Suspended sediment transport in the ... - Wiley Online Library

JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 118, 5568–5590, doi:10.1002/jgrc.20411, 2013

Suspended sediment transport in the Deepwater Navigation Channel, Yangtze River Estuary, China, in the dry season 2009: 2. Numerical simulations Dehai Song1,2 and Xiao Hua Wang2,3 Received 23 March 2013; revised 15 September 2013; accepted 18 September 2013; published 22 October 2013.

[1] A three-dimensional wave-current-sediment coupled numerical model with wetting and drying process is developed to understand hydrodynamics and sediment transport dynamics in the Deepwater Navigation Channel (DNC), the North Passage of the Yangtze River Estuary (YRE), China. The model results are in good agreement with observed data, and statistics show good model skill scores and correlation coefficients. The model well reproduces the spring-neap variation between a well-mixed estuary and a highly stratified estuary. Model results indicate that the estuarine gravitational circulation plays the most important role in the estuarine turbidity maximum (ETM) formation in the DNC. The upstream nonlocal sediment intrusion through the spillover mechanism is a major source of sediment trapping in the North Passage after the morphological changes. Numerical studies are conducted to show scenarios in the YRE under the effects of different forcings (river discharges, waves, and winds). Between these study cases, surface-wave-breaking relieves the sediment trapping and bottomwave-current-interaction aggravates the bed erosion and elevates the SSC in the ETM; the former and the latter have the least and largest influence on the suspended sediment transport in the DNC. The wind effects have a greater influence on sediment trapping than the river discharges, and the steady northwesterly wind condition favors the siltation in the DNC most. The significance of density-driven turbidity current is also assessed, which can enhance the saline-water intrusion and suppress the turbulent mixing in the bottom boundary layer. Citation: Song, D., and X. H. Wang (2013), Suspended sediment transport in the Deepwater Navigation Channel, Yangtze River Estuary, China, in the dry season 2009: 2. Numerical simulations, J. Geophys. Res. Oceans, 118, 5568–5590, doi:10.1002/jgrc.20411.

1.

Introduction

[2] Hydrodynamic and sediment transport processes in estuaries are very complex due to the presence of irregular coastlines, islands, shoals, channels, and anthropogenic structures, mixing fresh and saline water, river runoff, tides, winds, waves, and offshore currents. Understanding these coastal processes is of great importance for nearshore structure design, environmental protection, and disaster prediction and prevention. [3] The estuarine turbidity maximum (ETM) or turbidity maximum (TM), characterized by higher elevated turbidity or suspended sediment concentrations (SSC) than that observed further landward or seaward, which has been Companion paper to Song et al. [2013] doi:10.1002/jgrc.20410. 1 Key Laboratory of Physical Oceanography, Ministry of Education, Qingdao, China. 2 School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra, ACT, Australia. 3 State Key Laboratory of Satellite Ocean Environment Dynamics, Hangzhou, China. Corresponding author: D. Song, Key Laboratory of Physical Oceanography, Ministry of Education, Qingdao 266003, China. ([email protected])

©2013. American Geophysical Union. All Rights Reserved. 2169-9275/13/10.1002/jgrc.20411

reported in many estuaries throughout the world, such as the upper Chesapeake Bay [Schubel, 1968], the Tamar Estuary [Uncles and Stephens, 1993], and the Hudson River Estuary [Traykovski et al., 2004]. The mechanisms of particle trapping in the turbidity zone are complex, with two of them proposed as fundamental. The first involves the residual currents associated with gravitational circulation in partially mixed estuaries, with the high suspended sediment concentration often reported to be located near the landward limit of salt intrusion [Postma, 1967]. Suspended matter flowing seaward on the surface settles in a near-bottom layer where it is carried landward by an upstream residual flow. The suspended matter is trapped and then accumulated at the convergence of the near-bottom flow due to the estuarine circulation [Dronkers, 1986]. The second mechanism is related to tidal distortion (in particular asymmetry in current velocities) induced by nonlinear interactions, as the ETM varies through the tidal cycle due to resuspension and deposition [Uncles et al., 1985]. A tidal wave travelling into shallow water typically generates strong landward currents, which usually results in an upstream sediment flux towards the head of the estuary, up to a tide decay zone, where river flows dominate in sediment transport [Allen et al., 1980]. The ETM is then to be found somewhere landward of the point where the tide becomes notably distorted [Dyer, 1986]. Another process for the ETM formation was

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SONG AND WANG: SS TRANSPORT IN DNC YRE

identified by Jay and Musiak [1994]: internal tidal asymmetry or tidal-mixing asymmetry; however, this mechanism appears to be not necessary for the existence of a stable ETM, and affects the ETM formation only quantitatively but not qualitatively [Burchard and Baumert, 1998]. In estuaries, strain-induced periodic stratification [Simpson et al., 1990] is a dominant mechanism creating tidal mixing asymmetry in the presence of a longitudinal density gradient. Tidal currents stratify the water column through the straining of the density field during ebb tides, but destratify it during flood tides, which leads to a residual flow seaward near the surface and landward near the bottom. As a consequence, an upstream net transport of suspended sediment can be generated by this mechanism [Geyer, 1993]. Cheng et al. [2011] also found that in some regime of the estuary, the asymmetric-tidal-mixing induced flow may even be greater than that of density-driven flow under weak stratification and tends to be smaller under strong stratification. [4] In addition, other tidal effects are also confirmed to favor sediment trapping, such as topographical effects [e.g., Friedrichs et al., 1998; Geyer et al., 1998], lag effects (scour lag and settling lag) [e.g., Postma, 1961; Bartholdy, 2000; Burchard et al., 2008], and asymmetry in flocculation processes [e.g., Scully and Friedrichs, 2007; Winterwerp, 2011]. [5] Since Festa and Hansen [1978], who confirmed the first mechanism mentioned above by means of a steady-state two-dimensional numerical model, modeling of ETMs generally enabled the location and magnitude to be correctly simulated. Thus, effects of multiple physical mechanisms involved in the ETM formation can be further investigated [e.g., Dyer and Evans, 1989; Lang et al., 1989; Jay and Musiak, 1994; Burchard and Baumert, 1998; Geyer et al., 1998; Brenon and Hir, 1999; Burchard et al., 2004; Warner et al., 2007; Park et al., 2008; Xu et al., 2010]. [6] Considerable numerical modeling of the Yangtze River Estuary (YRE) has been carried out in recent years, most of which were focused on the hydrodynamics, such as salt water intrusion [e.g., Qiu et al., 2012 ; Xue et al., 2009], transport time [e.g., Wang et al., 2010 ; Li et al., 2011], and storm surges [e.g., Hu et al., 2009] ; little involved suspended sediment transport processes. On the other hand, most previous studies of the suspended sediment transport and the ETMs in the YRE have been based on field work [e.g., Su and Wang, 1986 ; Shen et al., 1993 ; Shi et al., 1997 ; Li and Zhang, 1998 ; Chen et al., 1999 ; Shi et al., 2006 ; Wu et al., 2006 ; Gao et al., 2008 ; Liu et al., 2010, 2011 ; Wu et al., 2012 ; Jiang et al., 2013]. Shi [2010] used a one-dimensional vertical model to study the fine suspended sediment distribution at the South Channel-North Passage of the partially mixed YRE. Subsequently, a two-dimensional numerical model was established to study the characteristics of tidal flow and suspended sediment concentration in the same region [Shi et al., 2010]. However, the depth-integrated momentum and convection-diffusion equations are unable to fully account for the effect of the complex topographic variations and baroclinic hydrodynamics in the YRE. Jiang et al. [2013] gave an analytical model to derive residual flow components and their contributions to the alongchannel net sediment transport. However, the vertically uniform eddy viscosity coefficients used in their model

