A Numerical Experiment on the Sedimentation Processes in the Yellow Sea...

Journal of OceanographyVol. 51, pp. 537 to 552. 1995

A Numerical Experiment on the Sedimentation Processesin the Yellow Sea and the East China Sea

TETSUO YANAGI and KOH-ICHI INOUE

Department of Civil and Ocean Engineering, Ehime University, Matsuyama 790, Japan

(Received 14 December 1994; in revised form 6 March 1995; accepted 13 March 1995)

Sedimentation processes of suspended matter supplied from the Huanghe (YellowRiver) and the Changjiang are investigated with the use of a three-dimensionalnumerical model of the Yellow Sea and the East China Sea which includes the tidalcurrent, residual flow and wind waves. Suspended matter supplied from theHuanghe mainly deposits in the Bohai Sea and that from the old river mouth of theHuanghe and from the Changjiang in the central part of the Yellow Sea or southof Cheju Island. The calculated results well reproduce the observed sedimentationpattern qualitatively except for the offshore area of the southeastern coast ofChina.

1. IntroductionMuch suspended matter is supplied from the Huanghe (Yellow River) and the Changjiang,

China and it is mainly advected by the residual flow and dispersed by the tidal current or thecurrent by wind waves in the Yellow Sea and the East China Sea (Fig. 1). The transport anddeposition processes of suspended matter supplied from the Huanghe and the Changjiang havebeen investigated near the river mouth (e.g. Milliman et al., 1984; Schubel et al., 1984; Wrightet al., 1990) and the budget of suspended matter in the Yellow Sea (Lee and Chough, 1989;Alexander et al., 1991) and that in the Yellow Sea and the East China Sea (Saito et al., 1994) havebeen investigated. However, the dynamical transport and sedimentation processes of suspendedmatter in the whole area of the Yellow Sea and the East China Sea have not been investigated yet.

In this paper, we carry out a numerical experiment in order to investigate the transport andsedimentation processes of suspended matter supplied from the Huanghe and the Changjiangwith the use of a three-dimensional numerical model of the Yellow Sea and the East China Seawhich includes the tidal current, residual flow and wind waves.

2. Numerical Model

2.1 Current systemNumerical models of currents in the Yellow Sea and the East China Sea have been already

established. Yanagi and Inoue (1994) well reproduced the tides and tidal currents there with theuse of a horizontally two-dimensional numerical model and they also calculated the tide-inducedresidual current. Yanagi and Takahashi (1993) investigated the seasonal variation of density-driven and wind-driven currents there with the use of a three-dimensional diagnostic numericalmodel which included observed water temperature, salinity and wind data. We combined theresults of both numerical models into one three-dimensional numerical model in this paper.

As for the tidal current in this model, only the M2 tidal current shown in Fig. 2 is includedbecause the M2 tidal current is the most dominant in the Yellow Sea and the East China Sea

538 T. Yanagi and K. Inoue

(Yanagi and Inoue, 1994). The M2 tidal current has a barotropic character, that is, its speed anddirection are the same in the vertical direction. The amplitude of M2 tidal current is large andnearly 90 cm s–1 in Hangzhou, Inchon and Seohan Bays as shown in Fig. 2.

As for the residual flow in this model, it is given as a linear superposition of tide-inducedresidual current due to M2 tidal current (Yanagi and Inoue, 1994), density-driven and wind-driven currents which were obtained by Yanagi and Takahashi (1993). The residual flows in theupper (0–20 m), middle (20–60 m) and lower (60 m–bottom) layers during winter of this modelis shown in Fig. 3. A clockwise circulation with a speed of about 2–3 cm s–1 develops from thesurface to the bottom in the Yellow Sea. On the other hand, a counter-clockwise circulation witha speed of about 2–3 cm s–1 exists in the upper and middle layers of the East China Sea.

Fig. 1. The Yellow Sea and the East China Sea. Numbers show the depth in meter.

A Numerical Experiment on the Sedimentation Processes in the Yellow Sea and the East China Sea 539

Fig

. 2.

