Numerical study of three-dimensional suspended sediment ...

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doi:10.1016/j.oc

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Ocean Engineering 34 (2007) 1569–1583

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Numerical study of three-dimensional suspended sediment transportin waves and currents

Bingchen Lianga, Huajun Lia,�, Dongyong Leeb

aCollege of Engineering, Ocean University of China, 238 Songling Road, Qingdao 266100, ChinabCoastal and Harbor Engineering Research Center, Korea Ocean Research and Development Institute, Ansan P.O. Box 29, Ansan, South Korea

Received 2 May 2006; accepted 3 December 2006

Available online 11 February 2007

Abstract

In the present work, a three-dimensional suspended sediment model (SED) is built. A three-dimensional hydrodynamic model

(COHERENS) and a third-generation wave model (SWAN) are fully coupled through accounting for mutual influences between wave

and current in them. SED is combined with the coupled model built up above. Damping function of suspended sediment on turbulence is

introduced into COHERENS. Then a coupled hydrodynamic–sediment model COHERENS-SED incorporating mutual influences

between wave and current is obtained. COHERENS-SED is adopted to simulate three-dimensional suspended sediment transport of

Yellow River Delta with wave–current co-existing. The simulated tidal current velocities and suspended sediment concentration match

well with field measurement data. The simulated significant wave height and wave period for a case with current’s effects can give better

agreement with measurement data than a case without current’s effects. Numerical simulation results of COHERENS-SED are

demonstrated to be reasonable though being compared with previous studies and field measurements [Wang, H., Yang, Z.S., Li, R.,

Zhang, J., Chang, R., 2001. Numerical modeling of the seabed morphology of the subaqueous Yellow River Delta. International Journal

of Sediment Research 16(4), 486–498; Wang, H., 2002. 3-dimensional numerical simulation on the suspended sediment transport from

the Huanghe to the Sea. Ph.D. Thesis, Ocean University of China, pp. 12–14 (in Chinese)].

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Yellow River Delta; Suspended sediment; Turbulence; COHERENS; SWAN

1. Introduction

Sediment transport plays an important role in coastlineand morphology changes of coastal and estuarine zonesusually. Wave can, sometimes, re-suspend much moresediment from the bed by enhancing much higher bottomshear stress. In the meantime, coastal and estuarine zonesare of great economic significance to mankind too. So themodeling of suspended sediment with current and wave co-existing has great economic value. In recent years, manywave–current-coupled numerical models (e.g. Mastenbrocket al., 1993; Zhang and Li, 1997; Xie et al., 2001) have beenapplied in such areas. Among them, Zhang and Li (1997)coupled a third-generation wave model and a 3D circula-

e front matter r 2007 Elsevier Ltd. All rights reserved.

eaneng.2006.12.002

ng author.

sses: [email protected] (B. Liang),

u.cn (H. Li), [email protected] (D. Lee).

tion model through boundary layers. They conclude thatthe total stress close to the sea surface is the sum of theturbulent part and a wave-induced part, and obtained idealresults. Xie et al. (2001) combined the circulation POMwith the wave model WAM to account for the wave–current interaction through surface and bottom stressesunder uniform winds and found that wave-induced windstress increases the magnitude of currents and wave-induced bottom stress weakens the currents. They con-tribute much to the current modeling with wave–currentco-existing. However, the present study couples anotherthird-generation wave model (SWAN) and another three-dimensional hydrodynamic model (COHERENS). Com-pared with other wave-generation models, SWAN can bemore reasonable in simulating waves in coastal andestuarine zones since it is a numerical wave model toobtain realistic wave parameters in coastal areas, lakes andestuaries from given wind, bottom and current conditions,

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Nomenclature

CDb bottom drag coefficient

CDs surface drag coefficient

N(s, y) energy density spectrums wave relative frequencyy wave propagation directioncx, cy,cs, cy wave propagation velocities in x-, y-, s-, y-

spaceS source term in terms of energy density repre-

senting the effects of generation by windinputting, dissipation and interaction of non-linear wave–wave

ra, rs, rw air density, sediment density, water density,respectively

~U10 wind speed at 10m level above sea surfaceCp wave peak frequency velocityg gravitational acceleration constantu*cw friction velocity arising from the combined

shear stressu*w friction velocity arising from wave onlyu*c friction velocity arising from current onlyfc the angle between wave propagation direction

and current directionC suspended sediment concentrationws settling speedlH, lT horizontal eddy viscosity and vertical diffusion

coefficientu, v, w current velocities at the x, y, z direction,

respectivelyya, yv implicit factor for vertical advection and diffu-

sion and they are given values of 0.501 and 1.0to adopt the semi-implicit and full-implicitnumerical method, respectively

