Field Studies and 3D Modelling of Morphodynamics in a Meandering River Reach Dominated by Tides and Suspended Load

fluids

Article Field Studies and 3D Modelling of Morphodynamics in a Meandering River Reach Dominated by Tides and Suspended Load

Qiancheng Xie 1,* , James Yang 2,3 and T. Staffan Lundström 1 1 Division of Fluid and Experimental Mechanics, Luleå University of Technology, 97187 Luleå, Sweden; [email protected] 2 Vattenfall AB, Research and Development, Hydraulic Laboratory, 81426 Älvkarleby, Sweden; [email protected] 3 Resources, Energy and Infrastructure, Royal Institute of Technology, 10044 Stockholm, Sweden * Correspondence: [email protected]; Tel.: +4672-2870-381

Received: 9 December 2018; Accepted: 20 January 2019; Published: 22 January 2019

Abstract: Meandering is a common feature in natural alluvial streams. This study deals with alluvial behaviors of a meander reach subjected to both fresh-water flow and strong tides from the coast. Field measurements are carried out to obtain flow and sediment data. Approximately 95% of the sediment in the river is suspended load of silt and clay. The results indicate that, due to the tidal currents, the flow velocity and sediment concentration are always out of phase with each other. The cross-sectional asymmetry and bi-directional flow result in higher sediment concentration along inner banks than along outer banks of the main stream. For a given location, the near-bed concentration is 2−5 times the surface value. Based on Froude number, a sediment carrying capacity formula is derived for the flood and ebb tides. The tidal flow stirs the sediment and modifies its concentration and transport. A 3D hydrodynamic model of flow and suspended sediment transport is established to compute the flow patterns and morphology changes. Cross-sectional currents, bed shear stress and erosion-deposition patterns are discussed. The flow in cross-section exhibits significant stratification and even an opposite flow direction during the tidal rise and fall; the vertical velocity profile deviates from the logarithmic distribution. During the flow reversal between flood and ebb tides, sediment deposits, which is affected by slack-water durations. The bed deformation is dependent on the meander asymmetry and the interaction between the fresh water flow and tides. The flood tides are attributable to the deposition, while the ebb tides, together with run-offs, lead to slight erosion. The flood tides play a key role in the morphodynamic changes of the meander reach.

Keywords: tidal meandering river; ﬁeld measurements; 3D numerical model; ﬂow features; sediment transport; erosion-deposition patterns

1. Introduction Meandering is one of the most common shapes formed by river streams, which is especially true for streams in the lowland alluvial plains [1]. Due to meandering, the characteristics of water flow, sediment transport and the resulting bed deformation are more complex than in relatively straight river reaches. For a coastal river, the tidal currents interact with the fresh-water run-off and they form a bidirectional flow, which also plays an essential role in the fluvial process. This is especially true if the tides are much stronger than the fresh-water discharges. With a landward decline in strength, the tidal influence descends. At the meander bend apex, its cross-sectional shape is usually asymmetrical, with a deep portion of channel along the outer bank and a broad, shallow section extending towards the inner bank.

Fluids 2019, 4, 15; doi:10.3390/ﬂuids4010015 www.mdpi.com/journal/ﬂuids Fluids 2019, 4, 15 2 of 19

The plane curvature and cross-sectional asymmetry topography are shown to produce significant secondary currents and transverse water-surface slopes [2,3]. The secondary currents derive from the centrifugal acceleration acting on the stratification between the upper and lower flow layers. It has also been proved that strong stratified currents have significant impacts on the distribution of bed shear stresses along the wetted perimeter of river, and thereby play an essential role in the sediment transport as well as morphology changes [3–6]. The bed changes induced by erosion and deposition affect the flow, which in turn influences the shear-stress distribution, sediment component and bed topography [7]. Therefore, the coupling of the stratified currents, sediment movement and bed-form changes makes up an interactive response that characterizes the meandering morphodynamics. Given its scientific and practical significance, the dynamic process in a meandering river, among several other issues, has to date been the object of numerous theoretical and experimental studies [8–11]. These contribute to the understanding of the meandering phenomena. Recently, the use of an acoustic doppler current profiler (ADCP) has permitted direct estimations of Reynolds stress in tidal environment rivers [12]. Further research, especially of field measurements, that focuses on river curvature and cross-sectional asymmetry and deals with the interaction between river run-off and tidal currents [3], is necessary. In recent years, many numerical simulations have been performed of tidal flow and sediment transport in meandering rivers. Instead of simplifications and assumptions in physical model tests, complex river geometries and boundaries are directly modelled. In a meander, its flow is three dimensional [13]. As compared with 2D depth-averaged models, an application of a 3D model generates, in terms of sediment transport, more reliable results [14]. For meandering rivers, most 3D models applied to simulations are based on the Reynolds-Averaged Navier-Stokes (RANS) equations assuming time-independent flow and isotropic turbulence [4,6]. A recent development is the application of large and detached eddy simulation (LES, DES) models to meandering flows [15,16]. LES aims to capture the time-dependent flow and resolves the large-scale anisotropy of turbulence. Limited by central processing unit (CPU) time and convergence, it is often used for issues with low Reynolds numbers and of limited domain dimensions [6]. In contrast, Delft3D (Version 4.04, Delft, The Netherlands) has the advantage of time-effective computations when applied to large-scale river and ocean simulations. Meandering with large curvatures is a characteristic of many streams in low-land coastal regions. Changes in both river curvature and bed topography are interrelated, and their geometric shapes need to be considered when assessing the effects of channel configuration on flow and sediment transport. In a tidal environment, the river reach is affected by both run-off and tides, in which shifts between flood and ebb tides induce, with regard to flow patterns and sediment transport, more complexity. As a result, in terms of erosion and deposition, the alluvial process is different, an issue of concern for practical applications, especially if the river is in an urban development area. The study focuses on a meandering reach of an alluvial river subjected to strong tidal currents (compared to much lower fresh-water discharges). Suspended load accounts for approximately 95% of the sediment in the river. Field measurements are performed to record the flow and sediment data and to map the river bathymetry at selected occasions. The field data help understand the sediment movement characteristics in both horizontal and vertical directions. A 3D suspended-load transport model is incorporated into a hydrodynamic model and computes the flow patterns and morphological changes. By means of the two approaches, the objective of the study is to provide insight into the interplay between fresh-water flows and tidal currents, to illustrate the circulatory patterns of suspended load transport during the tidal rising and falling, and to make predictions of the bed deformation associated with the meandering properties (curvature, cross-channel asymmetry, etc.). The results provide a reference for studies of tidal fluvial processes in similar situations. The paper includes a study area description, field measurements of flow and sediment, field data analyses, mathematical formulation, model setup with calibration and validation, major flow features and morphological changes.

Fluids 2019, 4, x 3 of 19 Article Zircon XenocrystsThe paper fromincludes Cenozoica study area description, Alkaline field measurementsBasalts of of flow and sediment, field data analyses, mathematical formulation, model setup with calibration and validation, major flow Fluids 2019, 4, 15 3 of 19 the Ratanakirifeatures and Volcanic morphological Province changes. (Cambodia), Southeast Asia—Trace Element Geochemistry, O-Hf 2. 2.Study Study Area Area Isotopic Composition,TheThe study study aims aims to to examineU examine-Pb anand an approximately approximately (U-Th)/He sinusoidalsinusoidal meanderingmeandering reach, reach, with with two two successive, successive, Geochronologynearlynearly S-shaped S-shaped—Revelations meander meander loops loops (Figure (Figure into 11).). TheThethe riverriver Underlying runs runs into into the the sea sea and and is is subjected subjected to to strong strong tides. tides. Lithospheric Mantle

Paula C. Piilonen 1,*, F. Lin Sutherland 2, Martin Danišík 3, Glenn Poirier 1, John W. Valley 4, Ralph Rowe 1

1 Mineralogy Section, Beaty Centre for Species Discovery, Research & Collections, Canadian Museum of Nature, P.O. Box 3443, Station D, Ottawa, Ontario K1P 6P4, Canada; [email protected] (G.P.); [email protected] (R.R.) 2 Geoscience, Australian Museum, 1 William Street, Sydney NSW 2010, Australia; [email protected] 3 John de Laeter Centre, The Institute for Geoscience Research (TIGeR), Curtin University, Perth WA 6845, Australia; [email protected] 4 Wisconsin Secondary Ion Mass Spectrometer Laboratory (WiscSIMS), Department of Geoscience, University of Wisconsin, Madison, Wisconsin 53706, USA; [email protected] * Correspondence: [email protected]

