sizes ( D50) from the field data. In the spring tide, the D50 values vary from 0.005–0.009 mm for the suspended load, and from 0.008–0.017 mm for the bed load. In the neap tide, the corresponding ranges are 0.006–0.009 mm and 0.009–0.020 mm, implying that the D50 values are slightly larger.

Table 2. Median grain sizes (D50) of suspended and bed load during the wet season (second half of June 2015).

Spring Tide, D50 (mm) Neap Tide, D50 (mm) Station Suspended Load Bed Load Suspended Load Bed Load FS1 0.005 0.008 0.008 0.009 FS2 0.007 0.013 0.007 0.016 FS3 0.007 0.011 0.008 0.012 FS4 0.008 0.019 0.006 0.020 FS5 (FS6) 0.008 0.011 0.007 0.011 FS7 0.009 0.017 0.009 0.013

The study area experiences a semi-diurnal tide—two nearly equal high and low tides each day, belonging to the category of incomplete standing waves. The second half of June 2015 includes 30 semi-diurnal tides, with 30 flood and ebb tides. S (kg/m3) denotes the mean sediment concentration at a cross-section. To look at its spatial changes during the period, Table3 summarizes the time-averaged S values at FS1–FS7. The following features were observed: (1) Going upstream from FS4, including the confluence, the suspended sediment experiences a trend of decrease in concentration during the semi-diurnal tides. The maximum value of S along the Yong River always occurs at FS4, with a peak value of 2.341 kg/m3 during the spring tides. (2) At the same location during the semi-diurnal tides, the sediment concentration during the spring tide is 3–8 times higher than that during the neap tide. (3) For either the spring or neap tide at the same location, the sediment concentration of the flood tides differs from that of the ebb tides; the spring tides feature higher values than the neap tides. This implies that the spring tides govern the transport of the suspended sediment from the coastal area. (4) At FS2, the flood tides carry more sediment than the neap tides, which means that the former dominates the sediment to the confluence.

Table 3. Time-averaged mean sediment concentration (S) values during the wet season (second half of June 2015).

Spring Tide (kg/m3) Neap Tide (kg/m3) Station Flood Tide Ebb Tide Semi-Diurnal Tide Flood Tide Ebb Tide Semi-Diurnal Tide FS1 - - 0.229 - - 0.069 FS2 0.780 0.541 0.677 0.121 0.089 0.106 FS3 1.247 1.615 1.441 0.200 0.215 0.208 FS4 2.341 2.117 2.207 0.232 0.318 0.282 FS5 (FS6) 1.673 1.476 1.578 0.314 0.214 0.265 FS7 0.895 0.920 0.909 0.142 0.141 0.141 Water 2018, 10, x FOR PEER REVIEW 6 of 20

Water 2018, 10, x FOR PEER REVIEW 6 of 20 Water 2018, 10, 1424FS7 0.895 0.920 0.909 0.142 0.141 0.141 6 of 21 FS7 0.895 0.920 0.909 0.142 0.141 0.141 To further unveil the streamwise influence of the tides on the sediment, cross-sections FS5 (FS6) andTo FS2To further further were selected unveil unveil the theon streamwisethestreamwise Yong River. influence influence The former of of the the istides tides close on on to the the sediment, sediment,river mouth cross-sections cross-sections and the latter FS5 FS5 to(FS6) the (FS6) andandconfluence. FS2 FS2 were were Figures selected selected 3 and onon the the4 compare, YongYong River. for the The spring former former and is is closeneap close totides, to the the theirriver river relationshipmouth mouth and and the between the latter latter toS andthe tothe confluence.confluence.V, where V Figures (m/s)Figures refers3 and3 and to4 compare,the4 compare, mean flow for for the velocitythe spring spring at and aand river neap neap cross-section, tides, tides, their their relationship positiverelationship toward betweenbetween the sea SS [38].andand V, whereVA, negativewhereV (m/s) V (m/s)V value refers refers implies to to the the tidal mean mean reversal flow flow velocity velocity of the current. at a a ri riverver cross-section, cross-section, positive positive toward toward the thesea sea[38]. [ 38]. AA negative negativeV Vvalue value implies implies tidaltidal reversal of the the current. current.

Figure 3. Station FS5 (FS6), mean flow velocity vs. mean sediment concentration (V–S) relationship for spring and neap tides: (a) Spring tide; (b) Neap tide. FigureFigure 3. 3.Station Station FS5 FS5 (FS6), (FS6), mean mean ﬂow flow velocity velocity vs. vs. mean mean sediment sedimentconcentration concentration ((VV––SS)) relationshiprelationship for springfor spring and neapand neap tides: tides: (a) Spring(a) Spring tide; tide; (b) ( Neapb) Neap tide. tide.

FigureFigure 4. 4.Station Station FS2, FS2,V V––SS relationshiprelationship for for spring spring and and neap neap tides: tides: (a ()a Spring) Spring tide; tide; (b) ( bNeap) Neap tide. tide. Figure 4. Station FS2, V–S relationship for spring and neap tides: (a) Spring tide; (b) Neap tide. TheTheV Vand andS Svalues values inin thethe springspring tides are are larger larger than than in in the the neap neap tides. tides. S variesS varies significantly significantly duringduringThe a a tidal tidalV and period, period, S values with with in twotwo thepeaks, peaks,spring implyingtides are thlarger thatat the the than sediment sediment in the concentration neap concentration tides. S isvaries dominated is dominated significantly by bythe the tidesduringtides along along a tidal the the period, river. river. The Thewith floodflood two peaks, tidaltidal V implying and SS areare th alwaysat always the sediment out out of of phase phaseconcentration with with one one isanother; dominated another; the the peakby peakthe S S appearstidesappears along during during the theriver. the floodflood The tides.floodtides. tidalAlong V andthe the river,S river, are alwaysthe the peak peak out of of ofSS phasealmostalmost with synchronizes synchronizes one another; with with the that peak that of VS of V exceptappearsexcept for for during during during the the the flood neap neap tides. tidetide atatAlong thethe riverriverthe river, mouth. the This Thispeak implies impliesof S almost that that the synchronizes the sediment sediment concentration with concentration that of Vis is subjectedexceptsubjected for to to during modifications modifications the neap byby tide thethe at tidestides the at river the the mouth.rive riverr mouth mouth This andimplies and other other that oceanic oceanic the sediment processes processes concentration like like coastal coastal up- is up- andsubjectedand downwelling, downwelling, to modifications storm storm surges, surges, by the etc. etc.tides at the river mouth and other oceanic processes like coastal up- andDuring downwelling,During the the spring spring storm tide, tide, surges, it isit the is etc. strongthe strong tidal tidal currents currents that dominatethat dominate the river the flowriver andflow that and transport that thetransport sedimentDuring the towardthe sediment spring the toward confluence.tide, it theis theconfluence. During strong the tidal Duri neap currentsng tide, the neap the that tide tide, dominate is the comparatively tide the is comparativelyriver weak;flow and its weak;S thatvalues aretransportits much S values lower the are sediment (Figuresmuch lower toward3b and (Figures4 theb). confluence. Judging 3b and from4b). Duri Judging this,ng onethe from neap can this, saytide, one that the can thetide say run-off is thatcomparatively the plays run-off a major weak; plays role. Thisitsa major S leads values role. to are the This much non-similarity leads lower to the (Figures non-similarity of S and3b andV between 4b). of S Judging and the V between springfrom this,and the one spring neap can tides. sayand that neap The the tides. tidal run-off currentsThe plays tidal are currents are essential for stirring sediment, modifying its peak duration, as well as its transport. If essentiala major forrole. stirring This leads sediment, to the non-similarity modifying its of peak S and duration, V between as the well spring as its and transport. neap tides. If there The tidal was no there was no tide, S would be directly proportional to the river discharge and sediment would only tide,currentsS would are essential be directly for proportionalstirring sediment, to the modifying river discharge its peak and duration, sediment as well would as its only transport. be diverted If be diverted downstream [39]. downstreamthere was no [39 tide,]. S would be directly proportional to the river discharge and sediment would only be diverted downstream [39]. 4. Numerical Modeling 4. Numerical Modeling 4. NumericalBased on Modeling the Delft3D package [40], a 2D depth-averaged model was used to help understand Based on the Delft3D package [40], a 2D depth-averaged model was used to help understand the complex flow features and morphology changes of the confluence. Delft3D-Flow is a separate the complexBased on flow the features Delft3D andpackage morphology [40], a 2D changes depth-averaged of the confluence. model was Delft3D-Flowused to help understand is a separate module in the package, in which sediment motion and morphology change are coupled with the flow modulethe complex in the package,flow features in which and morphology sediment motion changes and of morphology the confluence. change Delft3D-Flow are coupled is witha separate the flow moduleto simulate in the flow package, patterns in andwhich morphological sediment motion changes. and morphology change are coupled with the flow to simulate flow patterns and morphological changes. to simulate flow patterns and morphological changes. 4.1. Mathematical Formulation The governing equations are based on the Navier–Stokes equations, with Leibniz integration in the vertical direction, to obtain depth-averaged flow parameters. The vertical flow acceleration Water 2018, 10, 1424 7 of 21 is neglected, leading to the hydrostatic pressure. The turbulence shear stress is solved by the k-ε turbulence model. The river-bed stability coefficient and resistance are parameters that govern the sediment scouring and deposition. The governing equations include, therefore, mass continuity, flow motion, sediment transport, and bed deformation. The depth-averaged continuity equation is ∂ξ 1 ∂ HUξ Gηη 1 ∂ HUη Gξξ + + = q, (1) ∂t Gξξ Gηη ∂ξ Gξξ Gηη ∂η where H is water depth, Uξ(ξ, η) and Uη(ξ, η) (m/s) are the depth-averaged velocities in the ξ and η coordinate system, Gξξ and Gηη (m) are coefficients for transformation of the curvilinear to orthogonal coordinates, q (m/s) is the global source or sink term per unit area, and t (s) is time. The momentum equations in the ξ and η directions are