cannot represent the variation on the vertical structure of turbulent mixing, e.g., changes between a well-mixed estuary and a highly stratified estuary from spring to neap tide [Song et al., 2013]. [7] The construction of the Deepwater Navigation Channel (DNC) project, which started in 1998 and was completed in 2011 (Figure 1), has significantly changed the morphodynamics and hydrodynamics of the North Passage. The project created a 92 km long channel with a water depth of 12.5 m below the mean lowest low water (MLLW) along the North Passage and South Channel. In addition, two dikes of length 48.1 km to the south of the channel and 49.2 km to the north, and 19 groynes, 30 km in total length, were constructed to increase current speed and decrease sediment deposition in the North Passage [Liu et al., 2011]. The flow pattern along the main channel of the North Passage changed from a rotational current into almost rectilinear flow due to the construction of dikes and groynes, and geometrically controlled eddies were produced in the groyne areas. Jiang et al. [2013] found that the amplitude of M2 tidal current considerably increased and the residual flow structure was significantly altered since the engineering works. Model simulations also reveal significant velocity increases due to the constraining effect of dikes in the downchannel section but small changes in the upchannel section [Ge et al., 2011]. In addition, the saltwater intrusion in the project area was intensified at the upchannel section but reduced at the downchannel section [Zhu et al., 2006]. Furthermore, the construction of two dikes has cut off the horizontal sediment transport between the North Channel and South Passage ; thus, the suspended sediment transport and associated ETM formation in the North Passage has likely been altered. It is important to understand the physical mechanisms resulting in the sediment trapping in the DNC and how these mechanisms are influenced by the anthropogenic changes to the system. [8] In Part 1 of this study [Song et al., 2013], we found spring-neap and flood-ebb tidal variations in suspended sediment in the DNC and proposed that the highly turbid water intruding into the DNC on flood tides is related to the ETM movement. To support our hypothesis, a numerical model is needed to interpret the hydrodynamics and sediment transport dynamics of this study region as our observations are based only on measurements in a single location in the middle of the DNC. Therefore, in Part 2 of this paper, we have developed a three-dimensional wavecurrent-sediment coupled coastal ocean model to study suspended sediment transport in the DNC, North Passage of the YRE, in the dry season 2009, when the dikes and groynes were completed, and the DNC was already dredged to 10.5 m below the MLLW. The main aim of the present paper is to find out the possible reasons that may have caused the siltation problem in the DNC. Additionally the following science questions will be addressed: (a) physical mechanisms resulting in the ETM formation in the DNC; (b) influences on suspended sediment transport by the anthropogenic changes ; (c) interaction between turbidity-driven and salinity-driven flows; (d) effects of external forcings i.e., river discharges, waves, and winds on the sediment transport and sediment trapping in the DNC. This paper is arranged as follows. The configuration and development of the numerical model are described in

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Figure 1. Bathymetry map of the Yangtze River Estuary with detailed structure of the Deepwater Navigation Channel project including channel cell names and groyne numbers. In the middle figure, the red star gives the quadrapod position (A0) and the numbered blue dots show the tide stations for model validation. The top figure shows the intensified mesh grid around the region of the Deep Navigation Channel project. section 2, and followed by model results and a discussion in section 3. Finally, conclusions of this study are presented in section 4.

2.

Model Descriptions

2.1. Hydrodynamic Model [9] The model used here is the three-dimensional Princeton Ocean Model (POM); it solves the primitive equations

for momentum, temperature, and salinity on a horizontal Arakawa C-grid and a vertical -coordinate system [Blumberg and Mellor, 1987; Mellor, 2004]. The level 2.5 turbulence closure scheme described by Mellor and Yamada [1974, 1982] and Mellor [2001] is used to compute the vertical mixing processes. The Smagorinsky diffusion scheme is used to calculate horizontal diffusivity, assuming that the horizontal diffusivity of momentum, temperature, and salinity are equal. The full set of model equations is described

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in Mellor [2004]. In the latest version (POM08), the wetting and drying (WAD) scheme is incorporated into the hydrodynamic model [Oey, 2005, 2006]. [10] Considering the price of computation time and data storage, the model area is given from 121.0 E to 123.0 E in longitude and 30.6 N to 31.9 N in latitude, with variable resolution from about 400 m 400 m in the DNC region to about 2000 m 2000 m near the open boundaries (Figure 1). Consecutive grids roughly along the two dikes are masked in the model and a no-slip condition is applied. In the DNC, it allocates about 15 grid cells in the cross-channel direction, which is sufficient to distinguish the groynes and shoal areas in this area. In addition, the field measurements in the dry season (March 2008) by Wu et al. [2012] illustrate a 20 km long salt front in the DNC with salinity ranging from 6 to 20 psu and also a 20 km wide ETM with the highest SSC of 2.5 kgm3 in the center, which indicates that the longitudinal model resolution is also sufficient to represent the salinitygradient and turbidity-gradient in the DNC. In the vertical dimension, 16 sigma layers are used with five logarithmically spaced layers near the bottom and another five near the surface to obtain finer resolution in these layers. Tidal forcing with eight primary tidal constituents (M2, S2, N2, K2, K1, O1, P1, and Q1) and two shallow water tides (M4 and MS4) are used at the open boundaries, in which the nodal modulation corrections and the astronomical argument for tidal constituents are included. The Yangtze River runoff is included as an inflow boundary condition by using the dailymeasured river discharge during the simulation period at the Datong hydrologic station, about 600 km upstream from the YRE. Monthly averaged salinity for the open boundaries is taken from the reanalyzed Analysis, Reconstruction, Indices of the Variability of the Ocean (ARIVO) gridded fields produced at Laboratoire de Physique des Oceans (available at http://wwz.ifremer.fr/lpo/SO-Argo/Products/Global-OceanT-S/Monthly-fields-2004–2010). This ARGO data set is monitored on a monthly basis and merged with other available measurements to produce gridded fields. Salinity at the upstream boundary is given 1 psu. Constant temperature (10 C) is used as the initial condition and the open/upstream boundary condition. The heat fluxes are assumed to vanish at the sea surface, and the heat and salt is adiabatic at the bottom. In this study, to limit the nonphysical mixing of the sharp horizontal salinity gradient, the horizontal diffusivity for salinity is set to be zero.

ities, respectively; w is the vertical velocity component normal to the surface ; ws is the particle settling velocity; and Kh is the vertical diffusivity. According to Wang and Pinardi [2002], ws is not affected by the transformation of coordinates from a Cartesian coordinate system to the coordinate system. For the sediment advection terms in equation (1), a first-order iterative upstream scheme was used, which reduces implicit diffusion with an antidiffusive velocity [Smolarkiewicz, 1984]. To couple the sediment transport model with the hydrodynamic model, a WAD scheme for sediment transport is also necessary. In this study, assuming that the sediment deposited on tidal flats dewaters rapidly, no SSC value is given for dry cells, where the erosion and deposition processes also cease. The effect of SSC on the equation of state is introduced by using a bulk-density relation [Adams and Weatherly, 1981]: ¼ w þ 1 w C; s

ð2Þ

where w is the seawater density and s is the sediment bulk density. [12] In highly turbid systems, suppression of turbulence due to turbidity-induced stratification leads to rapid accumulation of sediment in fluid mud layers [Allen et al., 1980] and enhancement of sediment trapping at ETM regions [Geyer, 1993]. Based on numerical simulations, Wang et al. [2005] also showed that the sediment-induced stratification in the bottom boundary layer (BBL) reduces the vertical eddy viscosity and bottom shear stress in comparison with the model prediction in a neutrally stratified BBL. In response to these apparent reductions, the simulated tidal current shear in the water column increased in their idealized estuary and on the western tip of southwest Korea [Byun and Wang, 2005]. Nevertheless, the phenomenon of drag reduction adjacent to the bed has been observed in sediment-laden flows [e.g., King and Wolanski, 1996; Dyer et al., 2004]. Wang [2002] introduced a flux Richardson number into the bottom friction coefficient Cd, which allows for the effect of sediment-induced BBL stratification in the model: " Cd ¼