M2

tida

l cur

rent

at t

he ti

me

of m

axim

um fl

ood

max

imum

ebb

and

at t

he m

outh

of C

hang

jian

g, a

ndth

e co

-tid

al a

nd c

o-am

plit

ude

char

ts o

f M

2 ti

dal c

urre

nt (

Yan

agi a

nd I

noue

, 199

4).


Fig

. 3.

Res

idua

l flo

ws

in th

e up

per,

mid

dle

and

low

er le

vels

dur

ing

win

ter.


Moreover, we include the effect of current by wind waves in this model because the currentby wind waves is expected to play a very important role in the transport and sedimentationprocesses of suspended matter in the shallow Yellow and East China Seas especially duringwinter.

In this paper, we consider the transport and sedimentation of suspended matter only in winterbecause the height of wind waves becomes the largest due to the strong northwesterly monsoon,and the resuspension or re-movement of settled suspended matter is considered to be the mostactive in winter in one-year. The interpolated sea surface wind in the Yellow Sea and the EastChina Sea in winter from Na et al. (1992) and the estimated significant wave height, period andlength on the basis of the fetch and wind speed from Wilson’s formula (Wilson, 1965) are shownin Figs. 4(a) and (b). Big waves with the significant wave height of 2–3 m, wave length of 60–90 m and wave period of 6–8 seconds develop in the southern part of the East China Sea.

2.2 Sedimentation processSuspended matter supplied from rivers is transported by the residual flow in the long term,

sinks downward and settles at some point of the sea bottom. Some suspended matter depositsthere and other suspended matter resuspends and moves again.

The Euler-Lagrange method is used to track the movement of suspended matter in thisnumerical model. The position of suspended matter Xn+1(xn+1, yn+1, zn+1) at time n + 1, which wasXn(xn, yn, zn) at time n, can be calculated by the following equation:

Xn+1 = Xn + V∆t + ∇ V( )V∆t2 + ws∆t + R 1( )

where V denotes the three-dimensional velocity vector of residual flow; ∆t, the time step; ∇ ,horizontal gradient; ws, the sinking velocity of suspended matter by the Stokes law;

ws = −2g ρp −ρw( )

9νr2 2( )

where g (=980 cm s–2) denotes the gravitational acceleration; ρp, density of suspended matter; ρw,density of sea water; ν (=0.0115 cm2s–1), viscosity of sea water; r, diameter of suspended matter.R is the dispersion due to the turbulence and is given by the following equation,

Rx and Ry = γ 2∆tDh( )1/ 2

Rz = γ 2∆tDv( )1/ 2

3( )

where γ is the normal random number whose average is zero and whose standard deviation is1.0. Dh and Dv are the horizontal and vertical dispersion coefficient and they depend on the M2

tidal current amplitude as follows;

Dh = 3000 ×Vamp2

Dv = 0.015 ×Vamp2

. 4( )


(a)


(b)

Fig

. 4.

Inte

rpol

ated

sea

sur

face

win

d in

win

ter (

a) a

nd th

e es

tim

ated

sig

nifi

cant

wav

e he

ight

, wav

e le

ngth

and

wav

e pe

riod

(b)

.


Here Vamp denotes the amplitude of M2 tidal current. Dh ranges between 105–107 cm2s–1 and Dv

between 10–103 cm2s–1 in the calculated area. When the suspended matter reaches the sea bottom,we judge whether it stops moving or removes by applying the critical tractive force theory(Tsubaki, 1974);

F = ρw

2CtUb

2 π4

r2

R = π6

r3 ρp −ρw( )Csg

5( )

where F denotes the tractive force; R, the resistance force; Ct (=0.4), the drag coefficient ofsuspended matter; Cs (=1.0), the static friction coefficient of suspended matter; Ub, the velocityjust above the sea bed. We assume that the velocity just above the sea bottom is 0.1 times thecalculated velocity in the lowest layer of the numerical model and it is given by the followingformula;