Received: 26 October 2018; Accepted: 19 November 2018; Published: date

Abstract: Zircon xenocrysts from alkali basalts in Ratanakiri Province, Cambodia represent a unique low-Hf zircon within a 12,000 km long Indo-Pacific megacryst zone. Colorless, yellow, brown, and red crystals ({100}, {101}, subordinate {211}, {1103}), with hopper growth and corrosion FigureFigure 1. 1.StudyStudy area: area: (a ()a Location;) Location; (b (b) )examined examined meandering meandering reachreach of of the the Yong Yong River; River; (c )(c measurement) measurement features range up to 20 cm in size. Zircon chemistry indicates juvenile, Zr-saturated, mantle- stationsstations of of water water levels levels (WL) (WL) and and flow flow & sediment (FS).(FS). derived alkaline melt (Hf 0.6–0.7 wt %, Y <0.2 wt %, U + Th + REE (Rare-Earth Elements) < 600 ppm, Zr/Hf 66–92, Eu/Eu*N ~1,The positive study areaCe/Ce* is partN, HREE of the (Heavy YongRiver, REE) enrichment). located in Southeast Incompatible China. element The total area of the catchment The study2 area is part of the Yong River, located in Southeast China. The total area of the depletion with increasingis 42.94 kmYb/Sm(theN from area core above to rim the at FS3 ~ constant gauge is Hf approximately suggests single 29 stage km). growth. The river runs roughly in the catchment is 42.94 km2 (the area above the FS3 gauge is approximately 29 km). The river runs roughly Ti-in-zircon temperaturesSW–NE (~570 direction.–740 C) The are lower river lengththan predicted and width by crystal are about morphology 26.5 km (800 and–900 150–250 C) m measured on the in the SW–NE direction. The river length and width are about 26.5 km and 150‒250 m measured on and decrease fromnormal core to water rim ( surface.T = 10–50 The C). average The 18 river-bedO values slope(4.88 to is 1.175.01‰. VSMOW The annual (Vienna average rainfall is 1505 mm; Standard Mean theOceanthe normal annual Water water) flow) are relatively volumesurface. isThe low 2.91 averagefor× xenocrysts109 mriver-bed3; its from annual slopethe averagezircon is 1.17‰. Indo fresh-water-Pacific The annual zone discharge average is 92rainfall m3/s is [17 1505]. 9 3 3 (ZIP). The 176Hf/mm;177InHf athe values pronounced annual (+ εHf flow way, 4.5 volume–10.2) the flow give is 2.91 andTDepleted sediment× 10 Mantle m model; its transport annual source inaverage ages the river of fresh-water260 are–462 affected Ma discharge by the tides is 92 from m /s the [17]. and TCrustal ages Inofcoastal a391 pronounced–754 area. Ma. TheThe way, annuallysource the magmasflow averaged and reflect sediment tidal variably flux transport is depleted 946 m 3in/s, lithosphericthe approximately river are mantle affected 11 times by the the tides fresh-water from the with little supracrustalcoastalflow discharge.input.area. TheZircon Theannually U tides-Pb (0.88 areaveraged– the1.56 dominating Ma) tidal and flux (U factor-Th)/He is 946 for (0.86m the3/s,– sediment 1.02approximately Ma) ages movement. are 11 times Due tothe deposition, fresh-water older than hostflow basaltthe discharge. river-bed ages (~0.7 rises, TheMa), andtides which the are widthsuggests the narrowsdominating limite ind residence many factor sections. for before the This sedimenttransport. water system Zirconmovement. has been Due well to manageddeposition, genesis suggeststhe sinceZr river-bed-saturated, 1959, with rises, Al regular-undersaturated, and dredgingthe width for carbonatitic narrows navigation -ininfluenced, [18many]. A singlesections. low- waterdegree This course partial water features system the has river been mouth, well melting (<1%) of peridotitic mantle at ~60 km beneath the Indochina terrane. managedwithout multiplesince 1959, branches, with regular either atdr presentedging orfor in navigation the past. [18]. A single water course features the river mouth,The tide without in the multiple river is abranches, semi-diurnal either tide, at present i.e., two or nearlyin the past. equal high and low tides each Keywords: zircon; xenocryst; alkali basalt; Ratanakiri Volcanic Province; trace elements; O-isotopes and Hf-isotopes; Uday,-Pb;The (U belonging- Th)/Hetide in the to theriver category is a semi-diurnal of incomplete tide, standing i.e., twowaves. nearly equal According high toand the low yearly tides statistics each day, belongingof hydrological to the stations, category the of average incomplete range ofstanding tidal levels waves. is 0.29–0.44 According m within to the one yearly circle. Thestatistics mean of hydrologicalriver depth stations, is about 8 the m, average with tidal range peak of velocities tidal levels close is to 0.29 1 m/s;‒0.44 the m tidalwithin range one increasescircle. The landwards mean river depthwith is the about narrowing 8 m, with river tidal width, peak with velocities an average clos rangee to 1 falling m/s; the between tidal 1.62–1.84range increases m. During landwards flood tides, with 1. Introduction thesediment narrowing follows river the width, currents with and an is average transported range from falling the outer between sea area 1.62 to‒1.84 the inland.m. During This flood flow and tides, sedimentsediment follows transport the processcurrents reverse and is during transported ebb tides. from the outer sea area to the inland. This flow and sedimentThe transport meandering process reach reverse of interest during has threeebb tides. consecutive parts of significant curvature (Figure2). Minerals 2018, 8, x; doi: FOR PEER REVIEW www.mdpi.com/journal/≈ minerals ≈ ◦ FromThe up- meandering to downstream, reach theof interest radius of has curvature three consec is R utive700, 500parts and of 300significant m; their curvature angles are (Figureθ 80 ,2). 100◦ and 120◦, respectively. The typical river width and water depth are about 200 m and 10 m. From up- to downstream, the radius of curvature is R ≈ 700, 500 and 300 m; their angles are θ ≈ 80°, In addition, the meandering reach features large areas of shoals associated with high tidal levels, 100° and 120°, respectively. The typical river width and water depth are about 200 m and 10 m. In especially close to the apex positions. With these geometrical features, it is a typical site to understand addition, the meandering reach features large areas of shoals associated with high tidal levels, the cross-sectional currents and asymmetric bed forms and their effects on sediment movement along especially close to the apex positions. With these geometrical features, it is a typical site to understand the reach. the cross-sectional currents and asymmetric bed forms and their effects on sediment movement along the reach. Fluids 2019, 4, x 4 of 19

Further upstream of the study area, a confluence exists, where the Yao and Fenghua Rivers merge into the Yong River (Figure 1). Its sedimentation pattern, associated with different flow Fluids 2019, 4, x 4 of 19 regimes,Fluids is 2019also, 4 ,an 15 issue of concern [19]. 4 of 19 Further upstream of the study area, a confluence exists, where the Yao and Fenghua Rivers Further upstream of the study area, a conﬂuence exists, where the Yao and Fenghua Rivers merge merge intointo thethe Yong Yong River River (Figure (Figure1). Its sedimentation 1). Its sedimentation pattern, associated pattern, with different associated ﬂow regimes,with different is also flow regimes,an is issuealso ofan concern issue of [19 concern]. [19].

Figure 2. Geometrical description of the meander, with flow and sediment stations FS3, FS4 and FS5. Each bend is described with a center position O, a radius R and an angle θ. The red line denotes the central line throughout the reach.

3. FieldFigure Measurements 2.Figure Geometrical 2. Geometrical description description of the of the meander, meander, with with flowflow and and sediment sediment stations stations FS3, FS4 FS3, and FS4 FS5. and FS5. Each bend is described with a center position O, a radius R and an angle θ. The red line denotes the Each bend is described with a center position O, a radius R and an angle θ. The red line denotes the 3.1. Data Collectioncentral line throughout the reach. central line throughout the reach. To3. record Field Measurements the hydrological data and map the river bathymetry, extensive field surveys were 3. carriedField Measurements3.1. out Data for Collectionthe study area during the period June 2015‒January 2016. The hydrological data used were acquired for a typical wet season in June 2015. The collected parameters included water levels, To record the hydrological data and map the river bathymetry, extensive field surveys were 3.1. Data Collection water-flowcarried velocity, out for the flow study discharge, area during sediment the period concentration June 2015–January and 2016. grain-size The hydrological distributions. data used The river bathymetry used for the study was achieved using an HY1600 bathymetric profiler. To recordwere acquired the hydrological for a typical wet data season and in map June 2015.the Theriver collected bathymetry, parameters extensive included field water surveys levels, were Also marked in Figure 1 are the recording stations for water levels (WL), at three locations carried outwater-flow for the velocity,study area flow during discharge, the sediment period concentrationJune 2015‒January and grain-size 2016. distributions.The hydrological The river data used (denotedbathymetry as WL4, used WL5 for and the studyWL6), was and achieved for flow using & sedi an HY1600ment (FS), bathymetric also at profiler. three locations (denoted as were acquired for a typical wet season in June 2015. The collected parameters included water levels, FS3, FS4 andAlso FS5). marked At ineach Figure FS,1 threeare the typical recording plumb stations lines for (A, water B and levels C, (WL), from at left three to locations right, looking water-flow(denoted velocity, as WL4, flow WL5 discharge, and WL6), andsediment for flow &concentration sediment (FS), alsoand at grain-size three locations distributions. (denoted as FS3, The river downstream) were arranged (Figure 3). Along each line, sampling was made at six points, i.e., hi = 0, bathymetryFS4 andused FS5). for At the each study FS, three was typical achieved plumb using lines (A, an B HY1600 and C, from bathymetric left to right, looking profiler. downstream) 20%, 40%, 60%, 80% and 100% of the water depth H0 (i = 1, 2, …, 6). All the data were recorded in a Alsowere marked arranged in (Figure Figure3). Along1 are eachthe line,recording sampling stations was made for at sixwater points, levels i.e., h i(WL),= 0, 20%, at 40%, three 60%, locations one-hour interval. (denoted80% as andWL4, 100% WL5 of the and water WL6), depth andH0 ( ifor= 1, flow 2, ... &, 6). sedi Allment the data (FS), were also recorded at three in a one-hour locations interval. (denoted as FS3, FS4 and FS5). At each FS, three typical plumb lines (A, B and C, from left to right, looking downstream) were arranged (Figure 3). Along each line, sampling was made at six points, i.e., hi = 0, 20%, 40%, 60%, 80% and 100% of the water depth H0 (i = 1, 2, …, 6). All the data were recorded in a one-hour interval.