#2 ; 1 þ ARf ln ðzb =z0b Þ

ð3Þ

2.2. Sediment Transport Model [11] If we assume that the horizontal velocity of the sediment is the same as that of the water and that the vertical velocity of the sediment only differs from the water velocity by the settling velocity, the three-dimensional sediment transport equation in the water column, based on the conservation equation for temperature or salinity in a sigma coordinate system [Wang, 2002], can be written as

where is the von Karman constant, zb is the near-bottom layer thickness, z0b is the bottom roughness, A ¼ 5.5 is an empirical constant, and Rf is the flux Richardson number, an index of the vertical density stratification in the MellorYamada Level 2 approximation. [13] No sediment flux is allowed at the water surface, so that

@ @ @ @ @ Kh @C ðCDÞ þ ðCuDÞ þ ðCvDÞ þ ; ½C ðw þ ws Þ ¼ @t @x @y @ @ D @

Kh @C Cws ¼ 0 as ! 0: D @

ð1Þ

ð4Þ

[14] Sediment flux at the bottom is the difference between the deposition and erosion rates, giving

where t is the time; C is the SSC; D ¼ H þ is the water depth with H the bottom topography and the surface elevation; u, v are the eastward velocity and northward veloc5571

Kh @C Cws ¼ Eb as ! 1; D @

ð5Þ


where Eb is the net sediment flux at the bottom due to erosion and deposition. The algorithms for Eb are given by Ariathurai and Krone [1976] : 8 j b j > > 1 < E0 ce Eb ¼ j b j > > : Cb ws 1 cd

if j b j ce erosion ;

ð6Þ

if j b j < cd deposition

where E0 is the empirical erosion coefficient, Cb is the SSC near the BBL, b is the bottom shear stress, ce and cd is the critical shear stress for erosion and deposition, respectively; note that ws is negative as positive z is upward. According to Ariathurai and Krone [1976], the critical shear stress for deposition may be the same or less than for erosion. [15] The critical shear stress for erosion, deposition, and the empirical erosion rate coefficient are the parameters difficult to be determined in estuaries since they may have a wide range of values within any one region. It depends on consolidation of the bed, which is influenced by interactions with physical, biological, and chemical factors, together with sediment composition [Houwing and Rijn, 1998]. Given the complexity of the sediment erosion and deposition processes and the lack of field measurements in the study area, constant value for ce, cd, and E0 was chosen through evaluation of model skill score (see section 3.1). Together with settling velocity, combination of these parameters summarized in Table 1 gives the highest skill score for SSC simulation, where values were tested for ce and cd ranging from 0.01 to 1.0 kgm1 s2, and for E0 ranging from 1.0106 to 2.0104 kgm2 s1. [16] In POM, the calculation of the three-dimensional (internal) variables is separated into a vertical-diffusion time step and an advection-plus-horizontal-diffusion time step [Mellor, 2004]. The former is implicit and solved by subroutine PROFT, whereas the latter is explicit and solved by subroutine ADVT. In contrast to Wang [2002], in this study the term associated with ws is solved in the subroutine for vertical diffusion rather than in the advection subroutine, which gives a more accurate description of the bottom and surface boundary condition. In addition, as ws is a function of SSC in this study (discussed later in section 2.4), it should be placed in the same elevation as SSC at each vertical layer in POM, which is different from w, necessitating interpolation (see Appendix A for details). 2.3. Wave Model [17] The Simulating WAves Nearshore (SWAN) model [Booij et al., 1999] driven by sea surface wind (6 hourly, and a 0.5 0.5 grid) obtained from QSCAT/NCEP Blended Ocean Winds from Colorado Research Associates (version 5.0, which is available at http://rda.ucar.edu/datasets/ds744.4/) is used to supply wave parameters for the hydrodynamic model. The SWAN model, driven by satellite-measured sea surface wind, was run first for the entire East China Seas (ECS) region, from 115.5 E to 132.5 E in longitude and 22.5 N to 43.5 N in latitude, with 50 50 spatial resolution (Figure 1). Then, wave parameters were calculated by SWAN on the YRE hydrodynamic model mesh grid, with wave boundary conditions supplied

Table 1. Parameters Used in the Suspended Sediment Transport Model Parameter ws0 m1 n1 m2 n2 C0 E0 ce cd z0b

Value

Reference

8.57106 (ms1) 0.006 2.20 1.70 2.80 0.20 (kgm3) 1.2 104 (kgm2s1) 0.8 (kgm1s2) 0.6 (kgm1s2) 1.0 104 (m)

Tested Tested Mehta and McAnally [2008] Mehta and McAnally [2008] Mehta and McAnally [2008] Mehta and McAnally [2008] Tested Tested Tested Tested

by the ECS SWAN model. Finally, the results were coupled one way to the hydrodynamic model. [18] The surface boundary condition for wind stress is modified through Xie et al. [2001] ; while those for turbulent kinetic energy (TKE) and the mixing length as a result of wave breaking are given according to Mellor and Blumberg [2004] (see Appendix B for details). In the shallow YRE, the combined effect of waves and currents on the bottom stress, which determines the resuspension rate for suspended sediment, may be significant. Here the wavecurrent BBL model of Madsen [1994] is implemented to present the shear stress enhanced by the nonlinear interaction of waves and currents in the BBL (see Appendix C for details). 2.4. Flocculation Processes [19] Flocculation and deflocculation has an important impact on the transport of fine-grained cohesive sediments in ETM through associated increases in the settling velocity of the sediment. Decades of efforts have been made to parameterize the flocculation and floc breakup processes [e.g., Hawley, 1982; Gibbs, 1985; Dyer, 1989; Kranenburg, 1994; Winterwerp, 1998, 2002; Winterwerp et al., 2006; van Leussen, 2011]; however, due to the uncertainties in the formulations, some poorly known empirical parameters are usually involved. In those formulae, the SSC and turbulent shear stress (or TKE to be more accurate [Winterwerp et al., 2006]) are the dominant physical parameters and control the flocculation and hence the settling properties of mud flocs in suspension in the YRE [Shi, 2010]. The latest survey showed that the median dispersed grain sizes are 7–11 m in the YRE, whereas in situ floc mean diameters range from 50 to 120 m [Guo and He, 2011]. They also found that the flocs formed in freshwater environments are not necessarily smaller than those formed in saline water, and can be larger. Therefore, the salt flocculation may play a minor role in the YRE, if any. [20] From Mehta and McAnally [2008], the following expression is used for settling velocity: 8 < ws0 n1 w s ¼ m1 C : C 2 þ m2 n2 2

C C0 C > C0 ;

ð7Þ

where ws0 is the free settling velocity; C0 is the critical concentration for flocculation, and m1, m2, n1, and n2 are empirical settling coefficients. It includes several essential

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Table 2. Difference in Harmonic Constants at Eight Tide Stations (Shown in Figure 1) Between the Standard Model Run (Case 0) and Measurements S2

M2 Station No. 1 2 3 4 5 6 7 8 RMS

Station Name

O1

Amp(m)

Pha( )

Amp(m)

Pha( )

Amp(m)

Pha( )

Amp(m)

Pha( )

0.02 0.01 0.00 0.08 0.00 0.02 0.01 0.01 0.030

14 11 5 5 1 3 4 2 7.0

0.05 0.00 0.05 0.05 0.04 0.01 0.03 0.01 0.035

14 6 3 3 10 18 8 1 9.6

0.01 0.01 0.00 0.01 0.04 0.02 0.04 0.05 0.028

5 2 1 7 7 12 7 8 6.9

0.02 0.01 0.01 0.03 0.00 0.01 0.00 0.01 0.013

4 4 2 1 1 8 2 2 3.2

DajiShan Lvhuashan Nanhui Jiuduansha Zhongjun Wusong Sheshan Beicao

physical processes, i.e., free settling, flocculated settling, and hindered settling. The suspended particles begin to flocculate when SSC exceeds C0. Once it increases and the flocculation processes are inhabited, hindered settling occurs. This is due to the low permeability coupled with increased buoyancy and viscosity of the sediment-water mixture. Hence, it reduces the ability of the interstitial water to escape upward easily. TKE is not involved in this flocculation model, as no empirical coefficients for this parameter have been obtained and validated from measurements in the YRE at current stage. Field measurements show that the sand/silt/clay proportions and the mean diameters of sediment has a spatial variability in the YRE [Liu et al., 2010], which cannot be well represented in this numerical model; thus a single set of parameters is used to describe the sediment properties in order to keep the model manageable. The coefficients in equation (7) used for the YRE model (some evaluated using model skill score) are also summarized in Table 1.