Ub = 0.1× Ut +Ur cos B( ) +Uwave . 6( )

Here Ut denotes the calculated M2 tidal current amplitude; Ur, the calculated residual flow ve-locity; B, the angle between the main axis of tidal current and the direction of residual flow; Uwave,the water velocity due to wind wave and it is given by the following formula on the basis of smallamplitude wave theory;

Uwave = HwavegT

2L cosh 2πH / L( )7( )

where H denotes the water depth and Hwave, T and L the significant wave height, wave period andwave length, respectively. The significant wave length depends on the water depth and thesignificant wave period and it is calculated as follows;

L = gT 2

2tanh 2

H

gT 2

1/ 2

1+ H

gT 2

1/ 2

. 8( )

The significant wave height and wave period in the Yellow Sea and the East China Sea arecalculated on the basis of the interpolated sea surface wind pattern shown in Fig. 4(a) and theyare shown in Fig. 4(b).

When R is larger than F, the suspended matter stops moving and deposits to the positionwhere the suspended matter reaches the sea bottom and when F is larger than R, it removes fromits position. When the suspended matter crosses the open boundary of this model we pick it up.

The loads of suspended matter from the Huanghe and the Changjiang are 1,100 × 106

tons year–1 and 480 × 106 tons year–1, respectively (Gao et al., 1992). Moreover, much suspendedmatter is supplied only in winter by the erosion of settled surface bottom sediment at the old river


Fig. 5. Small sized 100 (a) and 200 (b) particles injected from the river mouth of this model. Middle andlarge sized particles have the similar distributions of density and size to these ones.

mouth of the Huanghe, which is situated south of Shandong Peninsula as shown in Fig. 1, andits load is nearly the same as that from the Changjiang (Milliman et al., 1985; Saito et al., 1994).Such fact means that the origin of suspended matter in the Yellow Sea and the East China Seaare three in winter, i.e. the present river mouths of the Huanghe and the Changjiang and the oldriver mouth of the Huanghe. Schubel et al. (1984) reported the variations in the grain size anddensity of the suspended matters which were supplied from rivers entering into the Yellow Seaand the East China Sea. On the basis of their results, three kinds of particles (small, middle andlarge) are injected from three origins of this numerical model. Small sized particles (fine silt)have the modal grain size of 8 µm with the standard deviation of 1 µm, middle sized particles(medium silt) the modal grain size of 30 µm with the standard deviation of 1 µm and large sizedparticles (coarse silt) the modal grain size of 50 µm with the standard deviation of 1 µm. Threekinds of particles have the same density distribution, that is, the modal density of 2.5 g cm–3 andthe standard deviation of 0.1 g cm–3. Three kinds of particles have the similar distributions ofdensity and diameter because they are decided with the use of random number as shown in Fig.5. Three kinds of 200 particles (total 600 particles) are injected from the present mouth of theHuanghe and three kinds of 100 particles (total 300) from the old river mouth of the Huanghe andfrom the Changjiang. The difference in number of injected particles among three origins isresulted from the difference of suspended matter load from each origin (Saito et al., 1994).

3. ResultsThe results of transport and sedimentation of suspended particles injected from three origins

are shown in Figs. 6(a), (b) and (c), respectively. Suspended particles from the present mouth ofthe Huanghe quickly deposit to the sea bottom of the Bohai Sea. Most of small sized particlesdeposit within 10 days or one month and most of the middle and large sized particles, within one-day and they do not move again. Such results are due to small velocities of tidal current and


current by wind waves in the Bohai Sea, which will be discussed in detail later.On the other hand, suspended particles supplied from the old river mouth of the Huanghe are

dispersed in the whole area of the Yellow Sea and the East China Sea as shown in Fig. 6(b).Number in the parenthesis in Figs. 6(b) and (c) denotes the number of suspended particles whichgo out through the open boundary of this model. Small sized particles deposit in the northern partof the Yellow Sea within 3 years after the injection and east of Cheju Island within 5 years after

(a)

Fig. 6. Results of the calculation. Large open circle denotes the injection point, cross mark the depositedparticle and small circle the moving particle. Number shows the total number of deposited particlesand that in the parenthesis particles which go out through the open boundaries.


