Journal of Oceanography
Vol. 51, pp. 537 to 552. 1995
A Numerical Experiment on the Sedimentation Processes
in 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 (Yellow
River) and the Changjiang are investigated with the use of a three-dimensional
numerical model of the Yellow Sea and the East China Sea which includes the tidal
current, residual flow and wind waves. Suspended matter supplied from the
Huanghe mainly deposits in the Bohai Sea and that from the old river mouth of the
Huanghe and from the Changjiang in the central part of the Yellow Sea or south
of Cheju Island. The calculated results well reproduce the observed sedimentation
pattern qualitatively except for the offshore area of the southeastern coast of
China.
1. Introduction
Much 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 the
current by wind waves in the Yellow Sea and the East China Sea (Fig. 1). The transport and
deposition processes of suspended matter supplied from the Huanghe and the Changjiang have
been investigated near the river mouth (e.g. Milliman et al., 1984; Schubel et al., 1984; Wright
et 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) have
been investigated. However, the dynamical transport and sedimentation processes of suspended
matter 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 and
sedimentation processes of suspended matter supplied from the Huanghe and the Changjiang
with the use of a three-dimensional numerical model of the Yellow Sea and the East China Sea
which includes the tidal current, residual flow and wind waves.
2. Numerical Model
2.1 Current system
Numerical 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 the
use of a horizontally two-dimensional numerical model and they also calculated the tide-induced
residual current. Yanagi and Takahashi (1993) investigated the seasonal variation of densitydriven and wind-driven currents there with the use of a three-dimensional diagnostic numerical
model which included observed water temperature, salinity and wind data. We combined the
results 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 included
because the M2 tidal current is the most dominant in the Yellow Sea and the East China Sea
538
T. Yanagi and K. Inoue
Fig. 1. The Yellow Sea and the East China Sea. Numbers show the depth in meter.
(Yanagi and Inoue, 1994). The M2 tidal current has a barotropic character, that is, its speed and
direction are the same in the vertical direction. The amplitude of M2 tidal current is large and
nearly 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-induced
residual current due to M2 tidal current (Yanagi and Inoue, 1994), density-driven and winddriven currents which were obtained by Yanagi and Takahashi (1993). The residual flows in the
upper (0–20 m), middle (20–60 m) and lower (60 m–bottom) layers during winter of this model
is shown in Fig. 3. A clockwise circulation with a speed of about 2–3 cm s–1 develops from the
surface to the bottom in the Yellow Sea. On the other hand, a counter-clockwise circulation with
a speed of about 2–3 cm s–1 exists in the upper and middle layers of the East China Sea.
Fig. 2. M2 tidal current at the time of maximum flood maximum ebb and at the mouth of Changjiang, and
the co-tidal and co-amplitude charts of M2 tidal current (Yanagi and Inoue, 1994).
A Numerical Experiment on the Sedimentation Processes in the Yellow Sea and the East China Sea
539
Fig. 3. Residual flows in the upper, middle and lower levels during winter.
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T. Yanagi and K. Inoue
A Numerical Experiment on the Sedimentation Processes in the Yellow Sea and the East China Sea
541
Moreover, we include the effect of current by wind waves in this model because the current
by wind waves is expected to play a very important role in the transport and sedimentation
processes of suspended matter in the shallow Yellow and East China Seas especially during
winter.
In this paper, we consider the transport and sedimentation of suspended matter only in winter
because 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 most
active in winter in one-year. The interpolated sea surface wind in the Yellow Sea and the East
China Sea in winter from Na et al. (1992) and the estimated significant wave height, period and
length on the basis of the fetch and wind speed from Wilson’s formula (Wilson, 1965) are shown
in 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 process
Suspended 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 deposits
there and other suspended matter resuspends and moves again.
The Euler-Lagrange method is used to track the movement of suspended matter in this
numerical model. The position of suspended matter Xn+1(xn+1, yn+1, zn+1) at time n + 1, which was
Xn (xn, yn , zn ) at time n, can be calculated by the following equation:
Xn +1 = Xn + V∆t + (∇V )V∆t 2 + 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 ρ p − ρ w
9ν
)r
(2 )
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 is
1.0. Dh and Dv are the horizontal and vertical dispersion coefficient and they depend on the M2
tidal current amplitude as follows;
2

Dh = 3000 × Vamp
.
2 
Dv = 0.015 × Vamp

( 4)
T. Yanagi and K. Inoue
(a)
542
Fig. 4. Interpolated sea surface wind in winter (a) and the estimated significant wave height, wave length
and wave period (b).
(b)
A Numerical Experiment on the Sedimentation Processes in the Yellow Sea and the East China Sea
543
544
T. Yanagi and K. Inoue
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);
ρw
π

CtUb2 r 2

2
4

π
R = r 3 ρ p − ρ w Cs g 

6
F=
(
)
(5)
where F denotes the tractive force; R, the resistance force; Ct (=0.4), the drag coefficient of
suspended matter; Cs (=1.0), the static friction coefficient of suspended matter; Ub , the velocity
just above the sea bed. We assume that the velocity just above the sea bottom is 0.1 times the
calculated velocity in the lowest layer of the numerical model and it is given by the following
formula;
Ub = 0.1 × (Ut + Ur cos B) + Uwave .
(6)
Here Ut denotes the calculated M2 tidal current amplitude; Ur, the calculated residual flow velocity; 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 small
amplitude wave theory;
Uwave =
Hwave gT
2L cosh(2 π H / L )
( 7)
where H denotes the water depth and Hwave , T and L the significant wave height, wave period and
wave length, respectively. The significant wave length depends on the water depth and the
significant wave period and it is calculated as follows;
  H  1/ 2   H  1/ 2  
gT 2
L=
tanh  2 2   1 +  2    .
  gT    gT   
2