3.

K1

Model Results and Discussion

3.1. Model Validation [21] To obtain the initial value of salinity in the model region, it was first spun up for 1 year with climatologically monthly-averaged river discharge and salinity at the open boundaries. It was verified that this spin-up time is sufficient for salinity in the YRE to reach a near-equilibrium state, which is independent of the initial salinity distribution. Then the model was run for another 40 days. This is marked as Case 0 for the standard run. [22] First, we compare the simulated primary tidal harmonic constants with observed at eight tide stations in the modal region (Figure 1). The root-mean-square (RMS) errors of the four main constituents indicate that the simulated tides are acceptable. The errors in amplitude are all under 10%, and in phase less than 10 (See Table 2 for details). Then the model skill score (SS) is adopted to quantify the model errors with the field measurements introduced in Part 1 of this study [Song et al., 2013]. The SS is defined as the ratio of the RMS error normalized by the standard deviation of the observation [Murphy, 1988], X

ðXmod Xobs Þ2 SS ¼ 1 X 2 ; Xobs Xobs

ð8Þ

where X is the variable being evaluated and X is the temporal average. For reference, an evaluation of a hydrodynamic and ecosystem model in the southern North Sea categorized an SS > 0.65 as an excellent simulation, 0.5–0.65 as very good, 0.2–0.5 as good, and 0 or 3(u) >0. Note that the scales differ. (bottom, g) The monthly-averaged erosion/deposition rate (unit: kgm2 s1, positive for deposition) along the DNC in Case 0. Channel cells are shown in Figure 1. 7b) and asymmetric-tidal-mixing-induced flow (Figures 7c and 7d). Both components can generate a downstream flow on the surface but an upstream flow near bottom. On spring tides, the estuarine gravitational circulation has a smaller magnitude in upstream currents than the asymmetric-tidalmixing-induced flow; however, on neap tides, the former outweighs the latter. Thus, both the estuarine gravitational circulation and the internal tidal asymmetry play roles in the sediment trapping on spring tides, but the latter is a little more important in the net upstream sediment transport; on neap tides, the gravitational circulation is dominant in producing the high SSC tongue. [30] Besides abovementioned two mechanisms, the role of tidal velocity asymmetry in the turbidity maxima formation also needs to be investigated. To quantify its relevance to sediment transport, Nidzieko and Ralston [2012] used sampling skewness of tidal-current velocity (the third moment about zero, normalized by the second moment about zero to the 3/2 power), as sediment transport is

roughly proportional to velocity cubed. Here we extend this method by means of harmonic amplitude and phase (see Appendix D for details), in order to examine the origins of tidal velocity asymmetry (i.e., the contribution of different tidal-constituent combination [Song et al., 2011]). Recall that the calculation gives a flood-dominant velocity skew when 2(u) > 0 or 3(u) > 0 (i.e., an upstream net sediment transport), but an ebb-dominant velocity skew when 2(u) < 0 or 3(u) < 0 (i.e., an downstream net sediment transport). In Part 1 of this study [Song et al., 2013], M4 and MS4 have been found as the first two largest contributors of tidal asymmetry. Here through the combination of different tidal current constituents, it shows that both the pair of M2 and M4 (Figure 4d) and the triplet of M2, S2, and MS4 (Figure 4e) can generate opposite asymmetric patterns between upchannel and downchannel sections, which cause suspended sediment to converge at around points J-N. Furthermore, as both 2 and 3 have maximum values of 0.82 [Song et al., 2011], the moderate magnitudes (about 0.3) of

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Figure 5. The daily-averaged near-bed suspended sediment concentration (contour lines, unit: kgm3) and suspended sediment flux (vectors, unit: kgm2 s1) during (top) (a) spring tides and (b) neap tides in Case 0 and (bottom) (c) spring tides and (d) neap tides in Case 2.

Figure 6. The along-channel near-bottom suspended sediment concentration (unit: kgm3) for (a) Case 0 and (b) Case 6. The white line shows the tidal elevation at site A0 with leftward indicating high tides. 5577


Figure 7. (left) Along-channel estuarine gravitational circulation (unit: ms1, positive seaward) during (a) spring tides and (b) neap tides in Case 0, and asymmetric-tidal-mixing-induced flow during (c) spring tides and (d) neap tides in Case 0, where the white lines indicate 0 ms1. (right) The difference between Case 0 and Case 1 (Case 0 Case 1) of along-channel density-driven flow (unit: ms1, positive seaward) during (e) spring tides and (f) neap tides, and of asymmetric-tidal-mixing-induced flow during (g) spring tides and (h) neap tides. For reference, the white contour lines give the simulated flows in Case 1. Note that the scales differ. 2(u) and 3(u) in the DNC with a semidiurnal regime, indicates that the tidal velocity asymmetry also contributes a lot to the formation of the ETM in the DNC. If we include the residual current in the tidal current skewness via equation (D3) in the Appendix D, we find larger opposite velocity skews, as shown in Figure 4f. It indicates the residual flow significantly enhances the velocity skews as well as the sediment trapping in the DNC. [31] Other mechanisms related to the suspended sediment transport can also be confirmed by the model results. The amount of resuspension depends on the magnitude of the near-bottom velocity, which tends to be higher during ebbing tides owing to the offshore fluvial flow. Meanwhile, due to much longer period of low current velocities around high tide (a smaller rate of velocity increase, as shown Figure 2b in Part 1 [Song et al., 2013]) than around low tide, this slack-water asymmetry is responsible for greater deposition of sediment due to sediment deposition during high slack water than during low slack water (Figure 6a). During spring tidal cycles, despite the fact that both estua-

rine gravitational circulation and asymmetric-tidal-mixinginduced flow may produce the SSC tongue, a larger tidal excursion generates a stronger tidal pumping effect, which dominates the landward suspended sediment transport in such a partial-mixing estuary. This has already been shown with the observation in Part 1 of this study [Song et al., 2013]. However, during neap tides, the strong stratification generates onshore baroclinic flow, and its strong shear effect plays a more significant role in the landward suspended sediment transport than the weak tidal-current excursion. 3.3. Turbidity-Driven Flow [32] In the ETM region, the large SSCs significantly affect the vertical density structure, leading to stratification and a reduction of mixing [Winterwerp, 2001], thereby affecting, for example, the tidal wave propagation [Gabioux et al., 2005]. Talke et al. [2009] developed a simple analytical model including salinity- and turbidityinduced circulation from density gradients. They found that

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Table 4. Summary of Case Configurationsa and the Monthly- and Spatial-Averaged Bed Erosion Rate and SSC in Each Case Case No. 0 1 2 3 4 5 6 7 8

Description Control run described in Section 2 Uncoupled SSC and seawater density Morphology and bathymetry before the DNC project High river discharge in dry season (40,000 m3s1) Low river discharge in dry season (10,000 m3s1) No surface wave-breaking effects No bottom wave-current interaction Steady northwesterly wind with 10 ms1 wind speed Steady southeasterly wind with 10 ms1 wind speed

Erosion Rate (kgm2s1)

SSC (kgm3)

2.94 5.00 3.08

1.28 0.84 3.23

4.43

1.06

4.52

1.82

2.23 7.42 0.04

1.54 0.46 2.35

4.35

2.97

a Cases 1–8 have identical configuration to Case 0, except as described above.

the turbidity-driven currents and salinity-driven currents act together to enhance tidally averaged circulation upstream of the ETM but significantly reduce residual circulation downstream, where salinity and turbidity gradients oppose each other. In Case 1, we take SSC out of the equation of state for seawater density (i.e., remove equation (2) from the model computation) in order to compare with the control run (Case 0), which considered the effects of suspended sediment on the density field. Cases discussed here and below are summarized in Table 4.