FigureFigure 3. Schematic 3. Schematic diagram diagram of ofcross-sectional cross-sectional measurement points points (looking (looking downstream). downstream). Fourbeam 600/1200-kHz RDI Workhorse Acoustic Doppler Current Profilers (ADCPs) (Nortek Four-beamgroup, Rud, 600/1200-kHz Norway), measured RDI flowWorkhorse velocities. Acoustic Each ADCP Doppler was attached Current to itsProfilers measurement (ADCPs) vessel. (Nortek group,The Rud, inaccuracy Norway), of measured the resulting flow flow velocities. discharges Ea wasch belowADCP± was5%. Theattached YJD-1 to type its pressuremeasurement sensors vessel. The inaccuracy(Tekscan, Inc., of Souththe resulting Boston, MA, flow USA) discharges were used forwas water-level below ±5%. measurements, The YJD-1 with type an inaccuracypressure ofsensors ±1 cm. Efforts were made on sampling of the suspended load, using point-integrative water samplers (Tekscan,Figure Inc., 3. South Schematic Boston, diagram MA, USA) of cross-sectional were used fo measurementr water-level points measurements, (looking downstream). with an inaccuracy of ±1 cm.(Hoskin Efforts Scientific, were Ltd., made Saint-Laurent, on sampling QC, Canada).of the suspended Samples of bedload, load, using though po smallint-integrative in amount, water samplersFour-beam (Hoskin 600/1200-kHz Scientific, Ltd., RDI Saint-Laurent, Workhorse Acoustic QC, Canada). Doppler Samples Current of bedProfilers load, (ADCPs)though small (Nortek in group,amount, Rud, were Norway), also taken measured with Shipekflow velocities. grab samplers Each ADCP (Envco, was Auckland, attached toNew its measurementZealand) and vessel.their Thepercentages inaccuracy were of thecalculated. resulting flow discharges was below ±5%. The YJD-1 type pressure sensors (Tekscan, Inc., South Boston, MA, USA) were used for water-level measurements, with an inaccuracy of ±1 cm. Efforts were made on sampling of the suspended load, using point-integrative water samplers (Hoskin Scientific, Ltd., Saint-Laurent, QC, Canada). Samples of bed load, though small in amount, were also taken with Shipek grab samplers (Envco, Auckland, New Zealand) and their percentages were calculated. Fluids 2019, 4, 15 5 of 19 were also taken with Shipek grab samplers (Envco, Auckland, New Zealand) and their percentages were calculated. The grain-size distribution of the suspended load was analyzed using an automatic sieving device (SFY-D) (Zhonghu Scientific Ltd., Nanjing, China) and an automated Laser particle-size analyzer (Mastersizer2000) (Malvern Panalytical Ltd., Malvern, UK). Particle sizes falling between the range 0.0002 and 2 mm were identified. The obtained data are well suited for calibration and validation of numerical models. The field data acquired for the wet season, including one spring and one neap tide, in June 2015 were used in the study. For each WL and FS station, the time-series of the raw hydrological data were analyzed. For each time period, the average value of the FS sampling was first obtained for each line with the six points. Based on the three lines, cross-sectionally averaged sediment concentration, S (kg/m3), and flow velocity, V (m/s), were then achieved by the weighted average method given below:

∑ S V h S = i i i i (1) ∑i Vihi

∑ V h V = i i i (2) ∑i hi where Si and Vi = sediment concentration and velocity of each measured points, respectively.

3.2. Suspended versus Bed Load Based on grain-size distribution, river sediment is classified as sand (0.05–2 mm), silt (0.005–0.05 mm) and clay (<0.005 mm) [20]. The field measurements show that suspended load consists of cohesive silt and clay and accounts for approximately 95% of the sediment. Table1 shows their median grain sizes ( D50), which differ during spring and neap tides. For the former, the D50 values vary between 0.007–0.008 mm for the suspended load and between 0.011–0.019 mm for the bed load. For the latter, the corresponding ranges are 0.006–0.008 mm and 0.011–0.020 mm.

Table 1. D50 of suspended and bedload during the wet season (2nd half of June 2015).

Spring Tide, D50 (mm) Neap Tide, D50 (mm) Station Suspended Load Bed Load Suspended Load Bed Load FS3 0.007 0.011 0.008 0.012 FS4 0.008 0.019 0.006 0.020 FS5 0.008 0.011 0.007 0.011

3.3. Cross-Sectional Difference in Sediment Concentration The second half of June 2015 includes 30 semi-diurnal tides, with 30 ﬂood and ebb tides, respectively. To reveal the spatial changes of S at FS3, FS4 and FS5, Table2 summarizes their time-averaged S values, with the following observations.

Table 2. Time-averaged S values during the wet season (2nd half of June 2015).

Spring Tide (kg/m3) Neap Tide (kg/m3) Station Flood Tide Ebb Tide Average Flood Tide Ebb Tide Average 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 1.673 1.476 1.578 0.314 0.214 0.265

(1) Going upstream from the river mouth, the S value is largest at FS4, with S = 2.341 kg/m3 during the spring tide. Fluids 2019, 4, 15 6 of 19

(2) At the same location for either the spring or neap tide, S during the ﬂood tides differs from that during the ebb ones. The spring tides feature much higher values than the neap ones. This implies

Fluids 2019that, 4, thex spring tides govern the sediment transport from the coastal area. 6 of 19 (3) At the same location, S during the spring tide is 6−8 times as high as during the neap tide. InIn a meander a meander bend, bend, the the cross-sectional cross-sectional asymmetry affectsaffects the the re-distribution re-distribution of ofS, S which, which in in turn turn aggravatesaggravates its its asymmetry. asymmetry. For For lines lines A, A, B B and C at FS3,FS3, FS4FS4 andand FS5, FS5, Figure Figure4 displays,4 displays, during during the the springspring and and neap neap tides, tides, its its distribution. distribution.

FigureFigure 4. 4. S Sdistributionsdistributions of of lines lines A, B and CC atat eacheach FS FS during during the the wet wet season season (2nd (2nd half half of of June June 2015). 2015).

The following features are evident. The following features are evident. (1)(1) ForFor each each line, line, the the spring-tide spring-tide SS valuevalue is is significantly signiﬁcantly largerlarger than than the the neap-tide neap-tide one. one. This This further further indicatesindicates the the former former dominates dominates the the sediment sediment transport fromfrom the the coastal coastal area. area. (2)(2) AtAt FS4, FS4, line line A Ais isnearest nearest to to the the outer outer bank. bank. In In the spring tide,tide, FS4-BFS4-B exhibits exhibits the the largest largestS value,S value, followedfollowed by by FS4-C FS4-C and and FS4-A. FS4-A. This This shows shows that, that, aroundaround thisthis bendbend apex, apex, the the water water along along the the inner inner bankbank carries carries more sedimentsediment than than along along the outerthe bank.outer Thisbank. is mainlyThis is ascribable mainly toascribable the asymmetry to the asymmetryin cross-channel in cross-channel shape. shape. (3)(3) DuringDuring the the neap neap tide, tide, the the SS valuesvalues are are much much lower andand areareclose close at at the the same same cross-section. cross-section.

3.3.3.4. Vertical Vertical Difference Difference in in Sediment Sediment Concentration Concentration To look at the sediment distribution in the vertical direction, the measured results are analyzed To look at the sediment distribution in the vertical direction, the measured results are analyzed along lines A, B, C at each FS location. Table3 shows, for each line, the time-averaged sediment along lines A, B, C at each FS location. Table 3 shows, for each line, the time-averaged sediment concentration (denoted as Si) at h = 0, 0.2H0, 0.4H0, 0.6H0, 0.8H0 and H0. As a showcase, Figure5 concentration (denoted as 𝑆) at h = 0, 0.2H0, 0.4H0, 0.6H0, 0.8H0 and H0. As a showcase, Figure 5 illustrates, at FS4, its distribution along the lines. illustrates, at FS4, its distribution along the lines.

Table 3. Time-averaged sediment concentration (Si) along lines A, B and C during the wet season (2nd nd Tablehalf of3. Time-averaged June 2015). sediment concentration (𝑆) along lines A, B and C during the wet season (2 half of June 2015). Spring Tide (kg/m3) Neap Tide (kg/m3) Vertical Line Spring Tide (kg/m3) Neap Tide (kg/m3) Vertical line 0 0.2H0 0.4H0 0.6H0 0.8H0 H0 0 0.2H0 0.4H0 0.6H0 0.8H0 1.0H0 FS3-A0 0.8720.2H0 - 0.4H -0 0.6 1.412H0 0.8 -H0 1.798H0 0.1390 0.1480.2H0 0.1600.4H0 0.1700.6H0 0.1810.8H0 0.241 1.0H0 FS3-AFS3-B 0.872 0.643 - 0.871- 1.062 1.412 1.233 1.581- 1.798 1.996 0.1570.139 0.1770.148 0.1910.160 0.2020.170 0.2140.181 0.279 0.241 FS3-BFS3-C 0.643 0.633 0.871 0.786 1.062 0.941 1.233 1.151 1.581 1.320 1.996 1.761 0.1890.157 0.2060.177 0.2160.191 0.2260.202 0.2390.214 0.273 0.279 FS4-A 0.809 1.201 1.509 1.773 2.187 2.925 0.156 0.192 0.215 0.249 0.310 0.390 FS3-CFS4-B 0.633 0.783 0.786 1.193 0.941 1.775 1.151 2.249 1.320 3.018 1.761 4.292 0.1580.189 0.1880.206 0.2410.216 0.2960.226 0.4260.239 0.611 0.273 FS4-AFS4-C 0.809 1.097 1.201 1.246 1.509 2.050 1.773 1.902 2.187 2.903 2.925 2.962 0.1720.156 0.2010.192 0.2520.215 0.2410.249 0.3750.310 0.423 0.390 FS4-BFS5-A 0.783 0.876 1.193 1.135 1.775 1.443 2.249 1.739 3.018 1.989 4.292 2.349 0.1330.158 0.1740.188 0.2780.241 0.3430.296 0.4930.426 0.600 0.611 FS4-CFS5-B 1.097 0.906 1.246 1.200 2.050 1.490 1.902 1.717 2.903 1.982 2.962 2.409 0.1190.172 0.1460.201 0.2460.252 0.3480.241 0.4830.375 0.747 0.423 FS5-C 0.564 - - 1.547 - 2.048 0.061 - - 0.202 - 0.385 FS5-A 0.876 1.135 1.443 1.739 1.989 2.349 0.133 0.174 0.278 0.343 0.493 0.600 FS5-B 0.906 1.200 1.490 1.717 1.982 2.409 0.119 0.146 0.246 0.348 0.483 0.747 FS5-C 0.564 - - 1.547 - 2.048 0.061 - - 0.202 - 0.385 Fluids 2019, 4, 15 7 of 19 Fluids 2019, 4, x 7 of 19 Fluids 2019, 4, x 7 of 19