2 ∂Uξ Uξ ∂Uξ Uη ∂Uξ Uη ∂Gηη UξUη ∂Gξξ 1 + + − + − f Uη = − Pξ + Fξ + Mξ, (2) ∂t Gξξ ∂ξ Gηη ∂η Gξξ Gηη ∂ξ Gξξ Gηη ∂η ρ0Gξξ

2 ∂Uη Uξ ∂Uη Uη ∂Uη Uξ ∂Gξξ UξUη ∂Gηη 1 + + − + + f Uξ = − Pη + Fη + Mη, (3) ∂t Gξξ ∂ξ Gηη ∂η Gξξ Gηη ∂η Gξξ Gηη ∂ξ ρ0Gηη 3 where ρ0 (kg/m ) is water density (except in the baroclinic pressure terms, variations in ρ0 are 2 2 neglected), Pξ and Pη (kg/(m s )) are pressure gradients, f (1/s) is the Coriolis parameter (i.e., inertial 2 frequency), Mξ and Mη (m/s ) refer to contributions from external sources or sinks of momentum 2 (within the computational domain Mξ = Mη = 0), Fξ and Fη (m/s ) are horizontal Reynolds stresses ∂τ ∂τ based on the eddy viscosity concept and change in both space and time, and F = 1 ξξ + 1 ξη , ξ Gξξ ∂ξ Gηη ∂η 1 ∂τηξ 1 ∂τηη 2 Fη = + , and τ ,τηη, τ , and τ (N/m ) are turbulence shear stresses. Gξξ ∂ξ Gηη ∂η ξξ ξη ηξ As noted from the in situ data, the bed load amount is small (below 5%). For the sake of simpliﬁcation, only the cohesive suspended sediment is considered in the sediment model. The 2D transport equations for suspended load are given by

∂(HS) 1 ∂ HUξ S 1 ∂ HUηS 1 ∂ H ∂S 1 ∂ H ∂S + + = vs + vs − FS, (4) ∂t Gξξ ∂ξ Gηη ∂η Gξξ ∂ξ Gξξ ∂ξ Gηη ∂η Gηη ∂η

2 where Fs is the function of the river-bed deformation and υs (m /s) is the sediment diffusion coefficient. 2 For large-scale river simulations, the recommended υs value is 10 m /s and it was used in the simulations. The river-bed deformation is dependent upon sediment erosion and deposition and it is expressed as ∂Z γ b = F , (5) 0 ∂t s

Fs = Db − Eb, (6)  τb ωsS 1 − τ ≤ τ b τd b d Db = , (7) 0 τd < τb  M τb − 1 τ ≥ τ τe b e Eb = , (8) 0 τb < τe

2 where Zb (m) is the bed elevation, γ0 (N/m) is the dry weight of suspended load, Db (kg/(m s)) is 2 the sediment ﬂux of deposition from suspended load, Eb (kg/(m s)) is the sediment ﬂux of erosion 3 resulting in suspended load, ωs (m/s) is the particle settling speed, Sb (kg/m ) is the sediment Water 20182018,, 1010,, 1424x FOR PEER REVIEW 88 of of 2120

concentrationWater 2018, 10, xat FOR h =PEER H, τREVIEWb (N/m 2) is the bed shear stress, τd and τe (N/m2) are the critical stresses8 of 20 of 2 2 concentrationdeposition and at erosion,h = H, τ andb (N/m M (kg/m) is the2s) bedis the shear bed stress,scouringτd rate.and τe (N/m ) are the critical stresses of 2 2 depositionconcentration and erosion,at h = H and, τb (N/mM (kg/m) is the2s) bed is the shear bed stress, scouring τd and rate. τe (N/m ) are the critical stresses of 2 4.2.deposition Grid and Bathymetryand erosion, and M (kg/m s) is the bed scouring rate. 4.2. Grid and Bathymetry 4.2.In Grid an andorthogonal Bathymetry curvilinear grid, the finite-difference method solves the partial differential equationsIn an in orthogonal Delft3D-Flow. curvilinear The variables grid, the of water finite-difference stage, bed level, method and solves flow velocity the partial were differential arranged equationsIn an in Delft3D-Flow.orthogonal curvilinear The variables grid, the of waterfinite-difference stage, bed method level, and solves flow the velocity partial were differential arranged in equationsa staggered in grid.Delft3D-Flow. Delft3D-Rgfgrid, The variables a module of water of thestage, package, bed level, generated and flow the velocity computational were arranged grid. A in a staggered grid. Delft3D-Rgfgrid, a module of the package, generated the computational grid. qualityin a staggered grid is the grid. prerequisite Delft3D-Rgfgrid, for reliable a module simulations. of the package, It should generated be smooth the computational enough to minimizegrid. A A quality grid is the prerequisite for reliable simulations. It should be smooth enough to minimize discretizationquality grid errors;is the prerequisitethe cells should for reliable be as orthogon simulations.al as Itpossible, should bewith smooth a non-orthogonal enough to minimize factor less discretization errors; the cells should be as orthogonal as possible, with a non-orthogonal factor less thandiscretization 0.02 [40]. Figure errors; 5 theshows cells the should grid begenerated as orthogon for althe as modeled possible, areawith witha non-orthogonal the confluence. factor The less total than 0.02 [40]. Figure5 shows the grid generated for the modeled area with the confluence. The total riverthan length 0.02 [40]. of the Figure study 5 showsarea was the about grid generated 32.5 km; thefor thearea modeled was covered area with by a the grid confluence. of 102,600 The cells, total with river760river streamwise length length of of thecells the studystudy and 135 area transverse was was about about cells. 32.5 32.5 km; Several km; the the area grids area was of was coveredvarying covered bycell a sizesgrid by aof were grid 102,600 oftested 102,600 cells, to withensure cells, withgrid760 independent 760 streamwise streamwise cellssolutions. cellsand 135 and Grid transverse 135 independence transverse cells. Several cells. was checked Severalgrids of varying gridsthrough of cell varyingsteady-state sizes were cell flow sizestested calculations. wereto ensure tested toFromgrid ensure a independent relatively grid independent coarse solutions. grid, solutions.Grid the mesh independence Gridrefinement independence was was checked made was through both checked globally steady-state through and locally. flow steady-state calculations. A larger flow cell calculations.densityFrom wasa relatively given From to acoarse relativelythe confluence grid, coarsethe mesh area, grid, refinement with the mesha minimum was refinement made cell both size was globally of made 5 m. and both locally. globally A larger and locally. cell A largerdensity cell was density given to was the given confluence to the area, confluence with a minimum area, with cell a minimum size of 5 m. cell size of 5 m.

FigureFigure 5. 5. Computational Computational domain domain with with cells. cells.

TheThe modulemodule module Delft3D-Quickin Delft3D-Quickin Delft3D-Quickin generated generatedgenerated the the river rive bathymetricalrr bathymetricalbathymetrical data. data. data. The The bathymetryThe bathymetry bathymetry of theof of studythe the areastudystudy with area area the with with conﬂuence the the confluence confluence is shown is is shown inshown Figure inin 6FigureFigure. 6.

Figure 6. Bathymetry of the study area with confluence. Figure 6. Bathymetry of the study area with confluence.confluence. 4.3.4.3. Boundary Boundary and and Initial Initial Conditions Conditions 4.3. Boundary and Initial Conditions There were three open boundaries in the model: two upstream inflows and one outflow. For the There were three open boundaries in the model: two upstream inflows and one outflow. For the formerThere (FS1 were and three FS7), open the boundariestime series of in thethe tribmodel:utary two flow upstream discharges inflows were andspecified; one outflow. for the latterFor the former (FS1 and FS7), the time series of the tributary flow discharges were specified; for the latter former (FS1 and FS7), the time series of the tributary flow discharges were specified; for the latter

Water 2018, 10, x FOR PEER REVIEW 9 of 20

Water 2018, 10, 1424 9 of 21 (WL6), the time series of the water level was given. The change in sediment concentration as a Waterfunction 2018, of10, timex FOR was PEER also REVIEW specified at all the boundaries. Figure 7 displays the measured Q, Z,9 and of 20 S (WL6),profiles the at the time three series boundaries, of the water where level Q was (m given.3/s) and The Z (m) change denote in sediment flow discharge concentration and the as water a function stage (WL6), the time series of the water level was given. The change in sediment concentration as a ofat a time cross-section, was also specified respectively. at all The the wetting boundaries. and dryi Figureng functions7 displays of the cells measured in the domainQ, Z, were and Sactivatedprofiles function of time was also specified at all the boundaries. Figure 7 displays the measured Q, Z, and S atto thereflect three the boundaries, rise and fall whereof the tides.Q (m3 /s) and Z (m) denote flow discharge and the water stage at a profiles at the three boundaries, where Q (m3/s) and Z (m) denote flow discharge and the water stage cross-section, respectively. The wetting and drying functions of cells in the domain were activated to at a cross-section, respectively. The wetting and drying functions of cells in the domain were activated reflect the rise and fall of the tides. to reflect the rise and fall of the tides.