C� the suspended sediment concentration after thefirst step calculation

n the nth time step levelCn suspended sediment concentration at time level

n

Ah (C n) horizontal advection at time level n

Dh (C n) horizontal diffusion term at time level n

Av(C(n, n+1)) vertical advection term at time level n,

and n+1

Dv(C(n, n+1)) vertical diffusion term at time level n, and

n+1E erosion fluxD deposition fluxzb the position of the bed surfacee turbulence dissipation rateu kinematic viscosity coefficientG the square root of gradient of turbulent velocity

fluctuationH depthU*, u friction velocity and mean flow velocity, re-

spectivelyWs0 settling velocity in stationary watertb bed shear stresstcd the critical deposition bed shear stressCb the sediment concentration near bedb deposition probabilityeb0, a empirical coefficients of the present bed surface

layertce(Zb) stress function varying with depth below bed

surfacevT, lT eddy viscosity coefficient and eddy diffusion

coefficient, respectivelyP the production of turbulent energy by energy

exchange with the mean flowDz the vertical diffusionAdh the horizontal advection and diffusionB gravity turbulence buoyancy effectsk turbulence energye0 a constant and defined as e0 ¼ Su0

3/4, Su0 iscoefficient of neutral stability

Bw the turbulence buoyancy destruction inducedby water density, which does not includesediment

Bs damping term on turbulence induced by sus-pended sediment

bT, bs respectively, thermal and salinity expansioncoefficients

vb, lb background viscosity and diffusivity coeffi-cients

Su, Sb stability functions

B. Liang et al. / Ocean Engineering 34 (2007) 1569–15831570

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and it represents reasonably the wave propagationprocesses of shoaling, refraction, reflection, and the wavegeneration and dissipation processes of wind input, depth-induced wave breaking bottom friction and wave–waveinteraction. In order to study sediment transport, in thispaper a three-dimensional suspended sediment model(SED) is built and introduced into the above-mentionedwave–current-coupled model. More details are givenbelow.

In the present work, the effects of waves are taken intoaccount in COHERENS, modified by introducing effects

of wave on bottom shear stress and on wave-dependentsurface drag coefficient. SWAN is introduced into COHE-RENS as a subroutine. COHERENS gets wave height,period and direction through calling SWAN. SWAN getscurrent velocity and surface elevation from COHERENSto account for their effects on wave simulation. The mutualinfluences between wave and current are included throughsuch exchanges. Moreover, the damping function ofsuspended sediment on turbulence is introduced intoCOHERENS-SED, since suspended sediment content iswell-known to be high around the Yellow River estuary.

ARTICLE IN PRESSB. Liang et al. / Ocean Engineering 34 (2007) 1569–1583 1571


Meanwhile, COHERENS-SED is adopted to simulate thesuspended sediment transport of Yellow River Delta withwave–current co-existing under realistic winds.

In terms of length, Yellow River is the second longestriver in China. She is famous for her high sediment contenttoo. She carries much sediment every year into Bohai.Moreover, the depth here is generally shallow. Wavefunction is very obvious. To analyze the sediment transportwith wave–current, the damping function of sediment onturbulence is very important. So the present study has threemain purposes:

The first purpose is to couple SWAN and COHERENS,which can give a more reasonably coupled model forcoastal hydrodynamic and wave analysis since SWAN isdesigned to simulate waves in shallow-water zonesprimarily. The second is to construct a three-dimensionalsuspended sediment model (SED) and to obtain ahydrodynamic-sediment coupled COHERENS-SEDthrough coupling SED, SWAN and COHERENS. Toapply COHERENS-SED in simulating suspended sedi-ment transport with wave–current co-existing in the YellowRiver Delta is the third purpose, which may demonstratethe validity of COHERENS-SED.

2. Model description

2.1. General

COHERENS is a three-dimensional, multi-purpose nu-merical model for coastal and shelf seas. The hydrodynamicmodel is coupled to biological, re-suspension and contami-nant models, and resolves mesoscale to seasonal processes.The code has been developed over the period 1990 to 1999by a multinational group as part of the MAST projectsPROFILE, NOMADS and COHERENS, funded by theEuropean Union (Patrick et al., 1999). Brief descriptions ofthe COHERENS-SED and SWAN are given in thefollowing sections. The modifications to COHERENS andthe setting up of sediment model are also presented.

The hydrodynamics governing equations consist of thecontinuity equation and momentum equations. The totalvariation diminishing (TVD) scheme is used to solveadvection terms of momentum equations. So the advectiveflux is evaluated as a weighted average between the upwindflux and either the Lax-Wendroff in the horizontal or thecentral flux in the vertical. Further details about thegoverning equations, numerical methods and discretizationschemes can be found in Patrick et al. (1999). The slipboundary conditions are applied for the horizontal currentat the bottom and surface. The effects of wave on bottomstress are implemented in the bottom drag coefficient Cs

D

and the effects of wave on surface wind stress are applied inthe surface drag coefficient Cs

D in the present work. Thedetails are shown in following sections.