Figure 5. Distributions of Si along lines A, B and C at FS4 during the wet season: (a) Spring tide; Figure 5. Distributions of 𝑆 along lines A, B and C at FS4 during the wet season: (a) Spring tide; (b) Figure 5. Distributions of 𝑆 along lines A, B and C at FS4 during the wet season: (a) Spring tide; (b) (bNeap) Neap tide. tide. Neap tide. The following patterns are observed: The following patterns are observed: The following patterns are observed: (1)(1) TheThe S𝑆 distributiondistribution fromfrom thethe waterwater surfacesurface toto thethe riverriver bedbed exhibitsexhibits anan increasingincreasing tendency. (1) The 𝑆 i distribution from the water surface to the river bed exhibits an increasing tendency. Close to the bed, the 𝑆 value reaches a maximum. The value close to the bed is 2−5 times that CloseClose to to the the bed, bed, the the 𝑆Si value reaches a maximum. The value close to the bed is 2−55 times times that that close to the surface. closeclose to to the the surface. surface. (2) For a given line, the 𝑆 values at h = 0.6H0 are approximately equal to the line-averaged value. (2)(2) ForFor a agiven given line, line, the the 𝑆Si values at h = 0.6 0.6HH00 areare approximately approximately equal equal to to the the line-averaged line-averaged value. value. (3) At the same cross-section, the averaged 𝑆 values along the B line are the largest. This implies (3)(3) AtAt the the same same cross-section, cross-section, the the averaged averaged 𝑆S i valuesvalues along along the the B B line line are are the the largest. This This implies implies that the main-channel flow carries most sediment. thatthat the the main-channel main-channel flow flow carries carries most most sediment. sediment. (4) For the same point, the 𝑆 value during the spring tide is 3−7 times during the neap tide. This (4)(4) ForFor the the same same point, point, the the 𝑆 S valuevalue during during the the spring spring tide tide is 3− is7 3times−7 times during during the neap the neaptide. This tide. means that much more sediment i is transported by the spring tide, which is a potential source of meansThis means that much that much more moresediment sediment is transported is transported by the by spring the spring tide, tide, which which is a ispotential a potential source source of sedimentation in the area. The observations are consistent with the findings by Chen et al. [17] sedimentationof sedimentation in the inthe area. area. The The observations observations are are co consistentnsistent with with the the findings findings by by Chen Chen et et al. al. [17] [17] and Shen [18]. andand Shen Shen [18]. [18]. 3.4. Tidal Effects 3.4.3.5. Tidal Tidal Effects Effects To further unveil the time dependence of sediment transport, Figures 6 illustrates, for the spring ToTo further further unveil unveil the the time time dependence dependence of of sediment sediment transport, transport, Figures Figure 66 illustrates,illustrates, forfor thethe spring and neap tides, the relationship between S and V at cross-section FS5 (close to the river mouth). A andand neap neap tides, tides, the the relationship relationship between between S Sandand V Vat atcross-section cross-section FS5 FS5 (close (close to the tothe river river mouth). mouth). A positive V value indicates flow towards the sea and a negative V implies a reversal of the current. The positiveA positive V valueV value indicates indicates flow flow towards towards the sea the and sea anda negative a negative V impliesV implies a reversal a reversal of the of current. the current. The FS3 and FS4 results are shown later in the numerical part. FS3The and FS3 FS4 and results FS4 results are shown are shown later laterin the in numerical the numerical part. part.

Figure 6. Relationship between V and S at FS5: (a) Spring tide; (b) Neap tide. FigureFigure 6. 6. RelationshipRelationship between between VV andand SS atat FS5: FS5: (a (a) )Spring Spring tide; tide; ( (bb)) Neap Neap tide. tide. At the river mouth, the V and S values in the spring tide are larger than in the neap tide. S varies AtAt the the river river mouth, mouth, the the V andV and S valuesS values in the in spring the spring tide are tide larger are than larger in thanthe neap in the tide. neap S varies tide. greatly during a tidal period, with two peaks, implying that the tides govern the sediment greatlyS varies during greatly a during tidal aperiod, tidal period, with two with peaks, two peaks, implying implying that that the the tides tides govern govern the the sediment sediment concentration. The flood tidal V and S are always out of phase with each other; the S peak appears concentration.concentration. The The flood flood tidal tidal VV andand SS areare always always out out of of phase phase with with each each other; other; the the SS peakpeak appears appears during the flood tides. The S is modified by the tides and other oceanic processes. duringduring the the flood flood tides. tides. The The SS isis modified modified by by the the tides tides and and other other oceanic oceanic processes. processes. The spring tide dominates the river flow and transports the sediment in the river. The neap tide TheThe spring spring tide tide dominates dominates the the river river flow flow and and transp transportsorts the the sediment sediment in in the the river. river. The The neap neap tide tide being relatively weak, the run-off plays a dominant role. As a result, S and V exhibit non-similarity beingbeing relatively relatively weak, weak, the the run-off run-off plays plays a a dominant dominant role. role. As As a a result, result, SS andand VV exhibitexhibit non-similarity non-similarity between the spring and neap tides. The tides stir sediment, affects its peak duration and transport. between the spring and neap tides. The tides stir sediment, affects its peak duration and transport. Without the tides, sediment would be diverted directly downstream [21]. Without the tides, sediment would be diverted directly downstream [21]. Fluids 2019, 4, 15 8 of 19 between the spring and neap tides. The tides stir sediment, affects its peak duration and transport. Without the tides, sediment would be diverted directly downstream [21].

4. Numerical Modeling 3D numerical modeling of flow and sediment is performed for the tidal reach and it considers the following typical aspects: (1) bidirectional flow environment under the interaction between river run-off and tides; (2) spatial variations of roughness and bed asymmetry topography; (3) submergence and exposure of shoals due to tidal rising and falling; (4) stratified currents in meanders; and (5) graded suspended load.

4.1. Mathematical Formulation The Delft3D 4.04 package [22] is used to examine the complex flow features and morphology changes. It is based on the finite-difference method and solves the Navier-Stokes equations. To simulate river-bed changes, it is necessary to supplement such control conditions as bed stability coefficient and riverbed resistance. Therefore, the governing equations include equations for flow continuity, flow momentum, sediment transport and the bed deformation. The flow continuity equation is ∂ζ ∂(HU ) ∂ HUy + x + = q (3) ∂t ∂x ∂y where Ux (m/s) and Uy (m/s) = depth-averaged velocities in the x and y coordinate system, ζ (m) is the tidal level, d (m) is the still water depth, H (m) is the total water depth (H = ζ + d), q (m/s) is the global source or sink term per unit area and t (s) is time. The momentum equations in the x and y directions are ∂u ∂u ∂u ω ∂u 1 1 ∂ ∂u + + + − = − + + u v f v Pu Fu 2 vv (4) ∂t ∂x ∂y H ∂σ ρ0 H ∂σ ∂σ ∂v ∂v ∂v ω ∂v 1 1 ∂ ∂v + + + + = − + + u v f u Pv Fv 2 vv (5) ∂t ∂x ∂y H ∂σ ρ0 H ∂σ ∂σ 3 2 2 2 where ρ0 (kg/m ) = water density, vv (m /s) = vertical eddy viscosity, Pu and Pv (kg/(m s )) = pressure 2 gradients, Fu and Fv (m/s ) = horizontal Reynolds stresses, f (1/s) = Coriolis parameter (inertial frequency) and u and v (m/s) = longitudinal and transversal velocity components. The vertical velocity ω (m/s) component is computed from the mass balance:

∂ω ∂ζ ∂(Hu) ∂(Hv) = − − − + H(q − q + P − E) (6) ∂σ ∂t ∂x ∂y in out where qin and qout (m/s) = local source and sink per unit volume, P (m/s) = precipitation and E (m/s) = evaporation. As seen from the ﬁeld data, the bed-load amount is comparatively small (below 5%). To simplify, only the cohesive suspended sediment is considered in the sediment transport model. For mass balance and advection-diffusion, the equation in 3D reads as

∂S ∂ ∂ ∂ ∂ ∂S ∂ ∂S ∂ ∂S + (us) + (vs) + [(ω − ω )s] − ε − ε − ε = − F (7) ∂t ∂x ∂y ∂σ s ∂x s,x ∂x ∂y s,y ∂y ∂σ s,z ∂σ s

