A NEW MODEL FOR PREDICTING BED EVOLUTION IN ESTUARINE AREA AND ITS APPLICATION IN YELLOW RIVER DELTA*

YANG Chen, JIANG Chun-bo

State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China, E-mail: yangchen07@mails.tsinghua.edu.cn

A NEW MODEL FOR PREDICTING BED EVOLUTION IN ESTUARINE AREA AND ITS APPLICATION IN YELLOW RIVER DELTA*

YANG Chen, JIANG Chun-bo

State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China, E-mail: yangchen07@mails.tsinghua.edu.cn

This article discusses the process of sediment transport and proposes a morphological model to predict the bed evolution in estuaries. The hydrodynamic module is based on an existent model-Depth Integrated Velocity And Solute Transport (DIVAST) and the wetting and drying method is adopted to deal with the moving boundary. Both cohesive sediment and non-cohesive sediment are taken into consideration in the sediment transport module with the capability of simulating the transport of graded sediments under non-equilibrium conditions. The fall velocity of the suspended sediment is modified in the present model due to the high sediment concentration. A 3-layer approach is adopted to simulate the variations of sediment gradations of bed materials. Furthermore, the model is used to simulate the bed evolution in the Yellow River Delta (YRD) from 1992 to 1995. Field data are used to calibrate the parameters. The numerical results show how the morphology was developed in the Yellow River Estuary with a good agreement with the field data.

bed evolution, graded sediments, morphology, numerical model, sediment transport, Yellow River Delta (YRD)

Introduction

The water bodies in estuaries feature a shallow water depth, a complicated geometry and a rather graded sediment. The interaction among the fluid flows, the sediment transport and the bed level changes is of great importance to some water environmental issues and river mouth wetland functions. The motion of the sediment is related with its particular characteristics, such as cohesive and non-cohesive properties, which play important roles in the long-term bed evolution. In the past decades, the bed evolution process in estuarine and coastal basins was extensively investigated both experimentally and numerically. Schramkowski et al.[1]analyzed the effects of geometry and bottom friction on local bed forms in a tidal embayment. In their study, the water motion was modeled by using the depth-averagedshallow water equations and driven by an externally prescribed M2tide, taking account of the transport of the suspended load. Zhang and Liu[2]developed a numerical model to simulate the suspended sediment transport, built in the vertical σ coordinate for fitting the free surface and bottom, and analyzed various parameters, in which the eddy diffusion, the fall velocity and the Rouse number are found to be the predominant factors of the sediment transport. Chung and Eppel[3]investigated the sensitivity of sediment transport and bed morphology with respect to the bed slope and grain size, and the non-hydrostatic pressure term was treated through numerical simulations based on a 3-D hydrodynamic and sediment transport model. Tan et al.[4]studied the erosion process of cohesive sediment after consolidation experimentally in a closed conduit system and derived a scour rate formula based on the experimental results. Li[5]developed numerical models of tidal current and sediment movement under the combined action of wave and current with an irregular triangular grid, carried out numerical simulations, and the effect of reclamation in Oujiang Estuary was analyzed by the models.

The Yellow River Delta (YRD) is located in a joint zone of Yellow River and Bohai Sea, and is the base of energy sources, petroleum and agriculture ofShandong Province of China. The Yellow River has the highest sediment concentration in the world, which takes nearly 109t of sediment to the YRD and Bohai Sea every year[6]. Because of the weak-tide in Bohai Bay, the tide current can only take 1/3 of the sediment into the outer sea, so most of the sediment is held up at the river mouth and make the topography of the YRD greatly changable all the time.