In SWAN, the waves are described with the two-dimensional wave action density spectrum, even whennonlinear phenomena dominate (e.g., in the surf zone). The

spectrum that is considered in SWAN is the action densityspectrum rather than the energy density spectrum N(s, y),since in the presence of currents, wave action density isconserved whereas energy density is not (e.g., Whitham,1974). The independent variables are the relative frequency(as observed in a frame of reference moving with currentvelocity) and the wave direction (the direction normal to thewave crest of each spectral component). The action density isequal to the energy density divided by the relative frequency.The numerical grid of SWAN is the same as COHERENS.The governing equation is the spectral action balanceequation described as (SWAN documents, 2004)

qqt

N þqqx

cxN þqqy

cyN þqqs

csN þqqy

cyN ¼S

s, (1)

where N is the action density which is obtained throughdividing the energy density by the relative frequency s;parameters cx, cy, cs, cy are, respectively, wave propagationvelocities in x-, y-, s-, y-space. The first term on the left-handside of this equation represents the local rate of change ofaction density in time, the second and third terms representthe propagation of action in geographical space. The fourthterm represents shifting of the relative frequency due to thevariations in depths and currents. The fifth term representsthe depth-induced and current-induced refraction. So currentvelocity and surface elevation information from COHE-RENS is used in the fourth and fifth terms. The termSat theright hand is the source term in terms of energy densityrepresenting the effects of generation by wind inputting,dissipation and interaction of nonlinear wave–wave.

2.2. The implementation of wave’s effects

2.2.1. Surface drag coefficient

As the boundary conditions at the free surface, theatmospheric wind forcing is applied at the sea surfacethrough the following surface wind stress ~ts:

~ts ¼ raCsDj~U10j~U10, (2)

where ra is air density and ~U10 is wind speed at a 10m levelabove sea surface. The concrete formulations of the dragcoefficient are shown in the following sections. Wave-dependent surface drag coefficient adopts the formulationgiven in Donelan et al. (1993), the procedures are describedin the following sections:The wave-dependent surface drag coefficient is described

as

CsD ¼

0:4

ln 10� lnZ0

� �2

; Z0 ¼ 3:7� 10�5U2

10

g

U10

Cp

� �0:9

.

(3)

Parameter Cp is the wave peak frequency velocity and g

is gravitational acceleration constant (9.81m/s2 in thispaper).

ARTICLE IN PRESS

Table 1

Empirical parameters

a b tcd e0 a tce(Zb)

0.3 0.09 0.15N/m2 0.00000012 1.0 0.5N/m2

37.8

38.2

38.4

2

4

6

8

10

12

14

16

18

20

22

latitu

de

38

37.6

37.4

118.4 118.6 118.8

longitude

119 119.2 119.4 119.6 119.8

depth

Fig. 1. The topography of the Yellow River Delta in 2000 (depth contours

in meters).

B. Liang et al. / Ocean Engineering 34 (2007) 1569–15831572


2.3. Bottom drag coefficient CDb with wave and current

co-exist

As shown by the numerical simulations of Davies andLawrence (1994, 1995), interaction between currents andsurface wave plays an important role in the circulation incoastal waters due to the enhancement of bottom stress. Inthis paper, the coupling procedure proposed by Signellet al. (1990) and used by Davies and Lawrence (1995) isadopted. Detailed discussion of this procedure can befound in Patrick et al. (1999). However, the only differencefrom the original procedures of Patrick et al. (1999) andDavies and Lawrence (1995) is the introduction of theangle factor between wave propagation and current in thispaper. In the present work, the friction velocity u*cw arisingfrom the combined shear stress is given by Lou and Peter(1996) as

u�cw ¼ ðu2�b þ u2

�w þ 2u�cu�w cosfcÞ1=2 (4)

with

u2�b ¼ Cb

Dðu2b þ v2bÞ ¼ Cb

Du2c , (5)

where the term fc is the angle between wave propagationdirection and current direction. More details of theinteraction procedures at the bottom layer can be foundin Patrick et al. (1999).