Figure 7. Boundary conditions with measured data: (a) Flow discharge (Q); (b) Water stage (Z); (c) S. FigureFigure 7. 7. BoundaryBoundary conditions conditions with with measured measured data: data: ( (aa)) Flow Flow discharge discharge ( (QQ);); ( (bb)) Water Water stage stage ( (Z);); ( c) S..

Initial conditions referred to specifications of water flow and sediment in the domain. The water InitialInitial conditionsconditions referredreferred toto specificationsspecifications ofof waterwater flowflow andand sedimentsediment inin thethe domain.domain. TheThe waterwater level was first patched and the corresponding flow velocity was estimated by the program. levellevel waswas firstfirst patchedpatched andand thethe correspondingcorresponding flowflow velocityvelocity waswas estimatedestimated byby thethe program.program. Approximately one hour was taken to reach a steady-state flow. Then, the sediment concentration was ApproximatelyApproximately oneone hourhour waswas takentaken toto reachreach aa steasteady-statedy-state flow.flow. Then,Then, thethe sedimentsediment concentrationconcentration patched. After another hour, the sediment conditions became steady, based on which the dynamic waswas patched.patched. AfterAfter anotheranother hour,hour, thethe sedimentsediment conditionsconditions becamebecame steady,steady, basedbased onon whichwhich thethe changes of flow and bathymetry governed by the boundary conditions were then updated. This is dynamicdynamic changeschanges ofof flowflow andand bathymetrybathymetry governedgoverned byby thethe boundaryboundary conditionsconditions werewere thenthen updated.updated. shown in Figure8. ThisThis isis shownshown inin FigureFigure 8.8.

Figure 8. Schematic diagram of the coupled flow ﬂow and sediment calculations. Figure 8. Schematic diagram of the coupled flow and sediment calculations.

Table4 summarizes the additional parameters, ωs, τd, τe, M, and γ0, in the set-up. Table 4 summarizes the additional parameters, ωs, τd, τe, M, and γ0, in the set-up. Table 4 summarizes the additional parameters, ωs, τd, τe, M, and γ0, in the set-up. Table 4. Parameter setting in the model. Table 4. Parameter setting in the model. Table 4. Parameter setting in the model. Parameter Data Range Source Parameter Data Range Source Parameter Data Range Source ω (m/s) 0.0005 Measurements s 𝜔 (m/s) 0.0005 Measurements 𝜔 (m/s)2 0.0005 Measurements τd (N/m ) 2 0.06–0.10 Equation (7) [39] 𝜏 (N/m2 ) 0.06‒0.10 Equation (7) [39] 𝜏 (N/m2 ) 0.06–0.10 Equation (7) [39] τe (N/m ) 2 0.10–0.20 Equation (8) [41] 𝜏 (N/m2 ) 0.10‒0.20 Equation (8) [41] 𝜏 (N/m2 ) 0.10–0.20 Equation (8) [41] M (kg/m s)2 0.0002–0.02 Equation (8) [41] M (kg/m3 2 s) 0.0002‒0.02 Equation (8) [41] γ0M(kg/m (kg/m) s) 0.0002–0.021600 Equation Measurements (8) [41] 3 𝛾 (kg/m ) 1600 Measurements

4.4. Time Step

Water 2018, 10, x FOR PEER REVIEW 10 of 20 Water 2018, 10, 1424 10 of 21

3 𝛾 (kg/m ) 1600 Measurements 4.4. Time Step 4.4. Time Step The choice of the time step (∆t) was based on the Courant number (C), the value of which should be lessThe than choice 10 [ 42of]. the It istime deﬁned step ( asΔt) was based on the Courant number (C), the value of which should be less than 10 [42]. It is defined as s 1 1 C = 2∆t gh( 1 + 1 ), (9) 𝐶=2∆𝑡𝑔ℎ(∆ξ2 + ∆η2), (9) ∆𝜉 ∆𝜂

2 wherewhere gg (m/s(m/s2)) is is the the acceleration acceleration due due to to gravity; gravity; Δ∆tt == 0.3 0.3 s s was was selected. selected. 5. Model Calibration and Validation 5. Model Calibration and Validation 5.1. Model Calibration 5.1. Model Calibration Model calibrations were based on the hourly observed data for the spring tide in 2015, occurring betweenModel 10:00 calibrations a.m. on were 17 June based and on 4:00 the p.m.hourly on obse 18rved June, data representing for the spring 30 h tide in total.in 2015, The occurring model wasbetween tested 10:00 with a.m. several on 17 optionsJune and for 4:00 boundary p.m. on 18 conditions—bed June, representing roughness, 30 h in total. grid The size, model and timewas step.tested Thewith purpose several options was to findfor boundary a reasonable conditions—bed match between roughness, the observed grid size, and and calculated time step. values The ofpurpose flow discharge, was to find water a level,reasonable and sediment match between concentration. the observed The commonly and calculated used criteria values including of flow Nash–Sutcliffedischarge, water efficiency, level, and the sedimentR-squared concentrat method,ion. and The the commonly percent bias used were criteria also usedincluding here forNash– the modelSutcliffe calibration efficiency,[ 43the,44 R]-squared. Table5 showsmethod, the and definitions the percent of thebias error were parameters also used here and for their the ranges, model calibration [43,44]. Table 5 shows the definitions of the error parameters and their ranges, where 𝑂 where Oi = measured value, Pi = predicted value by the model, O = average of measured values, 𝑃 𝑂 𝑃 P= measured= average value, of predicted = predicted values, and valuen = by the the total model, number = of average values. of measured values, = average of predicted values, and n = the total number of values. Table 5. Definition of error parameters and their accepted ranges for calibration. NSE—Nash–Sutcliffe efficiency;Table 5. DefinitionPBIAS—percent of error bias. parameters and their accepted ranges for calibration. NSE—Nash– Sutcliffe efficiency; PBIAS—percent bias. Parameter Optimal Value Satisfactory Equation

Parameter Optimal Value Satisfactory Equationn 2 ∑i=1(O i −Pi ) NSE 1 >0.5 E = 1 − ∑( 2 ) n O −O NSE 1 >0.5 𝐸=1−∑i=1( i ) ∑( ) R2 = !2 2 n ∑( )( ) 2 R 1 >0.5 ∑i=1(Oi −O)(Pi −P) R 1 >0.5 𝑅q = q n 2 n 2 ∑i=1(Oi∑(−O) ∑i=)1(P∑(i −P) ) ± n ±25% for25% flow for rate ﬂow rate ∑i=∑(1(Oi −Pi )×100) PBIAS 0 PBIAS𝑃𝐵𝐼𝐴𝑆= = n PBIAS 0 ±55% for sediment ∑i=1 Oi ±55% for sediment ∑

The river-bedriver-bed roughnessroughness ( n(n)) is is a a key key parameter parameter of of concern concern that that is governedis governed by factors,by factors, such such as the as river-bedthe river-bed morphology, morphology, flow flow patterns, patterns, etc. Based etc. Base on triald on and trial error, and its error, range its was range finally was set finally between set 0.015between and 0.015 0.030, and with 0.030, 0.015–0.018 with 0.015–0.018 for the main for channel the main and channel 0.018–0.030 and for0.018–0.030 the shore for beach. the shore Figures beach.9–11 showFigures the 9–11 final show calibration the final results calibration of V and resultsS at FS2,of V FS3,and S and at FS2, FS4. FS3, and FS4.

Figure 9. Model calibration, numerical vs. field ﬁeld resultsresults at FS2 (spring tide, June 2015): (a) ||V𝑉||;(; (bb)) SS..

Water 2018, 10, x FOR PEER REVIEW 11 of 20

WaterWater 20182018, ,1010, ,x 1424 FOR PEER REVIEW 1111 of of 20 21

Figure 10. Model calibration, numerical vs. field results at FS3 (spring tide, June 2015): (a) |𝑉|; (b) S. FigureFigure 10. 10. ModelModel calibration, calibration, numerical numerical vs. vs. field ﬁeld re resultssults at at FS3 FS3 (spring (spring tide, tide, June June 2015): 2015): (a (a) )||𝑉V|;| ;((bb) )SS. .