2 where ωs (m/s) = sediment settling velocity, εs,x, εs,y and εs,z (m /s) = eddy diffusivity of sediment fraction in three directions and Fs = function of the river-bed deformation, which is dependent on sediment erosion and deposition and is proposed as follows by Partheniades-Krone [23]. Fluids 2019, 4, x 9 of 19

𝜕𝑍 𝛾 = 𝐹 (8) Fluids 2019, 4, 15 𝜕𝑡 9 of 19

𝐹 =𝐷 − 𝐸 (9)

∂Zb γ0 =𝜏Fs (8) 𝜔 𝑆 1∂t − 𝜏𝜏 𝐷 = 𝜏 (10) Fs = Db −Eb (9)  0𝜏 𝜏 τ ωsS 1 − τ ≤ τ b τd d Db = (10)  𝜏0 τd < τ 𝑀 −1 𝜏𝜏 𝐸 = 𝜏 (11) M τ − 1 τ ≥ τ τ0𝜏𝜏e e Eb = (11)  0 τ < τe where Zb (m) = change in bed elevation, γ0 (N/m) = dry weight of bed load, Db (kg/(m2s)) = sediment 2 fluxwhere of depositionZb (m) = change from in suspended bed elevation, load,γ0 (N/m) Eb (kg/(m = dry2s)) weight = sediment of bed load, fluxD bof(kg/(m erosions)) =resulting sediment in 2 suspendedflux of deposition load, Sb (kg/m from3 suspended) = bottom load,sedimentEb (kg/(m concentration,s)) = sediment τ (N/m flux2) = ofbed erosion shear resultingstress, τd inand 3 2 τe (N/msuspended2) = critical load, stressesSb (kg/m of) deposition = bottom sediment and erosion concentration, and M (kg/mτ (N/m2s) = )bed = bed scouring shear stress, rate. τd and τe (N/m2) = critical stresses of deposition and erosion and M (kg/m2s) = bed scouring rate. 4.2. Grid and Bathymetry 4.2. Grid and Bathymetry The river reach of interest is composed of three consecutive bends. The bathymetry is based on The river reach of interest is composed of three consecutive bends. The bathymetry is based on the measured topography data in June 2015 (Figure 1c). The computational domain is 13.2 km long the measured topography data in June 2015 (Figure1c). The computational domain is 13.2 km long andand includes includes 1000 1000 m m upstream upstream and and 1200 1200 m m downstream downstream toto reducereduce boundary boundary effects. effects. Several Several grids grids of of variedvaried cell cell sizes sizes are are evaluated evaluated to to ensure ensure grid grid independence. GridGrid independenceindependence is is checked checked through through steady-statesteady-state calculations. calculations. Based Based on on a acoarse coarse mesh mesh (Figure (Figure7 7a),a), both both global global and and local local refinements refinements are are mademade to toachieve achieve a afiner finer mesh. mesh. Figures Figure7 7b,cb,c show show the the local local refinements refinements of twoof two sections. sections. AfterAfter refinement, refinement, the the domain domain is covered is covered by 10 by 5 1000 cells, 500 cells, comprising comprising 350 streamwise 350 streamwise cells and cells 30 transverseand 30 transversecells. Grid cells. size varies Grid sizebetween varies 10 between and 20 10m, anda typical 20 m, range a typical for most range river for mostsimulations river [7,13,22].simulations Denser [7,13 cells,,22]. with Denser a minimum cells, with cell a minimum size of 5 m, cell are size given of 5 m,to the are outer given bank to the to outer account bank for largeto accountflow velocity for large gradients. flow velocity As recommended gradients. As recommended by the Deltares by systems the Deltares [22], systems 10 layers [22 are], 10 specified layers in arethe specifiedvertical direction, in the vertical with direction, a thickness with of a thickness2%, 3%, 4%, of 2%, 6%, 3%, 8%, 4%, 10%, 6%, 12%, 8%, 10%, 15%, 12%, 20% 15%, and 20%20% and of H. The20% difference of H. The between difference two between neighboring two neighboring layers should layers not should exceed not exceedthe lower the lowerlayer’s layer’s thickness. thickness.

FigureFigure 7. 7.NumericalNumerical grids: grids: (a ()a )A A coarse coarse grid grid over over the the domain; ((bb)) LocalLocal refinement refinement in in the the vicinity vicinity of of WL5;WL5; (c) ( cLocal) Local refinement refinement upstream upstream of of WL6. WL6. 4.3. Boundary Conditions 4.3. Boundary Conditions For flow computations, time-series of boundary conditions are specified with discharge, Q (m3/s), 3 atFor the flow upstream computations, end (FS3) time-series and with water of boundary level, Z (m),conditions at the downstreamare specified endwith (WL6) discharge, (Figure Q 8(ma)./s), at the upstream end (FS3) and with water level, Z (m), at the downstream end (WL6) (Figure 8a). The FluidsFluids2019 2019,,4 4,, 15x 1010 of 1919

time series of sediment concentration needs also be specified at both ends (Figure 8b). For the closed Thesediment time seriesboundary of sediment (river bed concentration and banks), needsa non-entr alsoy be condition speciﬁed specifies at both endsa zero (Figure normal8b). gradient For the of closedsediment sediment content. boundary The wetting (river and bed anddrying banks), function a non-entry of cells condition is activated speciﬁes to account a zero for normal the tidal gradient rise ofand sediment fall. content. The wetting and drying function of cells is activated to account for the tidal rise and fall.

FigureFigure 8.8.Measured MeasuredQ, Q,Z Zand andS Sas as boundary boundary conditions: conditions:( a(a)) Q~t Q~t andand Z~t;Z~t; ((bb)) S~t.S~t.

River-bedRiver-bed roughness,roughness, representedrepresented byby Manning’sManning’s roughnessroughness equation,equation, isis anan essentialessential parameterparameter dependentdependent on such such factors factors as as river-bed river-bed morphology, morphology, flow ﬂow patterns patterns including including water water depth, depth, etc. The etc. −1/3 −1/3 Therange range of Manning’s of Manning’s roughness roughness falls falls within within n n= =0.015 0.015 to to 0.030 0.030 m m-1/3 s, withs, with 0.015 0.015–0.018‒0.018 m m-1/3 s fors forthe −1/3 themain main channel channel and and 0.018 0.018–0.030‒0.030 m-1/3 m s for thes for shore the shorebeach, beach, which which is based is based on field on investigations. ﬁeld investigations. For a Forgiven a given position, position, interpolation interpolation is made is made in light in light of ofwater water depth. depth. Table Table 44 summarizes thethe additionaladditional parameters,parameters, ωωss,, τd,, ττee, ,MM andand γγ0,0 ,in in the the model model setup. setup.

TableTable 4.4. ParameterParameter valuesvalues adoptedadopted inin thethe model.model.

ParameterParameter DataData Range range Source Source ωs𝜔(m/s) (m/s) 0.0005 0.0005 Field Field measurements measurements 2 τd (N/m ) 0.06–0.10 Equation (10) [23] 𝜏 (N/m2 2) 0.06‒0.10 Equation (10) [23] τe (N/m ) 0.10–0.20 Equation (11) [24] 2 2 M (kg/m𝜏 (N/ms)) 0.0002–0.020.10‒0.20 Equation Equation (11) (11) [24 [24]] 3 γ0 (kg/m ) 1600 Field measurements M (kg/m2s) 0.0002‒0.02 Equation (11) [24]

3 𝛾 (kg/m ) 1600 Field measurements To achieve numerical stability, the chosen time step is 0.3 s. For each time step, the ﬂow is ﬁrst calculated and the sediment transport and the resulting bed-level change are updated accordingly. To achieve numerical stability, the chosen time step is 0.3 s. For each time step, the flow is first 5.calculated Model Calibration and the sediment and Validation transport and the resulting bed-level change are updated accordingly.

5. ModelCalibration, Calibration as well and as Validation validation, is a prerequisite for modelling accuracy. By adjusting specific parameters, a reasonable match is achieved between observed and simulated results. In the study, varyingCalibration, roughness as coefficientwell as validation, in space, is timea prerequisite step and openfor modelling boundary accuracy. conditions By adjusting and refining specific the meshparameters, are the a tuning reasonable aspects. match As is in achieved many other betwee studies,n observed the results and turnsimulated out to results. be most In sensitive the study, to thevarying roughness. roughness Time coefficient steps (dependent in space, on time the step grid and density) open and boundary boundary conditions conditions and also refining have the an influencemesh are onthe the tuning model aspects. convergence; As in many the gridother density studies, has the a results bearing turn on theout accuracy to be most of sensitive the results. to the roughness.As shown Time in Tablesteps 5(dependent, three model on criteria, the grid i.e., den Nash-Sutcliffesity) and boundary efficiency conditions ( NSE), R-Squared also have ( Ran2) influence on the model convergence; the grid density has a bearing on the accuracy of the results. and Percent bias (PBIAS) are often used for model evaluation, where Oi = observed (in situ) value, As shown in Table 5, three model criteria, i.e., Nash-Sutcliffe efficiency (NSE), R-Squared (R2) O = average of Oi, Pi = predicted value, P = average of Pi and n = total number of observed or 𝑂 predictedand Percent values. bias (PBIAS) are often used for model evaluation, where = observed (in situ) value, 𝑂 𝑂 𝑃 𝑃 𝑃 = Theaverage model of calibration, = predicted is based value, upon the = hourlyaverage data of observed and n = fortotal the number spring of tide observed occurring or betweenpredicted the values. period from 10:00 2015-06-17 to 16:00 2015-06-18; totally 30 h. Comparisons of water levels at WL4The and model WL5 calibration and of V and is Sbasedat FS4 upon are shownthe hourly in Figure data9 .observed for the spring tide occurring between the period from 10:00 2015-06-17 to 16:00 2015-06-18; totally 30 hours. Comparisons of water levels at WL4 and WL5 and of V and S at FS4 are shown in Figure 9. Fluids 2019, 4, x 11 of 19