[33] In Case 0, we consider the SSC contribution to seawater density and thus generated turbidity effects. The direct turbidity effect is to establish a flow caused by a turbidity-induced density gradient (compare the zero residual current lines between Figures 4c and 8c). During spring tides, the turbidity-driven flow enhances the vertical skew of the density-driven flow between surface and bottom (Figure 7e). In addition, the turbidity-driven flow can also intensify the sediment trapping induced by the internal tidal asymmetry (Figure 7g). Thus, an ETM with a greater magnitude in Case 0 than Case 1 is expected (compare Figure 4a with Figure 8a). During neap tides, the turbidity-driven flow enhances the salt intrusion (compare Figure 4b with Figure 8b) and largely increases the density-driven flow at the salt wedge (Figure 7f). The bottom salt shift intensifies the stability of stratification and reduces the intertidal asymmetry of turbulent mixing (Figure 7h), which accelerates the suspended sediment settling and generates strong vertical turbidity gradients within the BBL (compare Figure 4b with Figure 8b). Note that the turbidity effect increases the vertical salinity gradients but not the horizontal salinity gradients, which is actually reduced due to the extension of the bottom salt tongue. In addition, the magnitudes of TMs in shoal waters are also increased in Case 0, which enlarges the sediment transport into the DNC (compare Figure 9a with Figure 9b), even though the TMs are closer to the DNC outlet in Case 1. [34] Therefore, coupling SSC into density equation of state, the intensified onshore current near the bottom pushes the salt front further landward, which increases the salinity-

Figure 8. (left) The suspended sediment concentration (unit: kgm3) along the DNC for (a) a dailyaverage during spring tides, (b) a daily-average during neap tides, and (c) a monthly-average for Case 1. (right) Same as the left but for Case 2. Isohalines (unit: psu) are given in white and zero residual current in black dotted lines. Note that the scales differ. 5579


Figure 9. The monthly-averaged near-bed suspended sediment concentration (contour lines, unit: kgm3) and suspended sediment flux (vectors, unit: kgm2 s1) for (a) Case 0, (b) Case 1, (c) Case 3, (d) Case 4, (e) Case 7, and (f) Case 8.

induced stratification in the DNC. It in turn changes the suspended sediment transport and enhances the sedimentinduced stratification in the turbidity zone. 3.4. Influences of DNC Project on Suspended Sediment Transport [35] To study the impact of the DNC on suspended sediment transport in the North Passage, another model (Case 2) is conducted with the same configuration as Case 0 but without the deepwater channel, dikes, and groynes. During spring tides, sediment residual flux (Figure 5c) shows that an ETM in the North Passage is formed by the convergence of the sediment transport between Jiuduansha Shoalwater and Hengsha Shoalwater. Fine sediment is eroded and resuspended by strong tidal currents or wind waves in those shallow waters, then brought into the North Passage, where

most of it is trapped in the deep middle-passage section (Figure 8d). Comparing the situations before and after the DNC construction, the position of the ETM does not change too much; the former has a greater magnitude but less diffuse turbidity gradients than the latter. During neap tides, the entire North Passage is occupied by highly turbid waters (Figure 5d). Fluid mud may also be generated, but the stratification is not as strong as the situation after the DNC construction (Figure 8e). [36] The construction of dikes and groynes, and dredging of the deepwater channel accelerated the fluvial flow on the surface, which dramatically reduced the maximum flooding-current velocity and enhanced the ebb dominance in the current (Figure not shown). This constraining effect reduces the salt intrusion, which induces a less turbid upper-channel section; however, the intensified

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Figure 10. The monthly-averaged suspended sediment concentration (unit: kgm3) along the DNC for (a) Case 3, (b) Case 4, (c) Case 5, and (d) Case 6. Isohalines (unit: psu) are given in white and zero residual current in black dotted lines. Note that the scales differ. stratification weakens the turbulent mixing in the DNC. The DNC project indeed relieved the turbidity in the North Passage, but it is unable to solve the silting problem completely (compare Figure 4c with Figure 8f). The spillover mechanism replaces the cross-channel sediment transport after the DNC project completion. The ETM still occurs at almost the same position during the spring tides ; while fluid mud still forms during the neap tides. 3.5. River Discharge [37] The Yangtze River discharge has a strong seasonal variation, and even varies significantly in the dry season, from about 10,000 m3 s1 in January to about 30,000 m3 s1 in March 2009. We do not have field measurements to validate our model in flood seasons. Therefore, we only compare the situations with different river discharges in the dry season. Two cases with constant river discharge of 40,000 m3 s1 in Case 3 and 10,000 m3 s1 in Case 4 were run to show the influence of the river runoff on suspended sediment transport in the DNC. The model configuration is the same as Case 0, except for the river boundary conditions. In Case 0, we use the daily measured river discharge at the Datong hydrologic station, which increased from 16,819 m3 s1 on 1 March to 28,277 m3 s1 on 13 March and then fell to 19,169 m3 s1 on 7 April 2009, with an averaged discharge of approximately 23,043 m3 s1. [38] In Case 3, the increased river discharge pushes the residual-flow convergence seaward ; the range of the saltfrontal zone is compacted as well as that of the ETM in the DNC (compare Figure 10a with Figure 4c). The increased river discharge reduces the magnitude of the ETM on spring tides and the sediment tongue on neap tides; however, the downstream flow can still not completely push the ETM out of the DNC. This is because the increased fresh water also moves the TM in the Hengsha Shoalwater further seaward in Case 3, in which it generates an even higher turbidity at the DNC outlet through the spillover mechanism (compare Figure 9c with Figure 9a) and thus may hinder the seaward movement of the ETM. [39] In Case 4, the tides are dominant in the entire DNC, when river runoff is low. None of asymmetric-

tidal-mixing-induced flow or the tidal velocity asymmetry could produce effective sediment traps (i.e., convergent residual flows) in this channel (Figure 10b). The TMs in Hengsha Shoalwater and Jiuduansha Shoalwater are not able to approach the DNC outlet (Figure 9d), leaving a clean downchannel section in this case. The turbid water in the upchannel section originates from the North Channel via the channel between Changxing Island and Hengsha Island (Figure 1) or from the South Channel via the DNC uphead. [40] Comparing these cases, we find that the ETM in the DNC can move over a channel-scale range in different

Figure 11. The monthly-averaged vertical diffusivity (Kh, unit: m2 s1, shown as log10 (Kh)) along the DNC in (a) Case 0, (b) Case 1, and (c) Case 5.