3. Description of sediment model

3.1. Governing, numerical discretization equation and model

parameters setting

The governing equation of suspended sediment is

qC

qtþ

qqxðCuÞ þ

qqyðCvÞ þ

qqz½Cðw� wsÞ�

¼qqx

lH

qC

qx

� �

þqqy

lH

qC

qy

� �þ

qqz

lT

qC

qz

� �. ð6Þ

In Eq. (6), C is the suspended sediment concentration; ws

is settling speed; lH and lT are horizontal eddy viscosityand vertical diffusion coefficient; u, v, w are currentvelocities at x, y, z direction. Eq. (6) is solved throughtwo steps. The first step is to solve the governing equationincluding all terms except for the stationary water-settlingvelocity:

C� � Cn

Dt3D

¼ � AhðCnÞ � yaAvðC

nþ1Þ � ð1� yaÞAvðCnÞ

þ yvDvðCnþ1Þ þ ð1� yvÞDvðC

nÞ þDhðCnÞ. ð7Þ

With respect to Eq. (7), the TVD scheme is used foradvection and coupled with a fractional time-step method(details are given in the COHERENS manual). ya and yv

are implicit factors for vertical advection and diffusion,

respectively, and they are given values of 0.501 and 1.0 toadopt the semi-implicit and full-implicit numerical method,respectively; C� is the suspended sediment concentrationafter the first-step calculation; n stands for time step; C n issuspended sediment concentration at time level n; Ah(C

n)and Dh(C

n) are horizontal advection and diffusion term attime level n; Av(C

(n, n+1)) and Dv(C(n, n+1)) are vertical

advection and diffusion term at time level n and n+1,respectively. All concrete expressions for these terms arenot given in order to save paper space since they are notessential to our purpose. At the same time, the changes ofconcentration induced by stationary water-settling velocityare calculated within the second step. The settling-inducedchanges of concentration is adopted to solve the equationof the second step, whose is

Cnþ1 � C�

Dt3D

¼qqzðwsC

nþ1Þ. (8)

In this paper, the flux boundary condition is adopted as

� lT

qC

qzþ ws � C

� ��z¼zb

¼ E �D, (9)

where, E and D are erosion flux and deposition flux,respectively, and zb is the position of the bed surface.



About settling speed ws, the contribution of turbulence isaccounted for in this paper (Van Leussen, 1994 [13]):

ws ¼ ws01þ aG

1þ bG2; G ¼

ffiffiffi�

u

r, (10)

where e is turbulence dissipation rate; u is kinematicviscosity coefficient; a, b are empirically determinedconstants; G is the square root of gradient of turbulentvelocity fluctuation and it can be obtained by G ¼

5 10 15

1

2

3

sig

nific

an

t w

ave h

eig

ht

m

2

3

4

5

sig

nific

an

t w

ave p

eriod s

2.5

3.5

4.5

5.5

0.5

1.5

2.5

t

5 10 15

t

Fig. 3. Significant wave height and wave period (Full line for measurement da

37.6

37.8

38

38.2

38.4Bohai

Yellow River Mouth

Gudong

# 2

# 1Feiyantan

TiaoHe Mouth

Bohai Bay

La

titu

de

N

37.4

118.4 118.6 118.8

Longitude E

119 119.2 119.4 119.6 119.8

compute grid

Qingshuigou

Laizhou Bay

Fig. 2. Grids for the region of Yellow River Delta (# stand for

measurement location).

U*(u/u �H)0.5; H is depth; U* and u are friction velocityand mean flow velocity, respectively; and ws0 is defined byKrone (1962) and Owen(1971). In the method, the effectsof turbulence on sediment flocculation are accounted for,which makes the method more reasonable to calculatecohesive sediment settling speed.Deposition D:

D ¼ vd � Cb ¼ �bwsCb

21�

tb

tcd

þ 1�tb

tb

� ��

� �(11)

where tb is bed shear stress; tcd is the critical deposition bedshear stress; Cb is the sediment concentration near bed; andb between 0 and 1, meaning deposition probability.About erosion E calculation, this paper uses the method

referred to in Mehta et al. (1982a, b):

E ¼ �b0 exp atb � tceðzbÞ

tceðzbÞ

� �(12)

where, parameters eb0, a are empirical coefficients of thepresent bed-surface layer and tce (zb) should be stressfunction varying with depth below the bed surface.However, tce (zb) is assumed as a constant because ofthe lack of relevant experiments in the present work. Allthese coefficients need to be defined by erosion experiment.All values of empirical parameters occurring amongEqs. (10)–(12) are given in Table 1.

3.2. Turbulence-associated parameters definition

Moreover, to solve the momentum and sedimentequations requires the following turbulence closure model

20 25 30 35

ime h

20 25 30 35

ime h

ta; Plus line for case without current; Dashed line for case with current).