With respect to the numerical investigations of the Yellow River, Zhang et al.[7]developed a 1-D model for unsteady sediment transport in the Ningxia reach of the Yellow River, the concentration distributions and the mean diameter distributions of suspended sediment in the transversal direction were also estimated by using this model, and after validation, the model was used to predict the riverbed deformation during the period of 1999-2019 in the Ningxia reach of the Yellow River. Cao et al.[8]established a 2-D numerical model based on “slot method” for unsteady flow and sediment transport and effectively simulated the sediment transport, scouring and silting of seabed and the variation of coastline. Li et al.[9]built a 2-D model based on the Volume Of Fluid (VOF) technique and applied it in Panjiatai Shoal, one of the important reaches in the Yellow River. Zhao et al.[10]derived a set of new 2-D equations for interchanges between suspended sediment and bed materials based on related studies for the Lower Yellow River. Kong et al.[11]applied the Environmental Fluid Dynamics Code (EFDC) code to simulate the bed evolution process in the YRD from 1992 to 2000 and obtained some reasonable results.

In the present study, a 2-D depth-integrated numerical model is developed to predict the hydrodynamic, sediment transport and morphological processes in the YRD. The model has the ability to simulate the transport of graded sediments under nonequilibrium conditions. The bed mixture is divided into fractions, with consideration of both the cohesive sediment and the non-cohesive sediment, and each fraction of sediment is simulated separately by assuming that the fractions do not interact with each other in the water body. The evolution of the bed is the result of erosion or sedimentation. In order to account for the influence of bed sediment composition on the overall transport process, a method of multiple bed layers is used to represent the spatial and temporal variations of sediment gradations of the loose bed layers. In view of the high sediment concentration of Yellow River, the fall velocity of the suspended sediment is modified in the present model according to the practical sediment concentration. The present model is used to simulate the bed evolution in the YRD from 1992 to 1995, and the numerical predictions by the present model are compared with experimental measurements and the predictions based on non-fractional models.

1. Numerical model details

1.1 Governing equations for hydrodynamic process

The hydrodynamic model for predicting the water elevation and velocity fields in coastal, estuarine and riverine waters involves the solution of the governing equations of fluid flow. The 2-D hydrodynamic equations are generally based on the depthintegrated 3-D Reynolds equations for incompressible and unsteady turbulent flows, with considerations of the effects of the earth’s rotation, bottom friction and wind shear. The hydrodynamic module in the present model is based on an existent model-Depth Integrated Velocity And Solute Transport (DIVAST), with its capacity in dealing with the flooding and drying processes as a useful feature. More details of the hydrodynamic governing equations and solution methods can be found in Falconer’s article[12].

1.2 Governing equations for sediment transport

process

In estuarine and coastal waters, the sediments are usually highly graded, ranging from very fine to rather coarse particles. The transport properties of such sediments may vary significantly. Thus in some situations it would not be reasonable to use a single diameter to represent all sediments. In the present study, the graded sediment is divided into N fractions according to the particle size distribution.

It is widely accepted that the suspended sediment concentration can be described by the advectivediffusion equation. For horizontal or quasi-horizontal flows, the 3-D solute mass balance equation can be integrated over the water depth to obtain the 2-D depth-integrated advective-diffusion equation, as whereiφ is the depth averaged suspended sediment concentration for the ith (i=1,2…N) fraction, Dxx, DxyDyx, Dyyare the depth averaged diffusion coefficients in the x and y directions. Ssiis a source term for the ith fraction which represents the erosion and deposition fluxes.

In coastal and estuarine waters, the water depth H may vary greatly, thus the monotonicity of the depth integrated concentration (φiH) may be different from that of the solute concentration (iφ). In order to achieve a high accuracy and the mass conservation, Eq.(1)could be recast with an additional source term being introduced into the 2-D depth integrated advectivediffusion equation. In the current study, this modification is included in the sediment transport equation, i.e.,

where Saiis the additional source term for the ith fraction, which can be formulated in the form as

The additional source term is shown to be vital for the mass conservation in modelling mass and solute transport.

For cohesive sediment (d＜0.063mm), where d is the sediment particle diameter, Ssiin Eq.(2) can be obtained as

where Diis the depositional flux and Eiis the erosion flux, whose most widely used expressions are[13]:

where wsiis the fall velocity of sediment particle, τbiis the flow induced bed shear stress, τcdand τceare the critical shear stresses for deposition and erosion, respectively, Sbiis the near sediment concentration, M is the erosion parameter which should vary with time and depth but is generally assumed as a constant. The exponent n0is generally unity. Details about the parameters could be found in Winterwerp and Van Kesteren[13].