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Figure 12. (left) Monthly-averaged maximum bottom orbital velocity (unit: ms1) in (a) Case 0, (b) Case 7, and (c) Case 8. (right) The monthly-averaged significant wave height (unit: m) in (d) Case 0, (e) Case 7, and (f) Case 8. river-discharge conditions. The tide itself is insufficient to generate strong convergent sediment flux in the DNC, which confirms the key role played by the estuarine gravitational circulation in the ETM formation. On the other hand, a larger river discharge can move the ETM seaward but cannot remove it from the DNC as the nonlocal turbid water landward intrusion is also enhanced by the larger river discharge. This is consistent with the observations in 2008 [Wu et al., 2012], in which a compact ETM occurred in the downchannel section during the flood season. 3.6. Wave Effects [41] The SWAN result shows a large bottom wave orbital velocity in the Hengsha Shoalwater, where sediment can be suspended by waves and then transported by tidal currents to the DNC outlet. To check the wave effects on

the suspended sediment transport in the North Passage region, we set up the following two cases. Different from Case 0, in Case 5, the wave-breaking effects (see Appendix B for details), which can enhance TKE dissipation on surface boundary layer [Stacey, 1999] and deepen the surface boundary layer [Mellor and Blumberg, 2004], are taken out of the model. In Case 6, the shear stress generated by current only (no waves) is considered. Grant and Madsen [1979] has shown that the shear stress is altered because the turbulence generated by the wave-current interaction near the bed is different from the stress expected in the case of pure waves or pure currents. Therefore, the effects of wave-current interaction in the BBL (see Appendix C for details) on the suspended sediment transport can be investigated through the comparison between Case 6 and Case 0.

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Figure 13. (left) The monthly-averaged suspended sediment concentration (unit: kgm3) along the DNC for (a) Case 7 and (b) Case 8. Isohalines (unit: psu) are given in white. (right) The monthlyaveraged current velocity (unit: ms1, positive seaward) along the DNC for (c) Case 7 and (d) Case 8. The white lines indicate 0 ms1. Note that the scales differ. [42] In Case 5, the wave-breaking-induced mixing on the surface vanishes as shown in Figure 11. It shows weak vertical diffusivity near the surface layer. In contrast, Case 0 shows great vertical diffusivity on the surface, and the layer depth gradually decreases as the significant wave height reduces from the open sea to the DNC. The erodible particles are less readily mixed to the surface layer in Case 5 but accumulate near the bottom, which generates an ETM with relatively larger turbidity (compare Figure 10c with Figure 4c). The increased stratification tilts the isohalines in the DNC and enhances the bottom salt intrusion (Figure 10c). [43] In Case 6, without the bottom wave-current interaction, the SSC in the turbidity zone is dramatically reduced (compare Figure 10d with Figure 4c) as well as the turbidity-induced stratification especially in the BBL (Figure 10d), which reduces the bottom salt intrusion. In this case, the ETM is located in the upchannel section, perfectly at the salt wedge. It indicates that in this case the ETM is formed without the interference of nonlocal turbid waters. As mentioned earlier, the wave-generated bottom orbital velocity is rather small in the DNC, but it is significant in the Hengsha Shoalwater and Jiuduansha Shoalwater, which are important origins of the trapped suspended sediment in the DNC. The SSC in those shoalwaters is largely reduced when the bottom wave-current interaction is neglected ; so the turbid water intrusion is also largely decreased or even disappears, and is hence unable to influence the ETM formation in the DNC (Figure 6b). [44] These numerical experiments illustrate that the wave itself has little effect on salt transport ; however, the wave-suspended sediment could drive circulation, which affects the salinity distribution and hence the salinity-induced flow, as we discussed in section 3.3. In addition, the case comparison confirms that the turbid water intrusion plays a significant role in the ETM formation in the DNC. The surface wave-breaking-induced mixing relieves the sediment trapping and siltation problem in the DNC.

3.7. Wind Effects [45] The YRE has four southeastward outlets, which are favored by southeasterly or southerly winds to generate larger waves. To examine the wind effects on the suspended sediment transport in the DNC, we established two cases with steady northwesterly (Case 7) and southeasterly (Case 8) winds, respectively. For these two cases, a constant wind speed of 10 ms1 is assumed. To generate the corresponding wave fields, we ran the ECS SWAN and YRE SWAN in sequence with the above wind fields again. Then, the results were used in the hydrodynamic model. Figure 12 shows the horizontal distribution of the monthlyaveraged significant wave height and maximum bottom orbital velocity for Cases 0, 7, and 8. The significant wave height is reduced with the decrease in water depth, but the maximum bottom orbital velocity is increased. Southeasterly winds generate higher wave and larger bottom orbital velocities than northwesterly winds. Correspondingly, the bottom SSC in Case 8 is expected to be larger than that in Case 7 (Figures 13a and 13b). [46] In these two cases, the steady strong winds mixing the water column better than the control run, especially in the surface layers (Figures 13a and 13b). The alongchannel direction winds powerfully affect the residual flow (Figures 13c and 13d), which changes the pattern of the ETM in the DNC. In Case 7, the northwesterly wind enhances the downstream surface flow, which induces a stronger compensatory flow near the bed than that in Case 0 (Figure 13c). In addition, the TMs outside the DNC are moved offshore by the northwesterly wind, which increases the chance for turbid water reaching the DNC outlet (compare Figure 9e with Figure 9a). Thus, the ETM can be extended to the entire channel (Figure 13a). Conversely, the southeasterly wind drives an upstream surface flow in Case 8, which reduces the downstream surface currents and hence the upstream bottom compensatory flow. Thus, the convergent estuarine gravitational circulation in the DNC is destroyed (Figure 13d). Although more sediment is eroded for the bed by stronger waves, most of them cannot

5583


be transported into the DNC, and hence trapped in the DNC (Figure 9f). [47] These model runs illustrate that the wind-induced wave affects the magnitude of ETMs or TMs, and the wind-driven circulation has a great influence on the ETM location. It also confirms the importance of the estuarine gravitation circulation to the ETM formation in the DNC.

4.

Conclusions

[48] To study suspended sediment transport in the Yangtze River Estuary, especially in the Deepwater Navigation Channel, we establish a three-dimensional wave-currentsediment coupled numerical model, which is validated with the in situ data measured in the DNC in late March and early April 2009 (details can be found in Part 1 of this study [Song et al., 2013]). The model captures the major spring-neap asymmetric patterns in salt transport and suspended sediment transport. The siltation in the DNC is generated by the joint effect of the tidal-asymmetry-induced (tidal velocity asymmetry and tidal mixing asymmetry) and the estuarine-gravitational-circulation-induced convergence (Figures 4c and 4g). The residual flow decomposition indicates that the estuarine gravitational circulation is dominant in the channel during neap tides ; however, the asymmetrictidal-mixing-induced flow is comparable to or even greater than the estuarine gravitational circulation during spring tides. Furthermore, a more skewed tidal velocity asymmetry can be generated with the estuarine gravitational circulation in the DNC. In addition, the low-river-discharge experiment (Case 4) indicates that tide itself is insufficient to the ETM formation. Therefore, the estuarine gravitational circulation plays the most important role in the ETM formation in the DNC. [49] Different from most previous studies, nonlocal sediment also greatly contributes to the mass of the observed deposits in the DNC through the spillover mechanism, in addition to the redistribution of sediment due to local erosion and deposition and the direct input of sediment from the river. Comparing these numerical experiments, we find the turbidity zone is usually confined to the landward limit of the upstream flow in all cases except Case 6, in which the ETM locates further upstream than the convergence point of residual current (Figure 10d) when the nonlocal sediment is largely reduced (Figure 6b). However, in that case the ETM magnitude is largely reduced. So the nonlocal sediment is the most important origin for sediment trapping within the ETM, which also have a significant influence on the ETM magnitude and location. [50] The external forcings (i.e., river discharges, waves, and winds) give effects on both the local environment and further afield. Due to the nonlocal sediment intrusion, ranking the effects of different forcing mechanisms is rather complicated. The monthly- and spatial-averaged bed erosion rate and SSC in the DNC at each case is given in Table 4; the latter indicates the suspended sediment trapped in the DNC. As shown, surface-wave-breaking relieves the sediment trapping in the DNC, but the bottom wavecurrent-interaction aggravates the bed erosion and elevates the SSC in the ETM; compared to other cases, the former and the latter has the least and largest influence on the suspended sediment transport (Table 4). The wind effects have