( 8)
The significant wave height and wave period in the Yellow Sea and the East China Sea are
calculated on the basis of the interpolated sea surface wind pattern shown in Fig. 4(a) and they
are shown in Fig. 4(b).
When R is larger than F, the suspended matter stops moving and deposits to the position
where the suspended matter reaches the sea bottom and when F is larger than R, it removes from
its 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 suspended
matter is supplied only in winter by the erosion of settled surface bottom sediment at the old river
A Numerical Experiment on the Sedimentation Processes in the Yellow Sea and the East China Sea
545
Fig. 5. Small sized 100 (a) and 200 (b) particles injected from the river mouth of this model. Middle and
large 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, and
its 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 Sea
are three in winter, i.e. the present river mouths of the Huanghe and the Changjiang and the old
river mouth of the Huanghe. Schubel et al. (1984) reported the variations in the grain size and
density of the suspended matters which were supplied from rivers entering into the Yellow Sea
and the East China Sea. On the basis of their results, three kinds of particles (small, middle and
large) 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 sized
particles (coarse silt) the modal grain size of 50 µm with the standard deviation of 1 µm. Three
kinds of particles have the same density distribution, that is, the modal density of 2.5 g cm–3 and
the standard deviation of 0.1 g cm–3. Three kinds of particles have the similar distributions of
density 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 the
Huanghe and three kinds of 100 particles (total 300) from the old river mouth of the Huanghe and
from the Changjiang. The difference in number of injected particles among three origins is
resulted from the difference of suspended matter load from each origin (Saito et al., 1994).
3. Results
The 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 of
the Huanghe quickly deposit to the sea bottom of the Bohai Sea. Most of small sized particles
deposit within 10 days or one month and most of the middle and large sized particles, within oneday and they do not move again. Such results are due to small velocities of tidal current and
546
T. Yanagi and K. Inoue
(a)
Fig. 6. Results of the calculation. Large open circle denotes the injection point, cross mark the deposited
particle and small circle the moving particle. Number shows the total number of deposited particles
and that in the parenthesis particles which go out through the open boundaries.
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 which
go out through the open boundary of this model. Small sized particles deposit in the northern part
of the Yellow Sea within 3 years after the injection and east of Cheju Island within 5 years after
A Numerical Experiment on the Sedimentation Processes in the Yellow Sea and the East China Sea
(b)
Fig. 6. (continued).
547
548
T. Yanagi and K. Inoue
(c)
Fig. 6. (continued).
A Numerical Experiment on the Sedimentation Processes in the Yellow Sea and the East China Sea
549
the injection but many small sized particles do not deposit and continue to move even 5 years after
the injection. In here, 5 years in the model means 5 times 3 winter months because the winter
condition of 3 months continues in this numerical experiment. Middle sized particles deposit in
the western part of the Yellow Sea within 1 year, south of Cheju Island within 3 or 5 years after
the injection. Large sized particles deposit in the southern part of the Yellow Sea and in the
eastern 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 of
the 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 south
of Cheju Island.
The horizontal distribution of total deposited particles supplied from three origins, i.e. the
present and old river mouths of the Huanghe and from the river mouth of the Changjiang, which
is obtained by the summation of Figs. 6(a), (b) and (c) is shown in Fig. 7. 947 among 1200 injected
particles (79%) deposit there within 5 years after the injection. The observed distribution of
surface bottom sediment is shown in Fig. 8 (Saito and Yang, 1993). The present sedimentation
is carried out in the silt or clay regions but there is no sedimentation at present in the sand region
in Fig. 8. The calculated regions of deposited particles in Fig. 7, that is, the Bohai Sea, the central
part of the Yellow Sea and the south of Cheju Island, well coincide with the silt or clay regions
in Fig. 8 except for the offshore area of the southeastern coast of China. Such results suggest that
our numerical experiment is qualitatively reliable except for the offshore area of the southeastern
coast of China.
Fig. 7. Summation of deposited particles injected from three origins shown by large open circles.
550
T. Yanagi and K. Inoue
Fig. 8. Observed surface bottom sediment (Saito and Yang, 1994).
4. Discussions
The 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 region
where the resistance force is larger than the tractive force but they cannot deposit in the white
region where the tractive force is larger than the resistance force. The suspended particles cannot
deposit in the offshore area of the southeastern coast of China because the bottom current due to
wind waves is large in this model. On the other hand, the silt or clay regions are distributed on
the sea bottom there from the field observation as shown in Fig. 8. One possibility of this
Fig. 9. Comparison of tractive and resistance forces. Shadow region shows the area where the resistance
force is larger than the tractive force and the white area the opposite case.
A Numerical Experiment on the Sedimentation Processes in the Yellow Sea and the East China Sea
551
552
T. Yanagi and K. Inoue
discrepancy is that the intermittent large supply of suspended matter from the Changjiang due
to flood during summer may play an important role in the transport and sedimentation processes
in the offshore area of the southeastern coast of China. For example, McKee et al. (1983) found
that the deposition rate of suspended sediment near the river mouth of the Changjiang was very
high, 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 model
but we may have to consider the intermittent large supply of suspended matter during summer
in order to examine the transport and sedimentation processes in the offshore area of the southeast
coast of China.
In any case, we will proceed with our investigation and solve the problem of discrepancy
between our calculated result and the observational result in the offshore area of the southeast
coast of China in the near future.
Acknowledgements
The 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 of
MASFLEX Project sponsored by the Science and Technology Agency of Japan.
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