For non-cohesive sediment, Ssican be obtained as[14]

wheresρ is the sediment density, n is a coefficient for the normal flow condition, which takes a value of about 4[15].

For equilibrium suspended sediment fluxes, φai=φaeiand Ssi=0. The reference level “a” is equal to the equivalent roughness height kswith a minimum value of a=0.01H.

The expression used in this study to define φaeifollows from Van Rijn[16]and it is written as

where D50iis the median grain size for the ith fraction, puiis the percentage of the ith fraction in the loose layer of bed, D∗iis the dimensionless particle size and Tiis the transport stage parameter for the ith fraction.

In a depth-integrated 2-D model, only the mean sediment concentrationiφ is considered. Hence the value of the reference concentration φaimust therefore be related to the depth mean concentrationiφ, which is assumed to be in the following form[14]

whereeiφ is the depth mean equilibrium concentration. Combining Eqs.(7) and (10), one obtains thefollowing net erosion or deposition rate

The depth mean equilibrium concentrationeiφcan now be calculated from the ratio of the depth integrated equilibrium suspended sediment fluxqsito the depth integrated fluid fluxqi, as

in whichαis a profile factor, being assumed to be 1.13[14].

Fig.1 Bed sediment layers

1.3Bed level change

For each fraction of the cohesive sediment, the corresponding bed elevation change during Δtcan be determined by

For each fraction of the non-cohesive sediment, the corresponding bed elevation change during Δtcan be obtained from the equation

wherep0is the porosity of the bed layer sediment. Within a time step, the total variation of the bed level ΔZBis obtained as

1.4Bed sediment size variation

The deformation of the bed, especially during the degrading process, is dominantly controlled by the composition of the bed material. The scoured bed tends to be armoured to prevent further erosion, or to become refined in the case of deposition. To account for the influence of the bed sediment composition, numerical models were developed to solve the spatial and temporal variations of the sediment gradation of the loose bed layers. This can be done by dividing the loose sediment bed into several vertical layers. As shown in Fig.1, the loose bed is divided into the top, middle and bottom layers, with the thickness and volumetric fractions of these layers being defined asHT,HM,HLandPTi,PMi,PLi, respectively. The superscript 0 indicates the values of last time step.

Fig.2 Location of Yellow River Estuary

Table 1 Average fractional diameters and corresponding percentages

Due to erosion or deposition, the fraction percentage of the top layerHT+ΔZBduring a small time interval can be obtained as

where ΔZBiis the scoured or deposited thickness ofan individual sediment fraction.

Fig.3 Inflow flux at Lijin Station from 1992 to 2000

Fig.4 Sediment concentration in Lijin Station from 1992 to 2000

In the case of deposition, i.e., ΔZB＞0, the fraction percentage of the top layer is calculated by Eq.(16). The fraction percentage of the middle layer can be calculated as

The fraction percentage of the bottom layer can be calculated as

On the other hand, in the case of erosion, i.e., ΔZB＜0, the position of the top layer should be adjusted. The adjusted fraction percentage of the top layer can be calculated as

The fraction percentage of the middle layer can be calculated as

The fraction percentage of the bottom layer keeps unchanged, but the thickness of the lower layer is adjusted according to

This method is not restricted to only 3 layers. In order to increase the accuracy, the number of layers can be increased.

Fig.5 Velocity field when the tide

2. Numerical simulation

In order to validate the present model, the bed evolution in the YRD from 1992 to 1995 is simulated. In 1992, the YRD is located between 37o35′N and 37o40′N, 119o15′E and 119o20′E, as shown in Fig.2. The computational domain is divided into 360×420 rectangular grids with side length ranging from 50 m to 500 m. The upstream boundary is located at Lijin Station, Station X is 4.20 km downstream from Lijin station along the river way, and the distance from the upstream to the Mouth into the Bohai Sea is about86 km, The Qing VII and Qing VIII are two cross sections near the Mouth. There are several gullies on the bay of Bohai Sea.