FigureFigure 11. 11. ModelModel calibration, calibration, numerical numerical vs. vs. field field re resultssults at atFS4 FS4 (spring (spring tide, tide, June June 2015): 2015): (a) ( a|)𝑉|V|; |(;(b)b S).S . Figure 11. Model calibration, numerical vs. field results at FS4 (spring tide, June 2015): (a) |𝑉|; (b) S. ForFor VV, the, the computed computed results results werewere inin goodgood agreement agreemen witht with the the measured measured ones; ones; the the differences differences were negligibly small for all the stations. For S, despite certain discrepancies between them, the matches were Fornegligibly V, the computedsmall for allresults the stations.were in goodFor S agreemen, despite tcertain with the discrepancies measured ones;between the differencesthem, the were generally satisfactory. The four S peaks within the tidal period were reasonably reproduced, matcheswere negligibly were generally small for satisfactory. all the stations. The fourFor SS, peaksdespite within certain the discrepancies tidal period between were reasonably them, the in terms of both magnitude and phase. For FS2, FS3, and FS4, Table6 shows the calibration results of reproduced,matches were in generallyterms of bothsatisfactory. magnitude The andfour phas S peakse. For within FS2, FS3,the tidaland FS4,period Table were 6 showsreasonably the the error parameters. All the values fell within the ranges required by the criteria. calibrationreproduced, results in terms of the of error both parameters. magnitude All and the valuesphase. fellFor within FS2, FS3,the ranges and FS4, required Table by 6 theshows criteria. the calibration results ofTable the error 6. Error parameters. estimations All of modelthe values calibration fell within (spring the tide, ranges June required 2015). by the criteria. Table 6. Error estimations of model calibration (spring tide, June 2015). Table 6. Error estimationsFS2 of model calibration FS3 (spring tide, June 2015). FS4 Parameter FS2 FS3 FS4 Parameter 3 3 3 VV (m/s)(m/s) FS2SS (kg/m (kg/m3)) V (m/s)(m/s) FS3SS(kg/m (kg/m)3) VV(m/s) (m/s) FS4SS(kg/m (kg/m ) 3) Parameter NSENSE (>0.50)(>0.50) 0.96 0.96 0.82 0.82 3 0.95 0.77 0.77 3 0.930.93 0.760.76 3 2 V (m/s) S (kg/m ) V (m/s) S (kg/m ) V (m/s) S (kg/m ) R2 (0–1)R (0–1) 0.970.97 0.80 0.80 0.95 0.79 0.79 0.940.94 0.780.78 NSE PBIAS(>0.50) 0.96 0.82 0.95 0.77 0.93 0.76 PBIAS2 (±25%) 1.231.23 −−12.5712.57 2.05 −−2.862.86 3.563.56 8.80 8.80 R ((0–1)±25%) 0.97 0.80 0.95 0.79 0.94 0.78 PBIAS (±25%) 1.23 −12.57 2.05 −2.86 3.56 8.80 5.2. Model Validation 5.2. Model Validation 5.2. ModelThe model Validation was validated against a neap tide that occurred during a 31-h period between 3:00 The model was validated against a neap tide that occurred during a 31-h period between 3:00 p.m. p.m. on 24 June and 10:00 p.m. on 25 June of the same year. In the validation, the procedure for result on 24The June model and was 10:00 validated p.m. on against 25 June a of neap the tide same that year. occurred In the validation,during a 31-h the period procedure between for result 3:00 evaluations was the same as for in the calibration. p.m.evaluations on 24 June was and the 10:00 same p.m. as for on in 25 the June calibration. of the same year. In the validation, the procedure for result The validation results are shown in Figures 12–14. The calculated V and S profiles matched well evaluationsThe validation was the same results as are for shown in the calibration. in Figures 12 –14. The calculated V and S profiles matched well with the measured data series. Table 7 shows the validation results of the error parameters for the withThe the validation measured dataresults series. are shown Table7 showsin Figures the validation12–14. The results calculated of the V error and S parameters profiles matched for the threewell three stations. All the values met the requirements of the criteria. The model generated acceptable withstations. the measured All the values data metseries. the Table requirements 7 shows ofthe the validation criteria. Theresults model of the generated error parameters acceptable for results the results and is suitable for prediction of flow and morphology changes of the area including the threeand isstations. suitable All for the prediction values met of flow the andrequirements morphology of changesthe criteria. of the The area model including generated the confluence. acceptable confluence.results and is suitable for prediction of flow and morphology changes of the area including the confluence.

Water 2018, 10, x FOR PEER REVIEW 12 of 20

Water 2018,, 10,, 1424x FOR PEER REVIEW 1212 of of 20 21

Figure 12. Model validation, numerical results vs. field data at FS2 (neap tide, June 2015): (a) |𝑉|; (b) S. Figure 12. Model validation, numerical results vs. field data at FS2 (neap tide, June 2015): (a) |𝑉|; (b) S. FigureFigure 12. 12. ModelModel validation, validation, numerical numerical results results vs. field ﬁeld data at FS2 (neap tide,tide, JuneJune 2015):2015): ((aa))| V|𝑉|;(|; b(b) )S S. .

Figure 13. Model validation, numerical results vs. field data at FS3 (neap tide, June 2015): (a) |𝑉|; (b) S.

FigureFigure 13. 13. ModelModel validation, validation, numerical numerical results results vs. field ﬁeld data at FS3 (neap tide,tide, JuneJune 2015):2015): ((aa))| V|𝑉|;(|; b(b) )S S. . Figure 13. Model validation, numerical results vs. field data at FS3 (neap tide, June 2015): (a) |𝑉|; (b) S.

FigureFigure 14. 14. ModelModel validation, validation, numerical numerical results results vs. vs. fieldﬁeld data data at FS4 (neap tide, JuneJune 2015):2015): ((aa)) |V|𝑉|;(|; b(b))S S. .

Figure 14. ModelTable validation, 7. Error numerical estimations results of model vs. field validation data at FS4 (neap (neap tide, tide, June June 2015). 2015): (a) |𝑉|; (b) S. Table 7. Error estimations of model validation (neap tide, June 2015). Figure 14. Model validation, numericalFS2 results vs. field data FS3 at FS4 (neap tide, June FS4 2015): (a) |𝑉|; (b) S. ParameterTable 7. Error estimationsFS2 of model validationFS3 (neap tide, June 2015).FS4 Parameter 3 3 3 V (m/s) S (kg/m ) 3 V (m/s) S (kg/m ) 3V (m/s) S (kg/m ) 3 Table 7.V Error (m/s) estimations FS2S (kg/m of model) V va(m/s)lidation FS3S (neap (kg/m tide,) JuneV (m/s) 2015). FS4S (kg/m ) NSEParameterNSE (>0.50)(>0.50) 0.96 0.96 0.83 0.83 0.94 0.94 0.81 0.81 0.97 0.97 0.78 0.78 2 V (m/s) S (kg/m3) V (m/s) S (kg/m3) V (m/s) S (kg/m3) 2R (0–1) 0.95FS2 0.84 0.93FS3 0.79 0.96FS4 0.75 NSEParameterR PBIAS (0(>0.50)‒1) 0.95 0.96 0.84 0.83 0.93 0.94 0.79 0.81 0.96 0.97 0.75 0.78 V2.21 (m/s) −S12.99 (kg/m3) 3.05V (m/s) −5.63S (kg/m3) 3.81V (m/s) 9.66S (kg/m3) PBIAS2(± (±25%)25%) 2.21 −12.99 3.05 ‒5.63 3.81 9.66 NSER (0(>0.50)‒1) 0.960.95 0.830.84 0.940.93 0.810.79 0.970.96 0.780.75 PBIAS (±25%) 2.21 −12.99 3.05 ‒5.63 3.81 9.66 R2 (0‒1) 0.95 0.84 0.93 0.79 0.96 0.75 6. Typical Typical Flow Features PBIAS (±25%) 2.21 −12.99 3.05 ‒5.63 3.81 9.66 6. TypicalAccording Flow to Features the statistics of the whole-year water-level data at WL6 during 2015, the tidal frequency6. TypicalAccording ininFlow thethe wettoFeatureswet the season season statistics (the (the 2ndof 2nd the half half whole-year of of June) June) was waswater-level 10%, 10%, 40%, 40%, anddata and 25% at 25% forWL6 thefor during spring,the spring, 2015, mid, mid, andthe neaptidaland neaptides, tides, respectively respectively [45]. Under[45]. Under the combined the combined action action of the of run-off the run-off and tides,and tides, the maximumthe maximum flood flood and frequencyAccording in the to wet the season statistics (the of 2nd the half whole-year of June) waswater-level 10%, 40%, data and at 25% WL6 for during the spring, 2015, mid,the tidal and andebb tidesebb tides of the of spring the spring tides dominatetides dominate the sediment the sedi transport;ment transport; they also they characterize also characterize the flow the features flow frequencyneap tides, in respectively the wet season [45]. Under(the 2nd the half combined of June) action was 10%, of the 40%, run-off and and 25% tides, for the the spring, maximum mid, flood and featuresand they and were they selected were tosele showcted theto show results. the results. neapand ebb tides, tides respectively of the spring [45]. tidesUnder dominate the combined the sedi actionment of transport; the run-off they and alsotides, characterize the maximum the floodflow features and they were selected to show the results. 6.1.and Tidal Tidalebb tidesCurrent of Fields the spring tides dominate the sediment transport; they also characterize the flow features and they were selected to show the results. 6.1. TidalWhen Current the maximum Fields flood tide from the Yong River approached the confluence, the confluence

flow6.1. Tidal saw Current an increase Fields in magnitude. The flow field at the maximum flood tide is shown in Figure 15a.