(b)

Fig. 6. (continued).


(c)

Fig. 6. (continued).


Fig. 7. Summation of deposited particles injected from three origins shown by large open circles.

the injection but many small sized particles do not deposit and continue to move even 5 years afterthe injection. In here, 5 years in the model means 5 times 3 winter months because the wintercondition of 3 months continues in this numerical experiment. Middle sized particles deposit inthe western part of the Yellow Sea within 1 year, south of Cheju Island within 3 or 5 years afterthe injection. Large sized particles deposit in the southern part of the Yellow Sea and in theeastern part of the East China Sea within 3 or 5 years after the injection.

A part of small sized particles supplied from the Changjiang deposit in the northern part ofthe Yellow Sea and east of Cheju Island within 5 years after the injection as shown in Fig. 6(c).Middle and large sized particles mainly deposit in the southern parts of the Yellow Sea and southof Cheju Island.

The horizontal distribution of total deposited particles supplied from three origins, i.e. thepresent and old river mouths of the Huanghe and from the river mouth of the Changjiang, whichis obtained by the summation of Figs. 6(a), (b) and (c) is shown in Fig. 7. 947 among 1200 injectedparticles (79%) deposit there within 5 years after the injection. The observed distribution ofsurface bottom sediment is shown in Fig. 8 (Saito and Yang, 1993). The present sedimentationis carried out in the silt or clay regions but there is no sedimentation at present in the sand regionin Fig. 8. The calculated regions of deposited particles in Fig. 7, that is, the Bohai Sea, the centralpart of the Yellow Sea and the south of Cheju Island, well coincide with the silt or clay regionsin Fig. 8 except for the offshore area of the southeastern coast of China. Such results suggest thatour numerical experiment is qualitatively reliable except for the offshore area of the southeasterncoast of China.


4. DiscussionsThe comparisons of the tractive force and the resistance force for small, middle and large

sized particles are shown in Fig. 9. Settled suspended particles can deposit in the shadow regionwhere the resistance force is larger than the tractive force but they cannot deposit in the whiteregion where the tractive force is larger than the resistance force. The suspended particles cannotdeposit in the offshore area of the southeastern coast of China because the bottom current due towind waves is large in this model. On the other hand, the silt or clay regions are distributed onthe sea bottom there from the field observation as shown in Fig. 8. One possibility of this

Fig. 8. Observed surface bottom sediment (Saito and Yang, 1994).


Fig

. 9.

Com

pari

son

of tr

acti

ve a

nd re

sist

ance

forc

es. S

hado

w re

gion

sho

ws

the

area

whe

re th

e re

sist

ance

forc

e is

larg

er th

an th

e tr

acti

ve f

orce

and

the

whi

te a

rea

the

oppo

site

cas

e.


discrepancy is that the intermittent large supply of suspended matter from the Changjiang dueto flood during summer may play an important role in the transport and sedimentation processesin the offshore area of the southeastern coast of China. For example, McKee et al. (1983) foundthat the deposition rate of suspended sediment near the river mouth of the Changjiang was veryhigh, that was 4.4 cm/month, in summer of flood season.

We only treat the steady supply of suspended matter from rivers during winter in this modelbut we may have to consider the intermittent large supply of suspended matter during summerin order to examine the transport and sedimentation processes in the offshore area of the southeastcoast of China.

In any case, we will proceed with our investigation and solve the problem of discrepancybetween our calculated result and the observational result in the offshore area of the southeastcoast of China in the near future.

AcknowledgementsThe authors express their sincere thanks to Dr. H. Takeoka of Ehime University and Dr. Y.

Saito of the Geological Survey of Japan for their fruitful discussions. This study was a part ofMASFLEX Project sponsored by the Science and Technology Agency of Japan.

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