ARTICLE IN PRESSB. Liang et al. / Ocean Engineering 34 (2007) 1569–15831574


to define the eddy viscosity coefficient vT. The evolution ofthe turbulent kinetic energy in a sediment-laden flow issubjected to five mechanisms, which are the produc-tion of turbulent energy by energy exchange with the meanflow P, the vertical diffusion Dz and the horizontaladvection and diffusion Adh, the dissipation e, andgravity-induced turbulence destruction B. So, the turbulentkinetic energy balance is usually described by (Winterwerp,1999)

dk

dt¼ Pþ Adh þDzðkÞ � �� B, (13)

2 4 6 8 10

0

0

1

2

3

4

5

6

7

0.7

0

1

2

3

4

5

6

7

curr

ent

speed o

f bottom

layer

m/s

curr

ent

direction o

f

bo

tto

m l

aye

ry

curr

ent

sp

eed o

f

top l

ayer

m/s

curr

ent d

irection o

f

top layer

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.8

0.6

0.5

0.4

0.3

0.2

0.1

0

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Fig. 4. Current velocity and direction of observation station 1 (Full

where k is turbulence energy. The production anddissipation of turbulence terms P, e can be defined as (14)

P ¼ nT

qu

qz

� �2

þqv

qz

� �2 !

; � ¼ �0k3=2=l, (14)

where e0 is a constant and defined as e0 ¼ Su03/4, Su0 is the

coefficient of neutral stability.The gravity-effect term B consists of two parts. First is

the effect induced by water-density stratification separatedfrom sediment-induced density stratification. The second isfrom sediment-induced density stratification. If turbulencebuoyancy destruction induced by water density, which does

12 14 16 18 20 22

time h

12 14 16 18 20 22

time h

12 14 16 18 20 22

time h

12 14 16 18 20 22

time h

line for observation data and dashed line for calculation results).



not include suspended sediment, is expressed as Bw and theturbulence buoyancy destruction induced by suspendedsediment is expressed as Bs, then one can obtain Eqs. (15)and (16)

B ¼ Bs þ Bw, (15)

Bw ¼ gnT

ss

bT

qT

qz� bS

qS

qz

� �. (16)

Eq. (16) is defined by Pacanowski R.C. and PhilanderS.G.H. in 1981. bT and bs are, respectively, ther-mal and salinity expansion coefficients. The eddy visco-

0

0.91

0

1

2

3

4

5

6

7

2 4 6 8 10

0

1

0

1

2

3

4

5

6

7

curr

ent

speed o

f bottom

layer

m/s

curr

ent

direction o

f

bottom

layer

curr

ent

speed o

f to

p

layer

m/s

curr

ent direction o

f

top layer

0.90.80.70.60.50.40.30.20.1

0.80.70.60.50.40.30.20.1

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

Fig. 5. Current velocity and direction of observation station 2 (Full

sity coefficient vT and diffusion coefficient lT arecalculated as

nT ¼ Suk2=�þ nb; lT ¼nT

ss

¼ Sbk2=�þ lb, (17)

where vb and lb are background viscosity and diffusivitycoefficients and Su, Sb are stability functions. The term Bs

will be discussed and defined in the following paragraph.The damping function of sediment on turbulence is

introduced into COHERENS-SED (Erik, 2002). Sediment-induced density stratification affects the production ofturbulence because turbulence continuously works to mixsediment upwards against the action of gravity. So part of

12 14 16 18 20 22

time h

12 14 16 18 20 22

time h

12 14 16 18 20 22

time h

12 14 16 18 20 22

time h

line for observation data and dashed line for calculation results).



the turbulent energy is consumed to keep the sedimentsuspended in a water column, which then increasesaccordingly the consumption of turbulent kineticenergy. The part of the energy that is consumed bysediment is considered as destruction of turbulent energyand is introduced into the turbulence kinetic-energyequation. The damping term Bs is defined as Bs ¼

2 4 6 8 10

0

0.5

0.6

0.7

0.8

1

sedim

ent concentr

ation

of to

p layer

kg/m

3sedim

ent concentr

ation o

f

bottom

layer

kg/m

3sedim

ent concentr

ation o

f to

p

layer

kg/m

3sedim

ent concentr

ation o

f

bottom

layer

kg/m

3

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

2 4 6 8 10

2 4 6 8 10

2 4 6 8 10

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.9

0.4

0.9

0.8

0.7

0.6

0.5

0.4

Fig. 6. Suspended sediment concentration of observation stations 1 and 2

ðg=rwÞgw0c0 (Sheng and Villaret, 1989). It stands for theincrease of potential energy required to keep the sedimentin suspension. In this paper, the damping term induced bysediment is defined as

Bs ¼grw

gw0c0 ¼grw

gnT

ss

qc

qz(18)

12 14 16 18 20 22

For station 2

time h

12 14 16 18 20 22

time h

12 14 16 18 20 22

time h

12 14 16 18 20 22

time h

For station1

(Full line for observation data and dashed line for calculation results).



with g ¼ (rs�rw)/rs, rs and rw are the densities of sedimentand water, respectively.