Water 2018, 10, x FOR PEER REVIEW 13 of 20 Water 2018, 10, 1424 13 of 21 When the maximum flood tide from the Yong River approached the confluence, the confluence flow saw an increase in magnitude. The flow field at the maximum flood tide is shown in Figure 15a. CurrentCurrent reversals reversals occurred occurred because because the the tides tides were were stronger stronger than than the the river river run-off. run-off. It It was was a aflow flow bifurcation.bifurcation. The The surface surface flow flow pattern pattern was was relatively relatively smooth smooth in the in theconfluence. confluence. In the In Yong the Yong River, River, the depth-averagedthe depth-averaged flow flow veloci velocitiesties were were largest largest (0.6 (0.6–0.8‒0.8 m/s). m/s). In the In the Fenghua Fenghua and and Yao Yao rivers, rivers, the the tidal tidal currentscurrents were were weak; weak; the the corresponding corresponding velocities velocities amounted amounted to to 0.4 0.4–0.6‒0.6 and and 0.2 0.2–0.3‒0.3 m/s, m/s, respectively. respectively. Furthermore,Furthermore, the the tidal tidal current current flowing flowing into into the the Ya Yaoo River River was was influenced influenced by by the the bend. bend. Due Due to to the the centrifugalcentrifugal force force [46], [46], its its mainstream mainstream was was close close to to the the concave concave river river bank. bank.

FigureFigure 15. 15. TidalTidal flow flow fields fields during thethe secondsecond halfhalf ofof JuneJune 2015: 2015: ( a(a)) At At the the maximum maximum flood flood tide; tide; (b ()b At) Atthe the maximum maximum ebb ebb tide. tide.

WithWith the the incoming incoming maximum maximum ebb ebb tide tide from from the the two two tributaries tributaries to to the the Yong Yong River, River, the the flow flow velocityvelocity reached reached its its peak peak in in the the confluence. confluence. The The ti tidaldal flow flow field field at at the the maximum maximum ebb ebb tide tide is is illustrated illustrated inin Figure Figure 15b. 15b. In the In theYao Yao andand Yong Yong rivers, rivers, the depth-averaged the depth-averaged velocities velocities were 0.7 were‒0.9 0.7–0.9m/s and m/s 0.4‒ and0.6 m/s,0.4–0.6 respectively. m/s, respectively. In the Fenghua In the River, Fenghua the tidal River, current the tidal was current comparatively was comparatively weak with its weak velocity with amountingits velocity to amounting 0.3‒0.5 m/s. to The 0.3–0.5 simulations m/s. The showed simulations that there showed was a thatsmall there zone was of flow a small circulation zone of closeflow to circulation the left bank close of to the leftconfluence. bank of The the confluence.occurrence was The ascribed occurrence mainly was ascribedto the confluence mainly to geometrythe confluence and also geometry to the anddifference also to in the momentum difference inbetween momentum the two between tributaries the two [47]. tributaries The relative [47]. strengthThe relative of the strength two meeting of the twostreams meeting plays streams a role playsin the alocation role in theand location size of andthe vortex size of zone. the vortex The separationzone. The separationzone occupies zone part occupies of the partchannel of the cross-section, channel cross-section, thus leading thus to leadinga reduction to a reductionin the capacity in the ofcapacity river conveyance. of river conveyance. It causes also It causes sediment also sedimentdeposition deposition in the zone. in the zone. TheThe flow flow velocity velocity in in the the confluence confluence was was smaller smaller than than the the nearby nearby velocities velocities in in the the river river streams. streams. TheThe discrepancy discrepancy was attributedattributed toto the the effect effect of of the th momentume momentum offsetting. offsetting. If twoIf two flows flows merge merge with with each eachother, other, there there is momentum is momentum exchange, exchange, which enhanceswhich enhances the turbulent the turbulent mixing, leading mixing, to leading energy dissipation.to energy dissipation.Moreover, the Moreover, water depths the water in the depths confluence in the were con larger,fluence also were explaining larger, thealso smaller explaining velocities. the smaller velocities.In the confluence, comparison of the velocities at the maximum flood and ebb tides show that the latterIn was the approximatelyconfluence, comparison 0.2 m/s larger of the than velocities the former, at the which maximum was due flood to the and addition ebb tides of theshow ebb that tide theto thelatter run-off. was approximately The volume of 0.2 the m/s ebb larger tide was than also the larger former, than which that ofwas the due flood to tide,the addition while, for of thethe floodebb tidetide, to the the run-off run-off. and The the volume tide were of the in oppositeebb tide was directions, also larger thus than offsetting that of each the other.flood tide, The prevalencewhile, for theheld flood that tide, the velocity the run-off of the and ebb the tide tide was were higher in oppo thansite that directions, of the flood thus tide. offsetting each other. The prevalenceIn summary, held that parting the velocity from the of water the ebb levels, tide thewas confluence higher than flow that at of the the maximum flood tide. flood tide differed in bothIn summary, flow direction parting and from magnitude the water from levels, that atthe the confluence maximum flow ebb tide,at the which maximum depended flood on tide the differedtidal flow in direction.both flow Atdirection the ebb and tide, magnitude a zone of flowfrom separation that at the alsomaximum existed ebb close tide, to leftwhich river depended bank. on the tidal flow direction. At the ebb tide, a zone of flow separation also existed close to left river bank.

6.2. Bed Shear Stress

Water 2018, 10, 1424 14 of 21

6.2. Bed Shear Stress → For a location in question, τb relates the flow regime to deposition and erosion patterns. It is a Water 2018, 10, x FOR PEER REVIEW→ 14 of 20 0.5 function of a quadratic of U and the 2D Chézy coefficient C2D (m /s) or an equivalent roughness → lengthFor [48 a ].location For 2D in depth-averaged question, 𝜏⃗ relates flows, theτb is flow given regime by to deposition and erosion patterns. It is a function of a quadratic of 𝑈⃗ and the 2D Chézy →coefficient→ C2D (m0.5/s) or an equivalent roughness → |U|ρ gU length [48]. For 2D depth-averaged flows, 𝜏⃗ =is given0 by τb 2 , (10) C2D 𝑈⃗𝜌𝑔𝑈⃗ → → →𝜏⃗ = → , (10) 𝐶 where |U| (m/s) is the magnitude of U = Uξ + Uη. C2D is expressed as where 𝑈⃗ (m/s) is the magnitude of 𝑈⃗ =𝑈⃗ + 𝑈⃗. C√2D is expressed as 6 H C = . (11) 2D √n𝐻 𝐶 = . (11) 𝑛 → Collins et al. [48] pointed out the variability of these parameters. In a tidal confluence, the τb Collins et al. [48] pointed out the variability of these parameters. In a tidal confluence, the 𝜏⃗ determination is complicated by factors such as confluence geometry, bed topography, and sediment. determination is complicated by factors such as confluence→ geometry, bed topography, and sediment. Flow perturbations make it difficult to measure τb in the field. Therefore, numerical models are often Flow perturbations→ make it difficult to measure 𝜏⃗ in the field. Therefore, numerical models are oftenused forused obtaining for obtainingτb in tidal𝜏⃗ in environments. tidal environments. → → → → 𝜏τ⃗b is is proportionalproportional to to| U𝑈|⃗U𝑈⃗and and is is also also affected affected by byH. H In. theIn the confluence, confluence, the |theU| and𝑈⃗ Handvalues H values were werebetween between 0.4–0.6 0.4 m/s‒0.6 andm/s 6.0–17.3and 6.0‒17.3 m (exclusive m (exclusive of the of scourthe scour hole). hole). At the At maximumthe maximum flood flood and and ebb → → ebbtides, tides, Figure Figure 16 shows 16 shows the distributionthe distribution of the of peak the peakτb values. 𝜏⃗ values. Their distributionsTheir distributions of τb were of 𝜏⃗ similar, were similar,with some with local some differences. local differences. For each tide,For each the spatialtide, the distribution spatial distributi and magnitudeon and magnitude followed the followed pattern theof the pattern velocity of the gradient velocity distribution. gradient distribution. For a given river,For a a given decay river, was exhibiteda decay was from exhibited the mainstream from the to mainstreamthe bank. to the bank. → → 𝜏τ⃗b reflects reflects thethe velocity gradient and is is affected affected by by both both run-off run-off and and tides. tides. The The peak peak 𝜏τ⃗b values occurredoccurred away fromfrom thethe confluence confluence in in the the Fenghua Fenghua and and Yong Yong rivers, rivers, which which was was true true for both for theboth flood the floodand ebb and tides. ebb tides. The occurrence The occurrence of these of these areas areas was similar was similar to the to situation the situation with onlywiththe only run-off the run-off in the inrivers the rivers [1,4,9]. [1,4,9]. → LowLow 𝜏τb⃗ valuesvalues occurredoccurred inin suchsuch areasareas asas alongalong thethe YaoYao RiverRiver andand inin thethe confluence.confluence. At At the the confluence,confluence, thethe YongYong and and Fenghua Fenghua rivers rivers run run almost almo alongst along a straight a straight line, while line, the while Yao Riverthe Yao intersects River intersectsthem at almost them aat right almost angle. a right As the angle. tide comesAs the from tide thecomes Yong from River, the the Yong tides River, are bathymetrically the tides are → → bathymetricallyconstrained and theconstrained bending accountsand the forbending the low accountsτb values for in the Yaolow River.𝜏⃗ valuesτb links in thethe flowYao conditionsRiver. 𝜏⃗ linkswith sedimentthe flow conditions transport, with providing sediment indications transpor oft, morphologyproviding indications change. of morphology change.

𝜏→⃗ FigureFigure 16. 16. DistributionsDistributions of of τb during the second half of June 2015: ( (aa)) At At the the maximum maximum flood ﬂood tide; tide; ((bb)) At At the the maximum maximum ebb ebb tide. tide.