Fig.6 Tidal elevation in a period at Shenxian Gully

Fig.7 Daily water elevations at X station from 1992-6-22

Fig.8 Sediment concentration at Shenxian Gully from 1991-5-22

Qingshui Gully is the tail channel of the Yellow River from 1976 to 1996 and Shenxian Gully and Diaokou Gully are on the north shore. OA, OB and OC are three cross sections with Point O at (20 696, 4 183). At Lijin Station, the bed elevation is found to be 12 m above the sea level while out of the Mouth the lowest bed elevation is approximately 18 m below the sea level. The sediments of YRD in 1992 are subdivided into 6 fractions, with the average diameters and the corresponding percentages being listed in Table 1. Initially, the bed sediments are assumed to be homogenously laid on the bed, fractions 1-4 are considered as cohesive sediments while fractions 5 and 6 are regarded as non-cohesive sediments.

The simulation starts in January 1992 and ends in September 1995 before the artificial diversion. The time step is 20 s and the total computational time for each run is about 80 h with a 4×2.4 GH PC. The simulations involve the open boundary tidal elevations, the surface wind stresses and the high sediment concentration inflows. The upstream inflow boundary condition is given as a time series of flux at Lijin Station as shown in Fig.3. Figure 4 shows the sediment concentration at Lijin station from 1992 to 2000. The seaward open boundaries are considered in the model as shown in Fig.2, and the tidal elevations at Points NE and SE are calculated by the harmonic constants taking into account of the M2and K1constituents[17]. The tidal elevations between NE and SE are obtained by the linear interpolations using these two points. The tidal elevation on the north open boundary is assumed to be uniform and equal to that at NE, and the tidal elevation on the south open boundary is also assumed to be uniform and equal to that at SE.

The salinity in the place out of the Mouth in Bohai Sea is around 30.4[11]. The mean porosity of the sediment in the YRD is found to be 0.45 by experiments[18]. The main parameters controlling the accuracy of the model are the roughness heightks, the critical bed-shear stress for depositiondτand thecritical bed-shear stress for erosioneτ. According to Kocyigit’s study[19], ksmay take a value twice of the mean particle diameter. Based on the value range proposed by Winterwerp and Van Kesteren[13], and by changing the parameters and comparing the model predictions with the measured data, the model is calibrated by choosing the best fit between the predicted results and the measured data. In the present case,dτ is 0.1 N/m2,eτ is 1 N/m2.

Figure 5 shows the velocity field during the rising and falling tides and we can see that Yellow river and Bohai Sea have an opposite flow direction during the rising tide, which helps water mixing in the river mouth. New lands are formed mainly in the rising tide period. When the tide falls, the velocity in the river mouth is increased and much sediment stayed in the river mouth will be carried into the outer sea during this tide period.

Figure 6 compares the measured and numerical tidal elevations in Shenxian Gully in a tide period, with the measured tidal elevation in Shenxian Gully being plotted in the dash line, and the numerical data obtained by the present model in the solid line.

Figure 7 shows the water surface level of the X Station from July 1992 to January 1994. The numerical water surface basically matches the measured data except for a delay of fall after the peak arrives, which is mainly due to the fact that a lot of flood plains come into being when the water level rises, and the newly-formed wet cells should be eliminated from the computational domain after the peak passes away, while the drying and wetting processes adopted by the present model would take some time.

Figure 8 displays the sediment concentration from January 1992 to January 1996 in Shenxian Gully, with the dash line indicating the measured data ranging from 350 mg/l to 140 000 mg/l, and the solid line the numerical data, and the general trend is shown to be consistent. The sediment concentration is extremely high in the summer time, nearly 140 000 mg/l, and the peak values simulated are in good agreement with the measurements.

Figures 6-8 show that the parameters and boundary conditions are reasonable, which are fundamentally important for the longtime bed evolution simulation.