4. Model setting

The horizontal spatial resolution of the model grid is0.95960 in the longitudinal direction and 0.78490 in thelatitudinal direction. The vertical water is divided into9 layers. The computed map ranges from 1181150

E�1191500 E in the longitudinal direction and from371170 N�381300N in the latitudinal direction. Fig. 1 showsthe topography of Yellow River Delta. Four maincomponent tides K1, O1, M2 and S2 are combined toprovide the time series surface elevation as open-boundaryconditions. The time step of the barotropic model is 15 sand that of the baroclinic model is 150 s. The numericalgrid for current and wave is shown in Fig. 2. COHERENS-SED calls SWAN every 30min. 600m3/s dischargeand 10 kg/m3 sediment concentration are defined as riverinput during wet season. During dry season, their valuesare zero.

Fig. 7. Flood tide tidal current of both the top and bottom layer.

5. Simulation results

5.1. Verification of wave height, wave period, current

velocity and suspended sediment concentration

In order to demonstrate the effect of interaction betweenwave and current, the measurement and simulation resultof wave height and wave period is given in Fig. 3. Themeasurement was carried out in 1999 and the location isaround Feiyantan, which is shown in Fig. 2. According toFig. 3, to include the effects of current in wave calculationimproves the higher value prediction, which can be foundin the time interval of beginning and another intervalbetween 25 and 30 h. So it may be safe to conclude thatwave calculation becomes better through accounting forcurrent and wave interaction.There are two more measurement locations around

Feiyantan. They locate around Feiyantan, which is in thenorthern part of the Delta (shown in Fig. 2). Themeasurement was carried out by 973 Project Group ofEstuarine and Coastal Research of East China NormalUniversity in 2004. Figs. 4–6 show the verification of

Fig. 8. Tidal current from flood tide to ebb tide of the both top and

bottom layer.



current velocities, current direction and suspended sedi-ment concentration process of both the bottom layerand the top layer of the three observation stations.According to the verification, COHERENS-SED can givea reasonable agreement of current velocities, direction andsediment concentration values with measurement, regard-less of both the bottom and top layer. Such matchingextent is still good since suspended sediment simulation isrelevant to many uncertain factors and currently there isno detailed information about the property of bottomsediment.

In terms of validation of sediment concentration of boththe bottom and top layer, COHERENS-SED can discoversediment transport rule in Yellow River Delta, specially forthe Feiyantan part being in the north of Yellow RiverDelta. Therefore, it can be further used to simulatesediment transport in zones around Feiyantan. Following3-D suspended sediment simulation for the wet season anddry season is implemented respectively. Here, the meaningof wet season stands for having river input and dry seasonmeans no river input.

Fig. 9. Ebb tidal current of both the top and bottom layer.

5.2. Simulation results discussion

5.2.1. Case with river input

Fig. 7 shows tidal current during flood tide. From thefigure, there are two zones with obviously high currentvelocity. Firstly, high current velocity exists aroundQingshuigou, which may be attributed to the compressionfunction of the spit of Qingshuigou on water flow. Theother one is around the northern part of the Delta, which isthe result of its being close to the amphidromi region of M2

tidal component (Wang, 2002). Fig. 8 gives the tidalcurrent from flood tide to ebb tide. According to Fig. 8,coastal tidal current begins to ebb while offshore tidalcurrent still floods. So there is obvious existence of tidalshear front in the Delta. Such a phenomenon is similar tothat of Wang (2002). Moreover, there is obvious currentvelocity gradient along the coast from Yellow Riverestuary to south of Qingshuigou, which can be attributedto the combined function of Coriolis force and the river’srunoff. Fig. 9 shows tidal current during ebb tide. LikeFig. 7, there are still two zones with obviously high current

Fig. 10. Tidal current from ebb tide to flood tide of both the top and

bottom layer.

ARTICLE IN PRESS

0.01

0.01

0.1

0.1

0.5

0.5

0.5

0.50.8

12 358

latitu

de

38.4

0.01

0.1

0.1

0.1

0.5

0.5

0.50.5

0.8

0.8

0.8

1

1

11.52358

38

38.2

38

37.8

37.6

37.4

118.4 118.6 118.8 119 119.2 119.4

longitude

sediment concentration of bottom layer, kg/m3

119.6 119.8

118.4 118.6 118.8 119 119.2 119.4

longitude

119.6 119.8

38.4

38.2

latitu

de

37.8

37.6

37.4

sediment concentration of top layer, kg/m3

Fig. 11. Distribution of sediment concentration during flood tide for the wet season.