7. Morphological Changes With the typical confluence flow features, predictions were made to look at the potential pattern of morphological changes. The construction of the sluice gates on the Yao River interrupted the natural run-off downstream. Another factor is that many wading structures were built on both rivers upstream of the confluence, which also affected the run-off in the water system. This means that the tides interact with the run-off in a different way than before; the intrusion of the tidal waves is further

Water 2018, 10, 1424 15 of 21

7. Morphological Changes With the typical conﬂuence ﬂow features, predictions were made to look at the potential pattern of morphological changes. The construction of the sluice gates on the Yao River interrupted the natural run-off downstream. Another factor is that many wading structures were built on both rivers upstream

Waterof the 2018 confluence,, 10, x FOR PEER which REVIEW also affected the run-off in the water system. This means that the tides interact15 of 20 with the run-off in a different way than before; the intrusion of the tidal waves is further upstream, upstream,which probably which results probably in more results sediment in more deposition. sediment Simulationsdeposition. Simulations were carried were out tocarried estimate out theto estimatepossible scenarios.the possible scenarios. As shown earlier, the tidal currents, especially fo forr the spring tides in wet seasons, dominate the sediment transport in the area. During the second half of June 2015, the 30-h spring tide was selected for the purpose. Along Along the the rivers rivers including including the the confluence, confluence, the the start start condition condition of of the the river bed corresponded toto thethe bathymetrybathymetry obtained obtained at at 10:00 10:00 a.m. a.m. on on 17 June17 June 2015. 2015. As shownAs shown in Figure in Figure 17, a 17, long, a long,oval-shaped oval-shaped scour scour hole existshole exists in the in confluence the confluen andce extends and extends into the into Yong the River.Yong ItsRiver. depth Its isdepth 10.8 mis 10.8at the m maximumat the maximum (the river (the bed river is bed 6.5 mis 6.5 below m below the mean the mean sea level, sea level, with with a bed a elevationbed elevation of − of6.5 − m).6.5 m).In the In simulation,the simulation, a morphological a morpholo scalinggical scaling factor wasfactor used was to accelerateused to accelerate the bed erosion the bed and erosion deposition, and deposition,a method of a common method practiceof common [39,49 practice–51]. The [39,49–51]. scaling factor The scaling was set factor to 100, was implying set to 100, that implying the prediction that theperiod prediction covered period 125 days. covered 125 days.

Figure 17. Contours of the confluence conﬂuence in June 2015 (T = 0).

Figure 18 illustrates, in the confluence confluence an andd its close vicinity, the bed evolution from T = 0, 0, 30, 30, 60, 60, 90, 120, and 125 days. The results show, as time elapses, that the three river reaches were subjected to continuous siltation. The The trend trend is is in in qualitativ qualitativee agreement agreement with with the the study study of of the water system by Chen et al. [36], [36], in which the cumulative influence influence of the wading structures, including the Yao sluice gates, bridges,bridges, and and wharfs, wharfs, was was analyzed. analyzed. Their Their results results showed showed that the that rivers the including rivers theincluding confluence the confluencealso suffered also from suffered gradual from siltation gradual of suspendedsiltation of suspended load. Figure load. 19 illustrates Figure 19 theillustrates change the in scour-hole change in scour-holedepth and thedepth averaged and the elevation averaged of elevation the river of bed the around river bed the around hole. Figure the hole. 20 shows, Figure as 20 a shows, function as ofa functiontime, the of simulated time, the longitudinal simulated longitudinal profiles of theprofiles bed-level of the changes bed-level along changes each riveralong at each the river confluence. at the confluence.Both the river Both bed the and river the bed scour and hole the showscour ahole tendency show ofa tendency gradual deposition.of gradual deposition. The hole depth The hole was depthinitially was 10.8 initially m and 10.8 became m and 9.25 became m at T 9.25= 125 m days.at T = 125 days.

Water 2018, 10, x FOR PEER REVIEW 15 of 20

upstream, which probably results in more sediment deposition. Simulations were carried out to estimate the possible scenarios. As shown earlier, the tidal currents, especially for the spring tides in wet seasons, dominate the sediment transport in the area. During the second half of June 2015, the 30-h spring tide was selected for the purpose. Along the rivers including the confluence, the start condition of the river bed corresponded to the bathymetry obtained at 10:00 a.m. on 17 June 2015. As shown in Figure 17, a long, oval-shaped scour hole exists in the confluence and extends into the Yong River. Its depth is 10.8 m at the maximum (the river bed is 6.5 m below the mean sea level, with a bed elevation of −6.5 m). In the simulation, a morphological scaling factor was used to accelerate the bed erosion and deposition, a method of common practice [39,49–51]. The scaling factor was set to 100, implying that the prediction period covered 125 days.

Figure 17. Contours of the confluence in June 2015 (T = 0).

Figure 18 illustrates, in the confluence and its close vicinity, the bed evolution from T = 0, 30, 60, 90, 120, and 125 days. The results show, as time elapses, that the three river reaches were subjected to continuous siltation. The trend is in qualitative agreement with the study of the water system by Chen et al. [36], in which the cumulative influence of the wading structures, including the Yao sluice gates, bridges, and wharfs, was analyzed. Their results showed that the rivers including the confluence also suffered from gradual siltation of suspended load. Figure 19 illustrates the change in scour-hole depth and the averaged elevation of the river bed around the hole. Figure 20 shows, as a function of time, the simulated longitudinal profiles of the bed-level changes along each river at the Waterconfluence.2018, 10, 1424Both the river bed and the scour hole show a tendency of gradual deposition. The16 hole of 21 depth was initially 10.8 m and became 9.25 m at T = 125 days.

Water 2018, 10, x FOR PEER REVIEW 16 of 20

Figure 18. River-bed morphology changeschanges inin thethe conﬂuence:confluence: ((aa))T T == 0;0; ((bb)) TT == 30 days; (c)) T = 60 days; ((dd)) TT == 90 days; (e) T = 120 days; ( f) T = 125 125 days. days.

Both the floodflood andand ebbebb tidestides contributedcontributed toto shapingshaping thethe confluenceconfluence scourscour hole.hole. The former gave riserise to deposition, while while the the latter latter led led to to erosion. erosion. However, However, the the flood flood tide tide played played a dominant a dominant part part in inthe the process. process. As Asa result, a result, the thescour scour hole hole shrank shrank both both upstream upstream and downstream and downstream as time as timeelapsed. elapsed. Two Twofactors factors accounted accounted for the for themorphological morphological feature. feature. On On one one hand, hand, the the change change was was associated associated with the sedimentsediment availabilityavailability inin eacheach river.river. TheThe fieldfield measurementsmeasurements indicatedindicated thatthat thethe floodflood tidestides carrycarry a large amount of suspended load upstream. upstream. When When flow flow velocity velocity fell fell below below 0.8 0.8 m/s, m/s, deposition deposition occurred occurred in inthe the confluence confluence area. area. Using Using morpho-sedimentologica morpho-sedimentologicall and and seismo-stratigraphic seismo-stratigraphic data, data, Silva Silva et et al. al. explained a similarsimilar phenomenonphenomenon of confluenceconfluence depositiondeposition [[15].15]. They foundfound thatthat thethe riverriver sedimentsediment waswas deflecteddeflected backback intointo thethe riverriver byby thethe floodflood tides,tides, thusthus producingproducing thethe sedimentsediment depositiondeposition on thethe scourscour hole’shole’s gentlegentle sideside (downstream(downstream slope).slope). On the other hand, the cumulativecumulative effect of river run-off and ebb tides was also attributable to the scour changes.changes. During the ebb tides, the deposited sediment inin thethe confluenceconfluence became became re-suspended re-suspended and and resulted resulted in slightin slight bed bed erosion. erosion. The dominanceThe dominance of the of flood the tideflood eventually tide eventually led to led the to sediment the sediment deposition depositio alongn thealong rivers the rivers inclusive inclus of theive confluence.of the confluence.

Figure 19. Change in scour-hole depth in the confluence.

Water 2018, 10, x FOR PEER REVIEW 16 of 20

Figure 18. River-bed morphology changes in the confluence: (a) T = 0; (b) T = 30 days; (c) T = 60 days; (d) T = 90 days; (e) T = 120 days; (f) T = 125 days.

Both the flood and ebb tides contributed to shaping the confluence scour hole. The former gave rise to deposition, while the latter led to erosion. However, the flood tide played a dominant part in the process. As a result, the scour hole shrank both upstream and downstream as time elapsed. Two factors accounted for the morphological feature. On one hand, the change was associated with the sediment availability in each river. The field measurements indicated that the flood tides carry a large amount of suspended load upstream. When flow velocity fell below 0.8 m/s, deposition occurred in the confluence area. Using morpho-sedimentological and seismo-stratigraphic data, Silva et al. explained a similar phenomenon of confluence deposition [15]. They found that the river sediment was deflected back into the river by the flood tides, thus producing the sediment deposition on the scour hole’s gentle side (downstream slope). On the other hand, the cumulative effect of river run-off and ebb tides was also attributable to the scour changes. During the ebb tides, the deposited sediment

Waterin the2018 confluence, 10, 1424 became re-suspended and resulted in slight bed erosion. The dominance 17of of the 21 flood tide eventually led to the sediment deposition along the rivers inclusive of the confluence.