Fluids 2019, 4, 15 Table 5. Error parameters and accepted ranges for model evaluation [25–27]. 11 of 19

Parameter Range Optimal value Satisfactory if Expression Table 5. Error parameters and accepted ranges for model evaluation [25–27]. ∑ ( ) 𝐸=1− NSE −∞–1 1 > 0.5 ∑ ( ) Parameter Range Optimal value Satisfactory if Expression

n 2 ∑ (Oi −Pi ) = − i=1 NSE −∞–1 1 > 0.5 E 1 n 2 ∑i=1(Oi −O) ∑ ( )( ) R2 0–1 1 > 0.5 𝑅 = R2 = !2 2 n∑ ( )∑ ( ) R 0–1 1 > 0.5 ∑i=1(Oi −O)(Pi −P) q q n 2 n 2 ∑i=1(Oi −O) ∑i=1(Pi −P) ±25% for streamflow ∑ ( ) ±25% for streamﬂow n (O −P )×100 PBIAS −∞–+∞ 0 𝑃𝐵𝐼𝐴𝑆∑i= 1 i i PBIAS −∞–+∞ 0 PBIAS = n ∑ ±55%±55% for forsediment sediment ∑i=1 Oi

Figure 9. 9. ModelModel calibration calibration with with meas measuredured versus versus predicted predicted for th fore spring the springtide (June tide 2015): (June (a 2015):) Z at (WL4;a) Z at(b WL4;) Z at (WL5;b) Z at (c WL5;) V at (FS4;c) V ( atd) FS4; S at (FS4.d) S at FS4.

The calibrationcalibration results results show show that that the calculatedthe calculatedZ and ZV andare inV goodare in agreement good agreement with the measuredwith the ones.measured All their ones. error All parameterstheir error meetparameters the criteria. meet Forthe Scriteria., the calculated For S, the and calculated simulated and results simulated do not exhibitresults do the not exactly exhibit same the pattern. exactly However,same pattern. the sediment However, peaks the sediment are, in terms peaks of phaseare, in andterms magnitude, of phase reasonablyand magnitude, reproduced. reasonably reproduced. The model validation is performed with a neap tide that occurred during the period between 15:00 2015-06-242015-06-24 andand 22:0022:00 2015-06-25,2015-06-25, lastinglasting aa total total of of 31 31 h. hours. It follows It follows the same the principlesame principle as model as calibration.model calibration. The validation The validation results results are shown are shown in Figure in 10Figure. 10. The calculated Z, V and S profilesprofiles match relatively well with the measured data series. All the error parameter values also meet thethe requirements.requirements. As in other numerical simulations, the match between thethe measured measured and and simulated simulated parameters parameters is better is better for Z forand ZV andthan V for thanS. The for interplay S. The interplay between fresh-waterbetween fresh-water flows and flows tides and accounts tides accounts for the difference for the difference in peak in sediment peak sediment concentration. concentration. The model The generatesmodel generates acceptable acceptable results results and it isand suitable it is suitab for predictionle for prediction of flow of and flow morphology and morphology changes changes of the meanderingof the meandering river reach. river reach. Fluids 2019, 4, 15 12 of 19 Fluids 2019, 4, x 12 of 19

FigureFigure 10. 10.Model Model validation validation withwith thethe neap tide (June 2015): 2015): ( (aa) )Z Z at at WL4; WL4; (b (b) )Z Z at at WL5; WL5; (c ()c V) Vat at FS4; FS4; (d()d S) S at at FS4. FS4.

6.6. Typical Typical Flow Flow Features Features InIn the the meandering meanderingreach, reach, thethe flowflow featuresfeatures are of significant significant variations variations with with stratified stratified currents, currents, inin which which cross-sectional cross-sectional velocityvelocity distributionsdistributions often deviate from from the the logarithmic logarithmic profile profile typical typical of of straightstraight reaches. reaches. Meanwhile,Meanwhile, the the bi-directional bi-directional curre currentsnts induced induced by byflood flood and and ebb ebbtides tides also make also make the theflow flow patterns patterns more more complex. complex. A A2D 2D depth-averaged depth-averaged model, model, with with the the assumption assumption of of a alogarithmic logarithmic velocityvelocity structure, structure, would would leadlead toto inaccurateinaccurate prediction in terms of, of, e.g., e.g., bed bed shear shear stress stress [22]. [22]. A A 3D 3D modelmodel is, is, therefore, therefore, necessary necessary for for predictionprediction ofof suchsuch aa tidaltidal meander reach.

6.1.6.1. Cross-Sectional Cross-Sectional Flow Flow Patterns Patterns InIn addition addition to cross-sectional cross-sectional and and streamwise streamwise changes changes of bed of forms, bed forms, the flow the patterns flow patterns in cross- in cross-sectionsection are also are influenced also influenced by the byrise the and rise fall andof th falle tides, of the which tides, is different which is from different non-tidal from situations non-tidal situationswith only with run-off. only Cross-section run-off. Cross-section WL5 is at WL5 the bend is at theapex bend and apex is chosen and isto chosen illustrate to illustratethe issue. the Figure issue. Figure11 shows, 11 shows, during during the spring the springtide, its tide, patterns its patterns of the falling of the fallingperiod period(a,b), low (a,b), water low slack water (c), slack rising (c), risingperiod period (d,e) (d,e)and high and water high water slack (f), slack respective (f), respectively.ly. Major Majorflow patterns flow patterns are summarized are summarized below: below: (1) During the tidal fall and rise, the cross-sectional flows behave differently in direction and (1) magnitude.During the For tidal the fall former, and rise,the flow the moves cross-sectional from the main flows stream behave of differentlyhigher velocity in direction toward the and banks.magnitude. For the For latter, the former,the cross-sectional the flow moves currents from are the driven main streamin the opposite of higher direction; velocity towardthe water the flowingbanks. Forfrom the the latter, banks the are cross-sectional likely to offset currents each other. are drivenThe alternating in the opposite flow causes direction; deposition the water or erosionflowing at from a bend. the banks are likely to offset each other. The alternating flow causes deposition or (2) Aterosion the low at aand bend. high water slacks, as shown in Figure 11c,f, the flow strength decreases to its (2) minimum.At the low The and reason high wateris that slacks,the motion as shown reverses in in Figure the subsequent 11c,f, the flowchanges, strength so that decreases the residual to its motionminimum. from The the reasonprevious is thattide thecounteracts motion reversesthe motion in thein the subsequent next period. changes, so that the residual (3) Atmotion the bend from apex, the previoussecondary tide circ counteractsulations in cross-section the motion in do the no nextt occur period. as commonly observed in (3) non-tidalAt the bend meandering apex, secondary rivers [4,6]. circulations The difference in cross-section is mainly do ascribed not occur to as the commonly tidal level observed changes, in resultingnon-tidal in meandering cross-sectional rivers currents [4,6]. moving The difference away from is mainly or toward ascribed the streamwise to the tidal mainstream. level changes, resulting in cross-sectional currents moving away from or toward the streamwise mainstream. Fluids 2019, 4, 15 13 of 19

Fluids 2019, 4, x 13 of 19 (4) At the maximum ebb and flood tides, the flow velocity of the mainstream reaches its peak, (4) At the maximum ebb and flood tides, the flow velocity of the mainstream reaches its peak, amounting to 0.8−1.0 m/s and 0.5−0.8 m/s (Figure 11b,e). The former is some 0.2 m/s larger amounting to 0.8−1.0 m/s and 0.5−0.8 m/s (Figure 11b,e). The former is some 0.2 m/s larger than than the latter, which is due to the addition of the ebb tide to the run-off. For the flood tide, the latter, which is due to the addition of the ebb tide to the run-off. For the flood tide, the run-off the run-off and the tide run in the opposite direction, thus offsetting each other. It holds true that and the tide run in the opposite direction, thus offsetting each other. It holds true that the velocity the velocity of the ebb tide is higher than that of the flood tide. of the ebb tide is higher than that of the flood tide. (5) The flow along the outer bank, during the falling period, is much stronger than that along the (5) The flow along the outer bank, during the falling period, is much stronger than that along the inner bank. With the rising tide, the flow pattern shifts and the flow along the inner bank becomes inner bank. With the rising tide, the flow pattern shifts and the flow along the inner bank becomes stronger instead. Along the banks in a bend, the opposing and offsetting flows are also visualised stronger instead. Along the banks in a bend, the opposing and offsetting flows are also visualised by Fenies and Faugeres [28]. by Fenies and Faugeres [28].

FigureFigure 11.11. Cross-sectionalCross-sectional ﬂowflow patterns patterns during during the the spring spring tide: tide: (a (,ba,)b Falling) Falling period; period; (c )(c Low) Low water water slack; (d,e) Rising period; and (f) High water slack. slack; (d,e) Rising period; and (f) High water slack.