B. Liang et al. / Ocean Engineering 34 (2007) 1569–1583 1579


velocity. The tidal shear front still exists in Fig. 10, whichgives the tidal current from ebb tide to flood tide.

Figs. 11, 12 show the sediment concentration distribu-tion of flood tide, and ebb tide respectively. The twopictures show that there are three high-concentration zonesin Yellow River Delta. They locate river estuary, spit ofQingshuigou and the north part of the Delta. These resultsare similar to former researches. Both of them show thehighest sediment concentration existing around the riverestuary as a result of river input. However, since freshwater flux is nearly normal to sea water flux around theestuary, sea current counteracts fresh water runoff to gofurther to deep sea and then reduces current velocityaccordingly, which results in the rapid depositing ofsediment around estuary, specially for coarse granule.Since most sediment from the river cannot be transportedto further deep sea, the range of high sediment concentra-tion is not wide. Finer sediment flowing out of the estuarydiffuses along the coast as the result of along-shore current.In comparison with suspended sediment diffusion in otherdirections, diffusion in the southeast direction dominates asa result of Coriolis force, which can be the result of theexistence of stronger longshore current in the southeastthan in other directions as shown in Figs. 7–10, and is alsoeasy to validate by checking Figs. 11 and 12 again.

According to them, a 0.5 kg/m3 contour value line ofsediment concentration gets to the spit of Qingshuigou andeven enters Laizhou bay. However, the high-concentrationzone cannot go far enough to get to the margin of anotherhigh-concentration zone located in northern the part of thedelta. Such diffusion law agrees with the real situation inthe whole, except for having shorter diffusion distance inthe north direction, which might be attributed to the exacteast set-up of the river estuary direction. In fact, runoff ofYellow River has a north component that forces sedimentto diffuse to the north partly. Another high-concentrationzone exists in the north part of the Delta according to thetwo pictures. The position has good agreement with theposition of high shear stress zone shown in Fig. 13. There isa similar distribution pattern of high shear stress duringebb tide. So, distribution of bottom shear stress during ebbtide is not shown in this paper. The center of highconcentration locates around 10m water depth contourline at the edge of Feiyantan. The location is around thecenter of high shear stress zone. Such a result further showsthat induced high sediment concentration in such a zone isbecause bottom of shear stress. Suspended sedimentconcentration during flood tide is higher than that of ebbtide, especially for the high-concentration zone locatedaround Feiyantan. For both the bottom and top layer, the

ARTICLE IN PRESS

0.010.010.01 0.1

0.1

0.5

0.5

0.5

0.81 22 3

37.4

38

38.4

0.01

0.01

0.1

0.1

0.1

0.5

0.5

0.5

0.8

0.8

1

1

1.51.523588

latitu

de

38.2

37.8

37.6

37.4

38

38.4

latitu

de

38.2

37.8

37.6

118.4 118.6 118.8

longitude

119 119.2 119.4 119.6 119.8

118.4 118.6 118.8

longitude

119 119.2 119.4 119.6 119.8


sediment concentration of top layer,kg/m3

Fig. 12. Distribution of sediment concentration during ebb tide for the wet season.

Fig. 13. Distribution of bottom shear stress with wave’s effects during

flood tide.

Fig. 14. Bed elevation changes induced by suspended sediment transport

within two days (unit: mm).

B. Liang et al. / Ocean Engineering 34 (2007) 1569–15831580中国科技论文在线 http://www.paper.edu.cn

ARTICLE IN PRESS

0.01

0.1

0.1

0.5

0.5

0.5

0.50.5

0.50.8

0.8

0.8

0.8

1

119

37.6

38

0.01

0.0

0.01

0.1

0.1

0.1

0.1

0.5

0.5

0.8

0.8

0.8

0.8

0.8

0.8

0.8

11

1

1

11.5

1.52

latitu

de

38.4

38.2

37.8

37.4

37.6

38

latitu

de

38.4

38.2

37.8

37.4

118.4 118.6 118.8

longitude

119.2 119.4 119.6 119.8

119118.4 118.6 118.8

longitude

119.2 119.4 119.6 119.8



Fig. 15. Distribution of sediment concentration during flood tide for the dry season.

B. Liang et al. / Ocean Engineering 34 (2007) 1569–1583 1581中国科技论文在线 http://www.paper.edu.cn

range of high sediment concentration during flood tide isobviously higher than that during ebb tide. In the authors’opinion, such a phenomenon results from the fact thatthere is higher current velocity during flood tide thanduring the ebb tide phase, which can re-suspend moresediment from the bed accordingly. At the same time, there-suspended sediment is transported to the southeastdirection with flood current. According to Fig. 14, there isa big erosion area in the north of delta, especially aroundTiaohe estuary. Gudong open sea and spit of Qingshuigouhave very weak erosion phenomena. However, aroundYellow River estuary, regardless of the high shearstress, there is much deposition because of much sedi-ment input from runoff. The deposition area spreadsfarther to the south than to the north along the coast,which agrees with the diffusion law of suspended sedimentfrom estuary.