Water 2018, 10, x FOR PEER REVIEW 17 of 20 FigureFigure 19.19. ChangeChange inin scour-holescour-hole depthdepth inin thethe conﬂuence.confluence.

Figure 20.20. Longitudinal bed-level changes in the conﬂuence:confluence: (a) DistanceDistance along thethe riverriver centerlinecenterline (accounted(accounted from the the lowest lowest scour scour position); position); (b ()b Along) Along the the Yao Yao River; River; (c) (Alongc) Along the the Fenghua Fenghua River; River; (d) (Alongd) Along the theYong Yong River. River.

The Yao RiverRiver alsoalso featuresfeatures gradualgradual siltation,siltation, whichwhich changes its river-bed slope and lowers the sediment carryingcarrying capacity.capacity. This This was was also also observed observed in in the the field field [38 [38].]. Two Two plausible plausible reasons reasons account account for it.for One it. One is ascribed is ascribed to theto the construction construction of theof the sluice sluice gates gates and and the the wading wading structures structures upstream. upstream. As As a result,a result, it notit not only only intercepts intercepts the river the run-off,river run-off, but also but deforms also deforms the tidal the waves tidal in thewaves river. in Accordingthe river. toAccording measurements to measurements [38], the mean [38], high the tidal mean level high increased tidal level by 0.17increased m; the meanby 0.17 low m; tidal the mean level decreasedlow tidal bylevel 0.11 decreased m. The floodby 0.11 tide m. durationThe flood became tide duration 9 min shorterbecame and 9 min the shorter ebb tide and duration the ebb became tide duration 9 min longer.became The 9 min other longer. reason The is other due to reason the bending is due towardto the bending the confluence. toward Thethe confluence. flow, either duringThe flow, the either flood orduring ebb tides,the flood fails or to ebb transport tides, fails the sediment to transport downstream, the sediment thus downstream, leading to deposition thus leading along to deposition the river. alongThe the periodicriver. changes in the tidal flow direction induce a complex morphological regime that doesThe not occurperiodic in unidirectional changes in the run-off tidal flows.flow direction Concerning induce the sedimentationa complex morphological pattern, the morphologic regime that featuresdoes not migrate occur streamwisein unidirectional with run-off run-off flows flow [3,s.49 ].Concerning With tidal waves,the sedimentation the pattern migratespattern, boththe ways,morphologic which agreesfeatures with migrate previous streamwise findings with of the run- tidesoff that flows both [3,49]. deposition With tidal and re-suspensionwaves, the pattern take migrates both ways, which agrees with previous findings of the tides that both deposition and re- suspension take place in the confluence [52]. The analysis showcases that the flow regime is the main driver of the confluence scour evolution. The morphological changes in the confluence subjected to strong tides are closely related to the interactions between the run-off and tidal currents. However, the latter plays a dominant role and governs the sedimentation pattern.

8. Conclusions In a river confluence subjected also to strong tidal currents, its flow and morphological changes are dependent on a number of factors, showing a complex pattern in both time and space. This study dealt with the typical features of such a confluence by means of field studies and numerical modeling. From the sea into the Yong River, the sediment is transported by the tidal currents, especially during the spring tides. During the selected period of two years, field measurements were made to examine the sediment behaviors. The data show that approximately 95% of the sediment in the study

Water 2018, 10, 1424 18 of 21 place in the confluence [52]. The analysis showcases that the flow regime is the main driver of the confluence scour evolution. The morphological changes in the confluence subjected to strong tides are closely related to the interactions between the run-off and tidal currents. However, the latter plays a dominant role and governs the sedimentation pattern.

8. Conclusions In a river confluence subjected also to strong tidal currents, its flow and morphological changes are dependent on a number of factors, showing a complex pattern in both time and space. This study dealt with the typical features of such a confluence by means of field studies and numerical modeling. From the sea into the Yong River, the sediment is transported by the tidal currents, especially during the spring tides. During the selected period of two years, field measurements were made to examine the sediment behaviors. The data show that approximately 95% of the sediment in the study area is suspended load. From the river mouth to its upstream including the confluence, the flow and sediment changes are not always in phase with one another; the sediment movement is significantly modified by the tides. The peak values of sediment concentration occur during both the flood and ebb tides in the rivers. Tidal currents are essential for stirring sediment, modifying its concentration and transport. If there was no tide, the sediment concentration would be directly proportional to the river flow, with the sediment diverted only downstream. With the field measurements in the background, numerical modeling helps understand the alluvial features of the confluence. Two-dimensional simulations of suspended sediment transport were performed to simulate the sediment patterns. At the confluence, the flow at the maximum flood tides differs, in both flow direction and magnitude, from that at the maximum ebb tides. During the ebb tides, a small zone of flow circulations exists close to the left bank of the confluence. The bed shear stress is proportional to the water depth and flow velocity, and it is affected by the river-bed topography. Its distribution reflects the sediment erosion potential in the confluence. By means of a morphological scale factor, the scour formation in the confluence was predicted. The initial hole in the confluence, extending along the Fenghua and Yong rivers, becomes gradually deposited as time elapses. The shifting tidal directions induce a complex morphological pattern that does not exist in unidirectional run-off flows. The erosion and deposition migrate in both directions. The flood tides govern the sediment transport and deposition, while the ebb tides with run-offs lead to erosion. For the scour-hole development, the flood tides play a dominant role.

Author Contributions: Q.X. was responsible for analyses of field measurement data and numerical simulations, with participation from S.L., J.Y., and W.D. The manuscript was written by Q.X. and J.Y. The research of river flow and sedimentation was supervised by J.Y. and S.L. Funding: Q.X. is supported by a four-year PhD scholarship from the Chinese Scholarship Council (CSC) and the Swedish STandUp for Energy project. The authors are members of the 111 Project “Discipline Innovation and Research Base on River Network Hydrodynamics System and Safety”, funded by the Ministry of Education and State Administration of Foreign Experts Affairs, China (Grant No. B17015), with Hohai University’s State Key Laboratory of Hydrology, Water Resources, and Hydraulic Engineering as the executive organization. Acknowledgments: The Hydrology and Water Resources Survey Bureau of the Lower Yangtze River is thanked for their support with the field measurements. Ahmed Bilal of Hohai University provided assistance with the model set-up and calibrations. The authors would like to thank Patrik Andreasson for his comments and the four anonymous reviewers for their suggestions that led to improvements in the quality of the article. Conflicts of Interest: The authors declare no conflicts of interest.

References

1. Roy, A.G. River channel confluences. In River Confluences, Tributaries and the Fluvial Network, 1st ed.; John Wiley & Sons Ltd.: West Sussex, UK, 2008; pp. 13–16. ISBN 9780470026724. 2. Best, J.L. Sediment transport and bed morphology at river channel confluences. Sedimentology 1988, 35, 481–498. [CrossRef] 3. Mosley, P. An experimental study of channel confluences. J. Geol. 1976, 84, 535–562. [CrossRef] Water 2018, 10, 1424 19 of 21