In summary, dependent on the rise and fall of the tides, the cross-sectional flow patterns in a meander differ in both flow direction and magnitude. Relative to the main stream, the major feature is an outward movement of water with the falling tide and an inward movement with the rising tide. Fluids 2019, 4, 15 14 of 19

In summary, dependent on the rise and fall of the tides, the cross-sectional flow patterns in a meander differ in both flow direction and magnitude. Relative to the main stream, the major feature is an outward movement of water with the falling tide and an inward movement with the rising tide. Fluids 2019, 4, x 14 of 19 6.2. Bed Shear Stress Distribution 6.2. Bed Shear Stress Distribution → For the flood and ebb tides, the bed shear stress (τb) is useful to judge flow regime and to interpret → For the flood and ebb tides, the bed shear stress (𝜏⃗ ) is useful to judge flow regime and to the resulting patterns of deposition and erosion. For 3D flows, τb is expressed in terms of a quadratic → interpret the resulting patterns of deposition and erosion. For 3D flows, 𝜏⃗ is expressed in terms of function of the ub and a drag coefficient [22,29]. a quadratic function of the 𝑢⃗ and a drag coefficient [22,29].

→ → → ρ𝜌0g𝑔𝑢ub⃗ |u𝑢b⃗ | = 𝜏τb⃗ = 2 (12)(12) C𝐶3D → 𝑢⃗ 3D where ub (m/s)(m/s) == horizontalhorizontal velocityvelocity inin thethe firstfirst layerlayer aboveabove√ thethe riverriver bedbed andand CC3D = a 3D-Ch3D-Chézyézy 6 coefficient.coefficient. For a relatively wide and shallow river, C𝐶3D == √𝐻H/𝑛/n. . →𝜏⃗ Determination of τb is is influenced influenced by by such such factors factors asas riverriver curvature,curvature, cross-sectionalcross-sectional asymmetry and sedimentsediment composition, composition, etc. etc. Due Due to flowto flow perturbations, perturbations, it is not it straightforwardis not straightforward to directly to measuredirectly measureit in the field. it in Numericalthe field. Numerical modeling modeling is employed is empl for itsoyed analysis for its of analysis the meandering of the meandering stream. For stream. the wet For the wet season (June 2015), Figure→ 12 displays 𝜏⃗ distributions at four instants, i.e., (a) high water, season (June 2015), Figure 12 displays τb distributions at four instants, i.e., (a) high water, (b) maximum → (b) maximum ebb tide, (c) low water and (d) maximum flood tide. 𝜏⃗ varies with discharge, bend ebb tide, (c) low water and (d) maximum flood tide. τb varies with discharge, bend curvature, curvature,cross-sectional cross-sectional asymmetry, asymmetry, etc., demonstrating etc., demonstrating the following the features. following features.

→ Figure 12. Distributions of τb during the wet season (June 2015): (a) High tide; (b) Maximum ebb tide; Figure 12. Distributions of 𝜏⃗ during the wet season (June 2015): (a) High tide; (b) Maximum ebb (c) Low tide; (d) Maximum ﬂood tide. tide; (c) Low tide; (d) Maximum flood tide.

(1) 𝜏⃗ is proportional to 𝑢⃗|𝑢⃗| and is also a function of H. In the meander reach, the |𝑢⃗| and H values are between 0.2−0.6 m/s and 6.0−14.0 m (exclusive of the scour hole at WL5). At the low

and the high water, a similar 𝜏⃗ distribution is exhibited (Figure 12a,c), with minor local discrepancy. 𝜏⃗ reflects the velocity gradient, governed by the run-off and tides. At the maximum ebb and flood tides, the peak 𝜏⃗ values are shown in Figure 12b,d. Fluids 2019, 4, 15 15 of 19

→ → → → (1) τb is proportional to ub ub and is also a function of H. In the meander reach, the ub and H values are between 0.2–0.6 m/s and 6.0–14.0 m (exclusive of the scour hole at WL5). At the low and → the high water, a similar τb distribution is exhibited (Figure 12a,c), with minor local discrepancy. → Fluids 2019τb reflects, 4, x the velocity gradient, governed by the run-off and tides. At the maximum ebb15 of and 19 → flood tides, the peak τb values are shown in Figure 12b,d. (2) Due to erosion, a deep hole exists at bend apex WL5. Its 𝜏⃗→ distribution features low values. (2) Due to erosion, a deep hole exists at bend apex WL5. Its τ distribution features low values. This is ascribed to the large water depth. Shoaling areas along bthe inner banks show always low This is ascribed to the large water depth. Shoaling areas along the inner banks show always low 𝜏⃗→ values. τ values. (3) Theb spatial distribution is also affected by the curvature. A salient feature is, following the main (3) The spatial distribution is also affected by the curvature. A salient feature is, following the main stream, a band of high 𝜏→⃗ values. In the flow direction, it shifts from the outer bank in one bend tostream, the outer a band bank of highin theτb values.subsequent In the bend. flow direction, This is true it shifts forfrom both the flood outer and bank ebb in onetides. bend The to occurrencethe outer bankof the in band the subsequent is similar to bend. the situation This is true with for a non-tidal both flood meander and ebb reach tides. [30,31]. The occurrence of the band is similar to the situation with a non-tidal meander reach [30,31]. 6.3. Sediment Carrying Capacity 6.3. Sediment Carrying Capacity The sediment carrying capacity (Sc, kg/m3) reflects, as an index, the amount of entrained 3 sedimentThe sedimenttransported carrying by the capacity flow if (erosionSc, kg/m and) reflects, deposition as an are index, in equilibrium. the amount ofIn entrained comparison sediment with transported by the flow if erosion and deposition are in equilibrium. In comparison with the actual the actual S in the water, predictions are made of morphological changes. If S > Sc, the flow is over- S in the water, predictions are made of morphological changes. If S > Sc, the flow is over-saturated saturated with sediment and deposition occurs. If S < Sc, it is under-saturated, and erosion takes place. with sediment and deposition occurs. If S < Sc, it is under-saturated, and erosion takes place. Sc Sc is shown to have a linear relationship with F2 (Froude number F = V2/(gH)) [17,32,33], with the 2 2 followingis shown expression to have a linear relationship with F (Froude number F = V /(gH)) [17,32,33], with the following expression 𝑆 =𝑆 +ƒ(𝐹)2 =𝑆 + 𝑘𝐹2 (13) S𝑐 c = S00 + f F = 0S0 + kF (13) where k = coefficient and S0 = background sediment concentration, i.e., the amount of sediment left where k = coefficient and S0 = background sediment concentration, i.e., the amount of sediment left fromfrom the the previous previous tide. tide. The The multivariate multivariate linear linear regression regression analysis analysis and and the the least least square square method method are are usedused for for their their estimations. estimations. At At each each time time interval, interval, a cross-section a cross-section has has3 × 36 ×= 186 =measured 18 measured values. values. For theFor 30-hour the 30-h measurement measurement period, period, 30 30 sets sets of of the the data data are are analysed. analysed. For For the the flood flood and and ebb ebb tides tides of of the the 2 wetwet season season in in June June 2015, 2015, Figure Figure 13 13 shows shows the the obtained obtained SS‒–FF2relationship.relationship.

Figure 13. S–F2 relationship for the wet season (June 2015): (a) Flood tides; (b) Ebb tides. Figure 13. S‒F2 relationship for the wet season (June 2015): (a) Flood tides; (b) Ebb tides.

The Sc expression for the meander reach is written as The Sc expression for the meander reach is written as 2 Flood tide, Sc = 103.86F + 1.09 (14) Flood tide, 𝑆 = 103.86𝐹 + 1.09 (14)

Ebb tide, S = 58.67F2 + 0.92 (15) Ebb tide, 𝑆 c = 58.67𝐹 + 0.92 (15)

TheThe kk valuevalue for for the the flood ﬂood tides is almost twicetwice asas highhigh asas forfor thethe ebb ebb tides. tides. It It is, is, therefore, therefore, reasonable reasonable to separately determine S —the former carries more sediment than the latter. Chen et al. [17,32] examined to separately determinec Sc—the former carries more sediment than the latter. Chen et al. [17,32] S during wet and dry seasons, which also show signiﬁcantly different S values. examinedc Sc during wet and dry seasons, which also show significantly differentc Sc values. In a meander subjected to the interaction of run-off and tides, Sc depends on a few factors and shows its complexity in both time and space. In consideration of the nature of the issue, it is not straightforward to find a unified Sc formula with accuracy. Though there are other forms of expressions, the commonly accepted expression is based on F, implying that Sc is mainly dependent on turbulence intensity [33,34].