Both Figs. 11, 12 show 0.01 concentration contour of thebottom layer extends to the northeast, which implies thatsome sediment from the high-concentration zone along thecoast disperses to the northeast. The distribution of highsuspended sediment concentration obtained in the presentstudy is similar to that of previous researches (Wang et al.,2001; Wang, 2002).

5.2.2. Case without river input

According to Figs. 15, 16, high suspended sedimentconcentration exists in the northern part of the Delta andaround Qingshuigou. Compared with river input seasons,suspended sediment concentration of the northern high-concentration part increases obviously, specially in west ofthe Tiaohe estuary. Such a phenomenon can be attributedto the action of big waves induced by strong northeastwind. The high-concentration zone around Qingshuigoumight be the result of erosion induced by accumulation ofwave energy since there is no sediment source from theriver. Attention also has to be paid to the small zonearound the river estuary where high concentration existstoo. The spit increases rapidly as the result of Yellow Riverinput, which is obvious through the dense distribution ofdepth contour around the river estuary shown in Fig. 1. So,as the current field is compressed, the current velocityincreases. This, combined with wave from the northeast,generates obvious higher bottom shear stress at the samezone. Therefore, this small high-concentration zone is theresult of erosion induced by bottom shear stress withcurrent-wave co-existing since there is no river input at thesame time. In short, within the dry season, the highsuspended sediment concentration must be the result of

ARTICLE IN PRESS

0.01

0.01

0.10.1

0.5

0.5

0.5

0.50.5

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0.81

38

0.01

0.01

0.01

0.01

0.1

0.1

0.1

0.5

0.5

0.50.5

0.80.8

0.8

0.8

0.8

0.8

11

11

1

latitu

de

38.4

38.2

37.8

37.6

37.4

38

latitu

de

38.4

38.2

37.8

37.6

37.4

118.4 118.6 118.8

longitude

119 119.2 119.4 119.6 119.8

118.4 118.6 118.8

longitude

119 119.2 119.4 119.6 119.8



Fig. 16. Distribution of sediment concentration during ebb tide for the dry season.

Fig. 17. Bed elevation changes induced by suspended sediment transport

within two days (unit: mm).

B. Liang et al. / Ocean Engineering 34 (2007) 1569–15831582中国科技论文在线 http://www.paper.edu.cn

erosion of the bed. Moreover, concentration of the toplayer is lower than that of the bottom layer. Fig. 17 giveschanges of bed elevation. Similar to the wet season, erosionaction is still obvious around Tiaohe estuary. However,more severe erosion than wet season occurs because of nosediment supplement of the Yellow River and because ofthe existence of high bottom shear stress. The small spitaround Yellow River estuary is eroded during the dryseason too.

6. Conclusions

In the present study, suspended sediment model CO-HERENS-SED is built by fully coupling COHERENS,SED and SWAN. Then it is applied to simulate suspendedsediment transport within the wet and dry season,respectively, with wave–current co-existing. Moreover, itis also adopted to simulate wave for two cases, one withoutaccounting for current and the other one accounting forcurrent. The damping function of sediment on turbulenceis introduced to COHERENS-SED since Yellow River hashigh suspended sediment content. The simulated results of



sediment concentration, current velocities, current direc-tion, significant wave height and period are, generally, inreasonable agreement with measurement. According tosimulation results, the following additional conclusions canbe drawn:

There are two high-concentration zones of suspendedsediment during the dry season. They are located in thenorthern part of the Delta and Qingshuigou, respectively.Both are the results of erosion induced by bottom shearstress. Within the wet season, there is one more highconcentration zone besides the two zones existing withindry season because of the Yellow River input, which isaround the Yellow River estuary. According to simulationresults, suspended sediment from the estuary spreads to thesoutheast and induces coastal high suspended sedimentconcentration zones. Wave simulation results show thataccounting for mutual influences between current and wavecan give a better agreement extent with measurementthan without accounting for such mutual influences. SoCOHERENS-SED is proved to be useful to simulatesuspended sediment and wave in the Yellow River delta.

Acknowledgements

This work was supported by the National Science Fundfor Distinguished Young Scholars (Grant No. 50325927)and the Cultivation Fund of the Key Scientific andTechnical Innovation Project, Ministry of Education ofChina (NO. 704031). The measurement data were providedby 973 Project Group of Estuarine and Coastal Researchof East China Normal University in 2004.

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