4. Best, J.L. Flow dynamics at river channel confluences: implications for sediment transport and bed morphology. In Recent Developments in Fluvial Sedimentology; Society for Sedimentary Geology (SEPM): Broken Arrow, OK, USA, 1987; pp. 27–35. 5. Best, J.L.; Reid, I. Separation zone at open-channel junctions. J. Hydraul. Eng. 1984, 110, 1588–1594. [CrossRef] 6. Yang, Q.Y.; Wang, X.Y.; Lu, W.Z.; Wang, X.K. Experimental study on characteristics of separation zone in confluence zones in rivers. J. Hydrol. Eng. 2009, 2, 166–171. 7. Rhoads, B.L.; Sukhodolov, A.N. Spatial and temporal structure of shear-layer turbulence at a stream confluence. Water Resour. Res. 2004, 6, 2393–2410. [CrossRef] 8. Rhoads, B.L.; Sukhodolov, A.N. Lateral momentum flux and the spatial evolution of flow within a confluence mixing interface. Water Resour. Res. 2008, 44, 27–143. [CrossRef] 9. Yuan, S.Y.; Tang, H.W.; Xiao, Y.; Qiu, X.H.; Xia, Y. Water flow and sediment transport at open-channel confluences: An experimental study. J. Hydraul. Res. 2017, 1686, 1–18. [CrossRef] 10. Boyer, C.; Roy, A.G.; Best, J.L. Dynamics of a river channel confluence with discordant beds: Flow turbulence, bed load sediment transport, and bed morphology. J. Geophys. Res. Earth Surf. 2006, 111, F04007. [CrossRef] 11. Rhoads, B.L.; Riley, J.D.; Mayer, D.R. Response of bed morphology and bed material texture to hydrological conditions at an asymmetrical stream confluence. Geomorphology 2009, 109, 161–173. [CrossRef] 12. Trevethan, M.; Martinelli, A.; Oliveria, M.; Ianniruberto, M.; Gualtieri, C. Fluid mechanics, sediment transport and mixing about the confluence of Negro and Solimões rivers, Manaus, Brazil. In Proceedings of the 36th IAHR World Congress, Hague, The Netherlands, 28 June–3 July 2015. 13. Pittaluga, M.B.; Tambroni, N.; Canestrelli, A.; Slingerland, R.; Lanzoni, S.; Seminara, G. Where river and tide meet: The morphodynamic equilibrium of alluvial estuaries. J. Geophys. Res.-Earth Surf. 2015, 120, 75–94. [CrossRef] 14. Ginsberg, S.S.; Perillo, G.M.E. Deep-scour holes at tidal channel junctions, Bahia Bianca Estuary, Argentina. Mar. Geol. 1999, 160, 171–182. [CrossRef] 15. Ginsberg, S.S.; Aliotta, S.; Lizasoain, G.O. Morphodynamics and seismostratigraphy of a deep hole at tidal channel confluence. Geomorphology 2009, 104, 253–261. [CrossRef] 16. Ferrarin, C.; Madricardo, F.; Rizzetto, F.; Kiver, W.M.; Bellafiore, D.; Umgiesser, G. Geomorphology of scour holes at tidal channel confluences. J. Geophys. Res. Earth Surf. 2018, 123, 1386–1406. [CrossRef] 17. Mignot, E.; Bonakdari, H.; Knothe, P.; Lipeme, K.G.; Bessette, A.; Riviere, N.; Bertrand-Krajewski, J.L. Experiments and 3D simulations of flow structures in junctions and their influence on location of flowmeters. Water Sci. Technol. 2012, 66, 1325–1332. [CrossRef][PubMed] 18. Guillén-Ludeña, S.; Franca, M.J.; Cardoso, A.H.; Schleiss, A.J. Hydro-morphodynamic evolution in a 90◦ movable bed discordant confluence with low discharge ratio. Earth Surf. Process. Landf. 2015, 40, 1927–1938. [CrossRef] 19. Guillén-Ludeña, S.; Franca, M.J.; Cardoso, A.H.; Schleiss, A.J. Evolution of the hydromorphodynamics of mountain river confluences for varying discharge ratios and junction angles. Geomorphology 2016, 255, 1–15. [CrossRef] 20. Ribeiro, M.L.; Blanckaert, K.; Roy, A.G.; Schleiss, A.J. Flow and sediment dynamics in channel confluences. J. Geophys. Res. Earth Surf. 2012, 117, F01035. 21. Shao, C.C. On the Existence of Deep Holes at Tidal Creek Junctions. Ph.D. Thesis, University of South Carolina, Columbia, SC, USA, 1977. 22. Kjerfve, B.; Shao, C.C.; Stapor, F.W. Formation of deep scour holes at the junction of tidal creeks: A hypothesis. Mar. Geol. 1979, 33, M9–M14. [CrossRef] 23. Sukhodolov, A.N.; Rhoads, B.L. Field investigation of three-dimensional flow structure at stream confluences: 2. Turbulence. Water Resour. Res. 2001, 37, 2411–2424. [CrossRef] 24. Biron, P.M.; Lane, S.N. Modelling hydraulics and sediment transport at river confluences. In River Confluences, Tributaries and the Fluvial Network, 1st ed.; John Wiley & Sons Ltd.: West Sussex, UK, 2008; pp. 17–43. ISBN 9780470026724. 25. Lane, S.N.; Parsons, D.R.; Best, J.L.; Orfeo, O.; Kostachuk, R.A.; Hardy, R.J. Causes of rapid mixing at a junction of two large rivers: Rio Parana and Rio Paraguay, Argentina. J. Geophys. Res. Earth Surf. 2008, 113, F02019. [CrossRef] 26. Dordevic, D. Numerical study of 3D flow at right-angle confluences with and without upstream planform curvature. J. Hydroinform. 2013, 15, 1073–1088. [CrossRef] Water 2018, 10, 1424 20 of 21

27. Rahimi, M.; Akbari, M.; Parsamoghadam, M.A.; Alsairafi, A.A. CFD Study on effect of channel confluence angle on fluid flow pattern in asymmetrical shaped microchannels. Comput. Chem. Eng. 2015, 73, 172–182. [CrossRef] 28. Styles, R.; Brown, M.E.; Brutschè, K.E.; Li, H.H.; Beck, T.M.; Sanchez, A. Long-term morphological modeling of barrier island tidal inlets. J. Mar. Sci. Eng. 2016, 4, 65. [CrossRef] 29. Ahmad, S.; Mohammad, R.M.T.; Amir, R.Z. Three-dimensional numerical study of flow structure in channel confluences. Can. J. Civ. Eng. 2010, 37, 772–781. 30. Serresa, B.D.; Roya, A.; Birona, P.M.; Bestb, J.L. Three-dimensional structure of flow at a confluence of river channels with discordant beds. Geomorphology 1999, 26, 313–335. [CrossRef] 31. Rhoads, B.L.; Sukhodolov, A.N. Field investigation of three-dimensional flow structure at stream confluences: 1. Thermal mixing and time-averaged velocities. Water Resour. Res. 2001, 37, 2393–2410. [CrossRef] 32. Cayocca, F. Long-term morphological modeling of a tidal inlet: The Arcachon Basin, France. Coast. Eng. 2001, 42, 115–142. [CrossRef] 33. Petti, M.; Bosa, S.; Pascolo, S. Lagoon sediment dynamics: A coupled model to study a medium-term silting of tidal channels. Water 2018, 10, 569. [CrossRef] 34. Sandbach, S.D.; Nicholas, A.P.; Ashworth, P.J.; Best, J.L.; Keevil, C.E.; Parsons, D.R.; Prokocki, E.W.; Simpson, C.J. Hydrodynamic modelling of tidal-fluvial flows in a large river estuary. Estuar. Coast. Shelf Sci. 2018, 212, 176–188. [CrossRef] 35. Weerakoon, S.B.; Tamai, N.; Kawahara, Y. Depth-averaged flow computation at a river confluence. Proc. Inst. Civ. Eng.-Water Marit. Eng. 2003, 156, 73–83. [CrossRef] 36. Chen, J.; Tang, H.W.; Xiao, Y.; Ji, M. Hydrodynamic characteristics and sediment transport of a tidal river under influence of wading engineering groups. China Ocean Eng. 2013, 27, 829–842. [CrossRef] 37. Wang, Z.Y.; Lee, J.H.W.; Melching, C.S. River Dynamics and Integrated River Management, 1st ed.; Tsinghua University Press: Beijing, China, 2014; pp. 13–16. ISBN 978-7-302-27257-1. 38. Wang, H.; Sha, H.; Lu, D.; He, L.; Guo, K. Hydrological and Topographic Survey of Ningbo Yongjiang Sluice Gates Constructon (2nd Phase); Technical Report; Hydrology and Water Resources Survey Bureau of the Lower Yangtze River: Chongqing, China, 2015. 39. Ranjan, A.; Ray, B.K. Mathematical modeling of sediment transport in estuaries. Estuar. Process. 1977, 98–106. [CrossRef] 40. Deltares. Delft3D-Flow, User Manual; Deltares: Delft, The Netherlands, 2014. 41. Emmanuel, P. Turbidity and Cohesive Sediment Dynamics. Elsevier Oceanogr. Ser. 1986, 42, 515–550. 42. Stelling, G.S. On the Construction of Computational Methods for Shallow Water Flow Problems; Tech. Rep. 35, Rijkswaterstaat: Dutch, The Netherlands, 1984. 43. Krause, P.; Boyle, D.P.; Base, F. Comparison of different efficiency criteria for hydrological model assessment. Adv. Geosci. 2005, 5, 89–97. [CrossRef] 44. Moriasi, D.N.; Arnold, J.G.; Van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE 2007, 50, 885–900. [CrossRef] 45. Kuai, Y.; Tao, J.F.; Zhang, Q.; Chen, W.Q.; Dai, W.Q. Mapping tidal residual currents and suspended sediment pattern in the Yongjiang estuary, China using a numerical model. In Proceedings of the 37th IAHR World Congress, Kuala Lumpur, Malaysia, 13–18 August 2017. 46. Marani, M.; Lanzoni, S.; Zandolin, D.; Seminara, G.; Rinaldo, A. Tidal meanders. Water Resour. Res. 2002, 38, 1225. [CrossRef] 47. Baranya, S.; Olsen, N.R.B.; Jozsa, J. Flow analysis of a river confluence with field measurements and rans model with nested grid approach. River Res. Appl. 2015, 31, 28–41. [CrossRef] 48. Collins, M.B.; Ke, X.; Gao, S. Tidally-induced flow structure over intertidal flats. Estuar. Coast. Shelf Sci. 1998, 46, 233–250. [CrossRef] 49. Briere, C.; Giardino, A.; van der Werf, J. Morphological modeling of bar dynamics with delft3d: The quest for optimal free parameter settings using an automatic calibration technique. Coast. Eng. 2010, 1, 60. [CrossRef] 50. Moerman, E. Long-Term Morphological Modeling of the Mouth of the Columbia River. Master’s Thesis, Delft University of Technology, Delft, The Netherlands, 2011. Water 2018, 10, 1424 21 of 21

51. Guo, L.C.; Wegen, M.V.D.; Roelvink, D.J.A.; Wang, Z.B.; He, Q. Long-term, process-based morphodynamic modeling of a fluvio-deltaic system, part I: The role of river discharge. Cont. Shelf Res. 2015, 109, 95–111. [CrossRef] 52. Achete, F.M.; Wegen, M.V.D.; Roelvink, D.; Jaffe, B. Suspended sediment dynamics in a tidal channel network under peak river ﬂow. Ocean Dyn. 2016, 66, 703–718. [CrossRef]

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