6.4. Erosion-Deposition Patterns Fluids 2019, 4, 15 16 of 19

Fluids 2019, 4, x 16 of 19 In a meander subjected to the interaction of run-off and tides, S depends on a few factors and Predictions are made to look at the potential sediment patternsc in the meander. The tidal shows its complexity in both time and space. In consideration of the nature of the issue, it is not currents, especially the spring tide in a wet season, dominate the sediment transport. During the 2nd straightforwardhalf of June 2015, to find the a 30-hour unified springSc formula tide is with chosen accuracy. for the Thoughpurpose, there corresponding are other formsto a critical of expressions, scenario the commonlyof interest. Compared accepted expression with river flow is based conditions, on F, implying morphological that Sc changesis mainly are dependent a slower process. on turbulence When intensityonly [simulating33,34]. a 30-hr period, changes in the bed level are hardly noticeable. A morphological scaling factor is thus used to amplify the bed-form change, a method of common practice [21,35,36]. 6.4. Erosion-Deposition Patterns It is set to 24, leading to a one-month prediction. A longer time series of measured sediment data is notPredictions available. are made to look at the potential sediment patterns in the meander. The tidal currents, especiallyThe the start spring condition tide incorresponds a wet season, to the dominate measured the bathymetry sediment at transport. 10:00 on June During 17, 2015. the 2ndFigure half of June14a− 2015,c illustrates the 30-h the springbed-form tide evolution is chosen from for T the = 0, purpose, 15 to 30 days. corresponding As time elapses, to a critical the results scenario show of interest.that, Comparedexcept for withthe slight river erosion flow conditions, in the vicinity morphological of WL4, gradual changes deposition are a slower features process. the Whenmeander only reach. The trend is in qualitative agreement with the observation made by Chen et al. [17,32], in which simulating a 30-hr period, changes in the bed level are hardly noticeable. A morphological scaling the influence of the wading structures, including bridges and wharfs, was also included. Figure 14d−f factor is thus used to amplify the bed-form change, a method of common practice [21,35,36]. It is set to illustrates, as a function of time, the cross-sectional bed profiles at WL4, FS4 and WL5. 24, leading to a one-month prediction. A longer time series of measured sediment data is not available. For a given cross-section, its inner bank is exposed to heavier deposition than the outer bank. The start condition corresponds to the measured bathymetry at 10:00 on 17 June 2015. Figure 14a−c The mainstream tends to switch more to the outer bank, aggravating the curvature of the bend. illustratesDuring the bed-form a tidal circle, evolution sediment from transportT = 0, 15 into to and 30 days. out of As the time reach elapses, is not in the balance, results leading show that,to exceptsediment for the storage slight erosionalong the in reach. the vicinity As shown of WL4,in the gradualfield measuremen depositionts, featuresthe flood the tide meander carries more reach. Thesediment trend is in and qualitative results in agreementdeposition. withFor an the ebb observation tide, its low made bed byshear Chen stress et al.can [ 17only,32 ],re-suspend in which thea influencelimited of amount the wading of the structures,deposited sediment including from bridges the flood and tides, wharfs, only was slight also erosion included. occurs. Figure The flood14d− f illustrates,tide plays as aa functiondominant of role. time, An the oblong cross-sectional scour hole exists bed profilesat WL5. atAt WL4,maximum, FS4 and its hole WL5. depth is initially 14.0For m a and given becomes cross-section, 13.05 m at its T inner= 30 days. bank The is hole exposed shrinks to both heavier up- and deposition downstream than as the time outer elapses. bank. TheBoth mainstream the flood tends and ebb to switch tides contribute more to the to shaping outer bank, the scour aggravating hole. the curvature of the bend.

Figure 14. Cont. Fluids 2019, 4, 15 17 of 19 Fluids 2019, 4, x 17 of 19

Figure 14. Morphological changes during the spring tide: (a) T = 0 (measured bed level); (b) T = 15 Figure 14. Morphological changes during the spring tide: (a) T = 0 (measured bed level); (b) T = 15 days;days; (c) T (=c) 30T = days; 30 days; cross-sectional cross-sectional bed bed level level changes changes at at (d ()d WL4;) WL4; ( e(e)) FS4; FS4; ((ff)) WL5.WL5.

DuringSediment a tidal deposition circle, sediment occurs easily transport around into the and flow out reversal, of the i.e., reach the is shift not between in balance, flood leading and ebb to sedimenttides, storagewhich is along dependent the reach. on the As duration shown of in slack the fieldwaters. measurements, As shown earlier the (Figure flood tide11c,e), carries the cross- more sedimentsectional and flow results momentum in deposition. during Forthe anslacks ebb decreas tide, itses lowto a bedminimum. shear stressThe offsetting can only effect re-suspend between a limitedthe amountflood tide of and the depositedrun-off results sediment in a long from slack the du floodration tides, around only the slight high erosion water. As occurs. a result, The more flood tide playssuspended a dominant sediment role. settles An oblong at the reversals. scour hole exists at WL5. At maximum, its hole depth is initially 14.0 m andTo becomes sum up, 13.05 the flow m at regimeT = 30 days.and imbalance The hole of shrinks sediment both transport up- and downstreamare the main asdrivers time elapses.of the Bothmeander the flood reach and ebbevolution. tides contribute Though there to shaping is no comp the scourlete bathymetry hole. data available to calibrate the morphologicalSediment deposition change for occurs the reach, easily the around simulation the flow suggests reversal, that i.e.,the bed-level the shift changes between are flood closely and ebb tides,related which to the isinteractions dependent between on the the duration run-off of and slack tides. waters. The latter As shownplays a earlierdominating (Figure role 11 andc,e), the cross-sectionalgoverns the sedimentation. flow momentum during the slacks decreases to a minimum. The offsetting effect between the flood tide and run-off results in a long slack duration around the high water. As a result, 7. Conclusions more suspended sediment settles at the reversals. To sumIf river up, run-off the flow and regime strong tides and imbalanceco-exist in a of meander sediment reach, transport its flow areand themorphological main drivers changes of the meanderare governed reach evolution. by several Thoughfactors and there exhibit is no both complete spatial and bathymetry periodical data changes. available Field toand calibrate numerical the morphologicalstudies are made change to forexamine the reach, such a the tidal simulation meander reach. suggests that the bed-level changes are closely related toField the measurements interactions between show that the approximately run-off and 95% tides. of the The river latter sediment plays is a suspended dominating load, role most and governsof which the sedimentation. is transported upstream into the reach by the flood tides, especially during the spring-tide period. Tidal currents stir sediment and modify its concentration, which leads to the fact that the flow 7. Conclusionsvelocity and sediment concentration are out of phase with one another. The asymmetry in cross- section and bi-directional flow affect the re-distribution of suspended load, leading to a higher concentrationIf river run-off in and the stronginner banks tides than co-exist in the in aoute meanderr banks. reach, Additionally, its flow andthe near-bottom morphological values changes are are governedusually 2− by5 times several thefactors surface and ones. exhibit Based bothon the spatial extensiv ande filed periodical data, a changes.formula of Field sediment and numerical carrying studiescapacity are made is formulated to examine as such a function a tidal meanderof the Froude reach. number, with which deposition and erosion patternsField measurements can be judged. show that approximately 95% of the river sediment is suspended load, most of which is transportedBased on the Delft3D upstream software, into the a 3D reach model by of the suspended flood tides, sediment especially transport during is setup the to spring-tide simulate period.the Tidalalluvial currents behavior stir of sediment the reach. and The modify flow exhibits its concentration, significant which vertical leads stratifications; to the fact thatthe velocity the flow velocitydistribution and sediment differs concentration from the logarithmic are out ofprofile phase vali withd for one a non-tidal another. Thestraight asymmetry river reach. in cross-section During the and bi-directionaltidal rise and flowfall, the affect cross-sectional the re-distribution flow moves of suspended in the opposite load, leading direction. to aAt higher the water concentration slacks, the in the innermomentum banks than decreases in the outerto a minimu banks.m. Additionally, Sediment settles the near-bottom mainly du valuesring the are flow usually reversal 2−5 timesand the the surfacedurations ones. Based of slack on water the extensive affects the filed deposited data, aamount. formula The of sedimentspatial distribution carrying capacityof the bed is shear formulated stress as a functionfollows the of pattern the Froude of velocity number, gradient withwhich and is depositionalso affected and by the erosion meander patterns asymmetry. can be judged. With a morphological scale factor, the bed-form change of the meander reach is predicted. The Based on the Delft3D software, a 3D model of suspended sediment transport is setup to simulate results show that, during a tidal circle, the suspended load transport in and out of the reach is not in the alluvial behavior of the reach. The flow exhibits significant vertical stratifications; the velocity balance and gives rise to gradual siltation, which is mainly owing to the flood tides that carry most distribution differs from the logarithmic profile valid for a non-tidal straight river reach. During of the load. The offsetting effect between the flood tide and run-off results in a long slack duration the tidalaround rise the and high fall, water, the cross-sectional facilitating the flowsediment moves deposition in the opposite when the direction. current reverses At the between water slacks, the the momentumflood and ebb decreases tides. to a minimum. Sediment settles mainly during the flow reversal and the Fluids 2019, 4, 15 18 of 19 durations of slack water affects the deposited amount. The spatial distribution of the bed shear stress follows the pattern of velocity gradient and is also affected by the meander asymmetry. With a morphological scale factor, the bed-form change of the meander reach is predicted. The results show that, during a tidal circle, the suspended load transport in and out of the reach is not in balance and gives rise to gradual siltation, which is mainly owing to the flood tides that carry most of the load. The offsetting effect between the flood tide and run-off results in a long slack duration around the high water, facilitating the sediment deposition when the current reverses between the flood and ebb tides. The tides interact with the fresh-water run-off and lead to varied sediment patterns in space and time, generating a different morphological regime from a non-tidal meander reach. The study, especially the collected field data, contributes to the understanding of the fluvial behaviors and is of reference to other investigations of similar tidal meander rivers.

Author Contributions: Field data analyses and numerical simulations are performed by Q.X., with supervision from J.Y. and T.S.L. The manuscript is written by Q.X. and J.Y., with comments from T.S.L. Funding: Q.X. is supported by a Ph.D. scholarship from the Chinese Scholarship Council (CSC) and the Swedish STandUp for Energy project. The authors are members of the 111 Project (Discipline Innovation & Research Base on River Network Hydrodynamics System and Safety, Grant No. B17015), from Ministry of Education and China State Administration of Foreign Experts Affairs, with Hohai University as executive organization. Acknowledgments: Hydrology and Water Resources Survey Bureau of the Lower Yangtze River is responsible for the field measurements. The authors acknowledge the assistance from Wenhong Dai and Chunhui Lu during the visits at Hohai University. Conflicts of Interest: The authors declare no conflict of interest.

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