a greater impact on the sediment trapping in the DNC than the river discharges, as the wind-driven circulation has an influence on the turbidity of upstream net flow, as well as on the magnitude of upstream net flow. These two cooperate with each other, for instance, the steady northwesterly wind moves the TMs downstream, increasing the turbidity of intrusion water; meanwhile, it enhances the bottom compensatory flow in the DNC, taking more sediment into the DNC. The river discharge transports suspended sediment offshore both in the DNC and in the shoalwaters, but the latter could generate stronger nonlocal sediment intrusion into the DNC, which moves against the former. Thus, the river discharge generally has a relatively small impact on the sediment trapping in the DNC. Based on the bed erosion rates (Table 4), we find the steady-northwesterly-wind condition favors the siltation in the DNC most. [51] The construction of the DNC project obstructs massive sediments being directly taken into the passage from its edges. In addition, the constraining effect of the dikes and the deepened channel increases the downstream flow, which moves the ETM offshore. However, this project failed to stop the nonlocal sediment intrusion. Therefore, the DNC project reduces the magnitude of the ETM in the North Passage (the averaged SSC is largely reduced in Table 4), but is not able to solve the silting problem completely (the bed erosion rate is changed little in Table 4). [52] The YRE provides a good example of a turbid estuary, with SSCs over 4 kgm3 near bed and over 30 kgm3 in fluid mud. The horizontal SSC gradient is usually significant between tidal flats and channels. Thus, turbiditydriven flow cannot be ignored in this study case. The model results confirm a positive feedback between turbiditydriven flow and salinity-driven flow. When saline-water intrusion is enhanced, the turbidity in the DNC will rise correspondingly, and vice versa. Furthermore, the turbidity-driven flow suppresses the turbulent mixing in the BBL and hence upper water column (Figure 11b), which increases the sediment settling and deposition (Table 4). The effect of turbidity-driven flow on suspended sediment transport may exist in any numerical case of this study due to its interaction with salinity-driven flow and turbidityinduced stratification. By removing the turbidity-driven flow completely out of the computation (i.e., Case 2), we find it even has a larger impact on the sediment trapping than the river-discharge cases (Table 4). [53] The suspended sediment transport in the Deepwater Navigation Channel has three different asymmetric patterns: flood-ebb tidal cycles, spring-neap tidal cycles, and flood-dry seasons (the first two are studied in Part 1 [Song et al., 2013] and Part 2 of this study; the last was observed by Wu et al. [2012] and Jiang et al. [2013]), which indicates the complication of this estuarine system. Furthermore, given the importance of wind and wind waves, a seasonal variation on the suspended sediment transport is also expected due to the change of wind direction and magnitude by monsoon. With the numerical models, we can explore the mechanisms and forcings on the suspended sediment transport in this coastal system; however, the fate of the sediment might be determined by more complex competition between different mechanisms, some of which might be still unknown to us or cannot be parameterized in numerical models.

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Appendix A: Subroutine for the Vertical Diffusion of Suspended Sediment Concentration

[54] To better represent the surface [equation (3)] and bottom [equation (4)] boundary condition of equation (1), the term associated with settling velocity ws in equation (1) is solved in the subroutine for vertical diffusion rather than that for advection. The subroutine for vertical diffusion is based on equation (25) in Mellor [2004]: ~ T~ Dnþ1 T nþ1 D 1 @ @T nþ1 @R ¼ nþ1 Kh ; @ 2Dti D @ @

2Dti khk khkþ1 ð f f Þ ð f f Þ k1 k kþ1 k dh2 dzk dzzk1 dzzk 2Dti ðrk rkþ1 Þ; dh dzk ðA2Þ

where fk, khk, and rk are the suspended sediment concentration (SSC), vertical diffusivity coefficient, and the product of fk and wsk in the kth vertical grid, respectively, dh is the internal mode water depth, dzk ¼ zk – zkþ1, where zk is the coordinate for the kth vertical grid index, dzzk ¼ zzk – zzkþ1, where zzk is the coordinate intermediate between zk and zkþ1, ~f k is the temporal SSC obtained from the subroutine for advection. Equation (A2) is the same as equation (33) in Mellor [2004]. Note that rk needs to be interpolated to zk from zzk, as ws is a function of SSC, and placed at the same elevation of SSC in the vertical, i.e., zzk. rk ¼ fk wsk þ

ðfk wsk fk1 wsk1 Þ ðzzk zk Þ : dzzk1

ðA3Þ

[56] To apply the surface boundary condition (k¼1), we specify zero sediment flux, thus, f1 ¼

~f 1 Dti r2 =ðdh dz1 Þ ; a1 1

ak ¼

2Dti khkþ1 : dh2 dzk dzzk

2Dti khk ; dh2 dzk dzzk1

ðA7Þ

eek ¼

ak ; ak þ ck ð1 eek1 Þ 1

ðA8Þ

ggk ¼

ck ggk1 þ dk ; ak þ ck ð1 eek1 Þ 1

ðA9Þ

2Dti dk ¼ ~f k þ ðrk rkþ1 Þ: dh dzk

ðA10Þ

ck ¼

and

Appendix B: Surface Boundary Condition for Wave Model Coupling [58] The surface boundary condition for wind stress is modified via the surface roughness in the presence of surface waves: s ¼ a ju s ju s ;

ðB1Þ

where s is the wind stress, a is the air density, and u s is the friction velocity : u s ¼ u10 =ln ðz=z0s Þ;

ðB2Þ

where u10 is the wind speed at 10 m above the sea surface and z0s is the surface roughness length. To estimate the effect of surface waves on wind stress, the empirical model in Donelan et al. [1993] is proposed to compute the surface roughness length [Xie et al., 2001]: z0s ¼

3:7 105 u10 2 u10 0:9 ; g cp

ðB3Þ

where cp is the wave speed corresponding to the spectral peak frequency and u10/cp is the wave age. [59] The surface boundary condition for turbulent kinetic energy (TKE) takes account of an enhanced source of turbulence in the surface layer due to wave breaking [Mellor and Blumberg, 2004]:

ðA4Þ

where

ckb1 ggkb2 ~f kb1 þ 2Dti ðrkb1 þ Eb Þ=ðdh dzkb1 Þ ; ckb1 ð1 eekb2 Þ 1 ðA6Þ

where

ðA1Þ

where is the vertical coordinate, Dti is the internal mode time interval, D is the water depth, T can be any threedimensional variable, n is the time step, Kh is the vertical ~ T~ diffusivity coefficient, R is the source or sink term, and D is the temporal results obtained from the subroutine for advection. [55] The finite difference with respect to of equation (A1) can be written as fk ~f k ¼

fkb1 ¼

q2 ¼ ð15:8 Þ2=3 u2 s at z ¼ 0;

ðB4Þ

where q2/2 is the TKE and is a wave age dependent coefficient, given by Terray et al. [1996] as ðA5Þ

[57] Near the bottom (k ¼ kb – 1, kb is the vertical grid index at the bottom), the bed erosion and deposition rate (Eb) is prescribed, so we get

h 4 i ¼ 15 cp =u s exp 0:04cp =u s :

ðB5Þ

[60] Following Mellor and Blumberg [2004], the surface boundary condition for the mixing length l is given as

5585

SONG AND WANG: SS TRANSPORT IN DNC YRE l ¼ max ðlz ; zw0 Þ; zw0 ¼ 0:85Hs at z ¼ 0