Figure 9 compares the numerical and measured bed levels along OA, OB and OC. Although the numerical level is a slightly higher, its trend is consistent with the measured data and the errors are small in most places, with the greatest error of about 2 m near Point C. Figure 10 shows the bed elevation from the Qing VII cross-section to the mouth of the Yellow River. It can be seen that thick sediment does not deposit on the river bed along the river way, but over the Mouth area. The dash-dot line is the measured bed morphology in January 1992 while the dash line shows the measured bed morphology in September 1995, and the solid line is the numerical data along the river way from Qing VII (referring to Fig.2) to the Mouth in September 1995. It is shown that the bed elevation on the river way rises just about 1.0 m during the four years while the Mouth moves forward into the sea altogether around 8.1 km. The numerical results agree well with the measured data. The estimate from the numerical results for the newlyformed area is 30.2 km2.

Fig.9 Bed elevations along OA, OB and OC in September of 1995

In order to see the difference between the present model and the non-fractional models, the following two non-fractional models are used to simulate the same case as described above, (1) all the sediments are regarded as non-cohesive, (2) all the sediments are regarded as cohesive. The sediment concentrations in Shenxian Gully obtained by the two non-fractional models and the present fractional model are shown in Fig.11 together with measured data. It is shown that the results obtained by model (a) are very different from the measured data, because most of the sediments in the YRD are cohesive, that is, it is fundamentally wrong only using non-cohesive sediments to simulate the sediment transport in the YRD. Although the trend of results by model (b) is consistent with the measured data, there is still a great error between them. That is mainly because (1) the mean diameter is usedto represent the sediment mixture, and the fine sediments are hidden in model (b), (2) there are still about 1/4 of sediments that are non-cohesive, and the results can not be precise when they are ignored.

Fig.10 Bed level from Qing VII to outer sea

Fig.11 Comparison of sediment concentration in Shenxian Gully among two non-fractional models, the fractional model and the measured data

3. Conclusions

A 2-D depth-integrated numerical model is refined for predicting the bed evolution process in estuarine and coastal waters. The model is capable of simulating the transport of graded sediments under unsteady flow and non-equilibrium conditions. A multiple bed layer approach is used to calculate the bed level and the sediment composition changes. The settling velocity is modified to account for the hindered effect in the high-concentration water.

The model is applied to simulate the bed evolution in the YRD. The hydrodynamic processes in the YRD are difficult to model because the inflow varies greatly with the seasons, particularly, a large area along the river way is dry in winter time, the water contains a very high sediment concentration, and most area has a mobile bed layer due to sediment deposition. The present model is applied to deal with such complicated environmental problems, and some reasonable results are obtained.

The hydrodynamic simulation and the sediment concentration on the river channel are both computed quite accurately, as is really essential for the longtime bed evolution prediction. The computational bed elevations agree well with the measured data in cross sections OA, OB and OC. The predicted annual morphologies show the development process of YRD between 1992 and 1995, and the newly-formed area is estimated to be 30.2 km2. According to the bed elevation from Qing VII to the mouth, the sediment mainly deposits just out of the YRD and the mouth moves forward into the sea in the average annual rate of 2.1 km. By comparing the sediment concentration in Shenxian Gully obtained by non-fractional models, the present fractional model and the measured data, the present model is shown to be better in simulating the bed evolution process in the YRD. The formed and eroded land area of the Yellow River Estuarine wetland can be estimated with the method in this article, which is ecologically important for protecting animals and vegetations in this foreshore wetland of the YRD.

Acknowledgement

This work was also supported by the Tsinghua University Initiative Scientific Research Program (Grant No. 2009THZ07060).

[1] SCHRAMKOWSKI G. P., SCHUTTELAARS H. M. and De SWART H. E. The effect of geometry and bottom friction on local bed forms in a tidal embayment[J].Continental Shelf Research,2002, 22(11-13): 1821-1833.

[2] ZHANG Jing-xin, LIU Hua. A vertical 2-D numerical simulation of suspended sediment transport[J].Journalof Hydrodynamics,2007, 19(2): 217-224.

[3] CHUNG D. H., EPPEL D. P. Effects of some parameters on numerical simulation of coastal bed morphology[J].International Journal of Numerical Methods for Heat and Fluid Flow,2008, 18(5): 575-592.

[4] TAN Guang-ming, JIANG Lei and SHU Cai-wen et al. Experimental study of scour rate in consolidated cohesive sediment[J].Journal of Hydrodynamics,2010, 22(1): 51-57

[5] LI Meng-guo. The effect of reclamation in areas between islands in a complex tidal estuary on the hydrodynamic sediment environment[J].Journal of Hydrodynamics,2010, 22(3): 338-350

[6] LIU Yan-xia. Sediment transport at the new outlet of Yellow River and changes of erosion and accumulation[D]. Ph. D. Thesis, Qingdao: Institute of oceanology, Chinese Academy of Sciences, 2006(in Chinese).

[7] ZHANG Hong-yi, ZHANG Hong-wu and HUANG Yuan-dong et al. A mathematical model for unsteady sediment transport in Ningxia reach of the Yellow River[J].Journal of Hydrodynamics, Ser. B,2001, 13(4): 1-7.

[8] CAO Wen-hong, HE Shao-ling and FANG Chun-ming. 2-D numerical model for unsteady flow and sediment transport in Yellow River Estuary[J].Journal of Hydraulic Engineering,2001, (1): 42-48(in Chinese).

[9] LI Zhi-qin, LI Jia and YI Wen-ming et al. Application of VOF technique to channel improvement for Panjiatai Shoal in the Yellow River[J].Journal of Hydrodynamics,2005, 17(2): 252-256

[10] ZHAO Lian-jun, JIANG En-hui and TAN Guang-ming et al. Horizontal 2-D basic equations and simulation of interchange between suspended sediment and bed materials in alluvial river[J].Journal of Hydrodynamics,Ser. B,2007, 19(4): 509-516.

[11] KONG Qing-rong, JIANG Chun-bo and QIN Jun-jie et al. Sediment transport and bed morphology reshaping in Yellow River Delta[J].Science in China, Series E: Technological Sciences,2009, 52(11): 3382-3390.

[12] FALCONER R. A. Flow and water quality modelling in coastal and inland water[J].Journal of Hydraulic Research,1992, 30(4): 437-452.

[13] WINTERWERP J. C., Van KESTERN W. G. M.Introduction to the physics of cohesive sediment in the marine environment[M]. Amsterdam, The Netherlands: Elsevier, 2004.

[14] LIN B., FALCONER R. A. Modelling sediment fluxes in estuarine waters using a curvilinear co-ordinate grid system[J].Estuarine, Coastal and Shelf Science,1995, 41(4): 413-428.

[15] Van RIJN L. C.Principles of sediment transport in rivers, estuaries and coastal seas[M]. Amsterdam, The Netherlands: Aqua Publications, 1993.

[16] Van RIJN L. C. Sediment transport, Part I, Bed load transport[J].Journal of Hydraulic Engineering,1984, 110(10): 1431-1456.

[17] HUANG Chen-hu, HOU Shi-xi and HUANG Mo-tao et al. Computation and application of nonharmonic constants of tide[J].Hydrographic Surveying and Charting,2005, 25(4): 22-24(in Chinese).

[18] GUO Xiu-jun, ZHANG Zhi-kuo and JIA Yong-gang et al. Electrical resistivity feature of saturated silty soil in Yellow River estuarine area and its engineering geology application[J].Rock and Soil Mechanics,2007, 28(3): 593-598(in Chinese).

[19] KOCYIGIT O., LIN B. and FALCONER R. A. Modelling sediment transport using a lightweight bed material[J].Maritime Engineering,2005, 158(1): 3-14.

January 6, 2011, Revised February 26, 2011)

* Project supported by the Key Project of National Natural Science Foundation of China (Grant No. 51039002), the State Key Laboratory of Hydroscience and Engineering, Tsinghua University (Grant No. 2009-TC-2).

Biography: YANG Chen (1981-), Male, Ph. D.

Corresponding: JIANG Chun-bo,

E-mail: jcb@mail.tsinghua.edu.cn

2011,23(4):457-465

10.1016/S1001-6058(10)60136-9