ðB6a; bÞ

l ¼ lz þ zw0 ; zw0 ¼ 1:60Hs at z ¼ 0;

ðB7a; bÞ

or

where lz is the mixing length computed using the MellorYamada model, zw0 is a wave-induced mixing length, and Hs is the significant wave height. In addition, we assume an exponentially decaying wave-induced mixing length to express its vertical variation: zw ¼ zw0 exp ½min ð0; Hs zd Þ;

Appendix C: Bottom Boundary Condition for Wave Model Coupling [61] The wave-current bottom boundary layer (BBL) model is implemented based on Madsen [1994]. The concept of this model is that the nonlinear interaction of the surface waves and currents enhances the shear stress in a much thinner wave boundary layer (WBL) that exists inside of the mean current BBL. The shear velocity, u wc, inside the WBL, z < wc, reflects the combined wavecurrent flow; outside the WBL, z > wc, but inside the current BBL, the shear velocity is a function of the averaged (over several wave periods) current shear velocity, u c. Thus, the eddy viscosity profile can be written as Km ¼

u wc z u c z

for z < wc ; for z > wc

ðC2Þ

[62] Based on the model of Madsen [1994], the maximum instantaneous shear stress for the combined flow is the vector sum of the time-averaged instantaneous shear stress induced by currents, c, and the maximum shear stress associated with waves, wm : b ¼ c þ wm :

ðC3Þ

[63] Equation (C3) can be rewritten in terms of the magnitude of shear velocities : u2 wc ¼ C u2 wm ;

ðC4Þ

where "

#1=2 u c 2 u c 4 C ¼ 1 þ 2 jcos ’wc j þ ; u wm u wm

ðC5Þ

ðC6Þ

where fwc can be approximated by the following explicit formulas [Madsen, 1994]:

fwc

" # 8 > C ubr 0:078 C ubr > > 8:82 for 0:2< < 102 > C exp 7:02 < kN ! r kN ! r " # ¼ : > C ubr 0:109 > 4 2 C ubr > > C exp 5:61 7:30 for 10 < < 10 : kN ! r kN ! r

ðC7Þ

[64] Here, kN is the equivalent Nikuradse roughness of the bottom and !r is the wave radian frequency. In the numerical model, the bed quadratic-drag law is usually calculated using the current velocity at the vertical midelevation of the bottom computational cell, which may vary throughout the domain. For such a current velocity ucr at a given elevation zr above the bed, the magnitude of current shear velocities is given as [Madsen, 1994] sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi! u wc ln ðzr =wc Þ ln ðwc =z0b Þ ucr 1þ 1 þ 4 u c ¼ for zr 2 ln ðwc =z0b Þ ln ðzr =wc Þ u wc > wc ; ðC8Þ

and

ðC1Þ

and the bottom shear stress b is parameterized as @u Km ¼ b =: @z

1 u2 wm ¼ fwc u2br ; 2

ðB8Þ

where zd is the distance below the sea surface and is an empirical coefficient determining the depth of mixing due to wind waves. Based on bubble observations [Thorpe, 1984, 1992], the depth scale of the wave-induced turbulence in wave breaking conditions is of the order of 4.0Hs (i.e., ¼ 4.0).

with ’wc the angle between the current direction and the direction of wave propagation. A wave-current friction factor fwc was introduced to relate the magnitude of the maximum shear stress for the wave, u wm, to the magnitude of the near-bottom orbital velocity, ubr :

u c ¼

rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ucr u wc for zr < wc ; ln ðzr =z0b Þ

ðC9Þ

where z0b ¼ kN/30 is the bottom roughness length, and the WBL thickness wc is defined as

wc ¼

8 > < 2u wc =!r > : kN

C ubr >8 kN !r : C ubr for j>k

3 ui uj uk cos 2

u20

!3 3 un 5

h i E4 u0 þ 3 E u ð t Þ n¼1 ðuÞ 33 ¼ h i3=2 ¼ 0 2 !2 313=2 ; N X E uðtÞ2 @E 4 u 0 þ un 5A

n¼1

u30 þ 32 u0

N X

þ

1 2

i

þ

N X

j

!3=2

k

þ

X 3 u2i uj cos 2 4 2!i ¼!j

i

j

:

ðD3Þ

u2i

i¼1

[70] The longer ebb duration is usually accompanied by stronger flood-current velocities and a longer flood duration with stronger ebb current velocities, as expected from mass conservation, provided u0 is small. There is no tidal frequency information included in equation (D3), and the residual flow (e.g., fluvial discharge or coastal circulation) contributes to the velocity skew through the net velocity term (the first term in the numerator on the right-hand side of equation (D3)) and its interaction with the tidal constituents (the second term in the numerator on the right-hand side of equation (D3)). This might alter the total direction of velocity skew generated by pure tides. Neglecting the residual flow, if currents and elevation are exactly in quadrature, fast-rising tides require flood-dominant velocities to convey the tidal prism in a shorter period and vice versa. [71] In the absence of residual current, the velocity skew created by the addition of two (N ¼ 2) or three (N ¼ 3) frequency-related constituents is 3 2 u u2 cos ð2 1 2 Þ 2 ðuÞ ¼ 4 1 ; 1 2 2 3=2 2 u1 þ u2

ðD4Þ

3 u1 u2 u3 cos ð 1 þ 2 3 Þ 3 ðuÞ ¼ 2 ; 1 2 2 2 3=2 2 u1 þ u2 þ u3

ðD5Þ

and

respectively, where 2!1 ¼ !2 in equation (D4) and !1 þ !2 ¼ !3 in equation (D5). Equation (D4) can be used to quantify velocity skew caused by one constituent and its first harmonic constituent, e.g., M2 and M4 in shallow water. The skew caused by triple constituents (e.g., O1, K1, and M2) can be quantified by equation (D5). The relative phase, 2 1 – 2 and 1 þ 2 – 3, is the only phase information retained in equation (D4) and equation (D5), respectively, and determines the direction of velocity skew. A symmetric tide has a relative phase 2 1 – 2 of 690 . If 90 < 2 1– 2 < 90 , then 2(u) > 0 and the distorted composite tide typically has more in the quantity of ebb current samples (by definition positive values of u indicate an onshore direction), which indicates a greater maximum flood-current velocity (i.e., flood dominance) due to mass conservation. If 90 < 2 1 – 2 < 270 , the relationship is reversed, typically resulting in an ebb-dominant tidal current [ 2(u) < 0]. Similarly, 90 < 1 þ 2 – 3 < 90 indicates a flood-dominant current velocity [ 3(u) > 0], and 90 < 1 þ 2 – 3 < 270 indicates a greater maximum ebb-current velocity [ 3(u) < 0]. In addition, the relative phase 1 þ 2 – 3 ¼ 690 shows a symmetric tide current. [72] Acknowledgments. D. Song has been supported by the China Scholarship Council and the University of New South Wales (UNSW) Top-up Scholarship for his PhD study in Australia. X. H. Wang was

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SONG AND WANG: SS TRANSPORT IN DNC YRE supported by 2011 Australian Research Council/Linkage Projects (LP110100652). This work was supported by the National Basic Research Program of China (Grant No. 2010CB428704), the National Nature Science Foundation of China (Grant No. 41276083), and the scientific research fund of the Second Institute of Oceanography, SOA (Grant No. JT1007). This paper benefited from reviews by Andrew Kiss and Peter McIntyre at UNSW Canberra, and two anonymous reviewers’ constructive comments and thorough reviewing. Computational and storage resources used in this work were provided by the National Computational Infrastructure National Facility in Canberra, Australia, which is supported by the Australian Commonwealth Government. This is a publication of the SinoAustralian Research Centre for Coastal Management, paper 16.

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