Coastal Dynamics 2009
Paper No.67

SEDIMENT MOVEMENT UNDER COMBINED WAVES, TIDE AND RIVER DISCHARGE IN A
RIVER MOUTH
Xiaojing Niu 1, 2, Satoshi Ueyama1, Shinji Sato1, Yoshimitsu Tajima1 and Haijiang Liu1
Abstract
Sediment movement around the river mouth is intensive and complicated, owing to the combined effects of shortwaves, long waves, tide currents and river discharge, which usually leads to great and frequent topography change.
This study aims to describe the sediment movement in a river mouth, further to distinguish the contribution of eachhydrodynamic component to sediment movement, and to get better understanding on the nonlinear effects to sedimenttransport and their interactions. A numerical model was developed to simulate the hydrodynamic environment and the
movement of color sand tracers. Both field survey and numerical modeling were carried out around the Magome Rivermouth, which is located on the Enshu Coast, Shizuoka Prefecture, Japan and drains into the Pacific Ocean.
Key words: sediment transport, wave-current interaction, color sand tracking, river mouth

1. Introduction
Sediment movement around the river mouth is of great importance for estuary environment and of great
influence on human being. Sediment accumulation at the river mouth caused by the intensive andcomplicated sediment movement may greatly reduce the discharge capability of the river and results inserious flood hazard. At some large river mouths, people are suffering from endless dredging to keep
enough water depth for shipping. According to some previous investigations (Tajima et al., 2008), sediment
movement could cause great topography change in a couple of days under some extreme conditions, suchas storm, flood etc. The primary objective of this study is to develop a model that can simulate thesediment movement in such complicated situations.

ShizuokaPrefecture
JAPAN

Magome River
N

Tenryu River

Nakatajima
Sand Dune

Enshu Coast

1 km

Figure 1. Location of the Magome River
The Magome River mouth studied in this paper is a reconstructed river mouth. In the past, thedownstream area of the river often suffered from flood because of the sinuousness and frequent changing
of the river mouth. In 1964, a double guide jetty was constructed to fix the river mouth, in order to enhancethe discharge capability of the river. It has been proved to be an efficient method to solve the flood problem.
However, the problem of shoreline retreat around this area emerged recently and became more and moresignificant after the construction of several dams along the Tenryu River, which is the main sediment1

Department of Civil Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
nxj@coastal.t.u-tokyo.ac.jp
2
Department of hydraulic Engineering, Tsinghua University, Beijing 100084, China.

1Coastal Dynamics 2009
Paper No.67
source for the Enshu Coast. The Tenryu River is located about 4km to the east of the Magome River mouth.
The decrease of sediment supply to this area resulted in abrupt shoreline retreat. Especially, the Nakatajima
sand dune on the west of the Magome River has been greatly eroded, because the jetty at the Magome
River mouth seems to block the westward longshore sediment transport from the Tenryu River mouth. To
maintain the sand dune, sand from other place is carried to the Nakatajima sand dune now. However, it’s atime-consuming and high-cost project. If some sediment inside the river mouth could be taken to the
Nakatajima sand dune by natural processes, then we might find out a much more feasible and efficient way
to maintain the sand dune. Therefore, the investigation on hydrodynamic environment and sediment
movement in this river mouth is required.
In most cases, the jetty at the river mouth can intercept the estuary turbidity belt and let tide bring clear
water upstream into river mouth. But in case of storm, a large amount of sediment can be brought from
offshore into the river mouth basin (Hiramatsu et al., 2008). The hydrodynamic condition in the rivermouth is rather complex. Beside tide current and river discharge, there is also a sewage flow draining into
the basin. Waves inside the river mouth are also significant, especially when incident wave direction isparallel to the jetty. Topography inside the river mouth might be modified greatly and frequently, due to thecomplex hydrodynamic environment and the intensive sediment movement.
To capture the feature of sediment movement inside the Magome River mouth, sediment movement istracked by using different kinds of color sand as tracers, which is a common method adopted in fieldsurvey. From field survey we can quantify the color sand content in each sampling point after a certain
period and estimate the speed and the amount of sediment movement. However, it’s a rather arduous work
to take lots of the samples. By numerical modeling we can look into the detail of sediment movement inany time and any place.
In this paper, a field survey in the Magome River mouth is introduced firstly. Then an associatednumerical modeling for the river month is described. Finally, the model is applied to the Magome Rivermouth, and compared with the observation data of field survey. The results of simulation agree with theresults of field survey reasonably, and several observed phenomena are demonstrated by numericalsimulation.
2. Field survey
Field survey in the Magome River mouth was carried out in 2008. Flow velocities and wave height were
measured on Sep13th -14th during the spring tide. Two kinds of color sands were placed inside the rivermouth basin in order to trace the sediment movement.

Figure 2. Magome river mouth and the setup of the field survey
2.1. Measurement of the hydrodynamic factors
Flow velocities were measured at the three points marked with squares, shown in Figure 2. Velocity meters‘V1’ and ‘V2’ were electromagnetic flow meters, installed upstream and inside the river basin respectively.
Velocity meter ‘V3’ at the right bank of outlet was an acoustic Doppler current meter.

2

Coastal Dynamics 2009
Paper No.67
Water surface elevations were recorded by wave gauges at the three points marked with triangles,
shown in figure 2. Wave gauge ‘H3’ was installed near the left bank at the seaward end of the outlet, wave
gauge ‘H2’ was installed near the right bank where the outlet becomes wide, and wave gauge ‘H1’ wasinstalled furthest inside the river mouth. Wave parameters were obtained from the FFT (the Fast Fourier
Transform) analysis.

(a) Sep 14th(b) Sep 22th(c) Sep 29th(d) Oct 13th(e) Nov 8th(f) Dec 12th

Figure 3. Spatial distribution of blue sand(a) Sep 14th(b) Sep 22th(c) Sep 29th(d) Oct 13th(e) Nov 8th(f) Dec 12th

Figure 4. Spatial distribution of yellow sand3

Coastal Dynamics 2009
Paper No.67

2.2. Tracing the color sandTwo kinds of color sand were placed at the blue and yellow points illustrated in Figure 2 during low tide on
Sep 13th 2008. The blue sand was placed near the left bank where the sewage drains into river mouth. The
yellow sand was placed upstream at the edge of shoal which emerged during the low tide. The amount of
injected color sand is about 500kg respectively, and the diameter of color sand is similar to that of local
sand, around 0.2mm to 0.4mm. In the following two days, we collected sand samples inside the rivermouth hourly. Subsequently, we continued surface sediment sampling during the low tide once in two
weeks for three months.
Color sand content in the collected sample was counted by an automated counting machine, whichtakes sand sample image and recognizes color sand particles by image analysis. Then we obtained thespatial distribution of the color sand after one day, one week, two weeks, one month, two mouths and threemouths, as shown in Figure 3 and Figure 4. The larger mark represents more color sand had been found in
the sample. Some blue sand had been found upstream and along the sewage flow. At first only a few yellow
sand particles were found in the samples, and after several weeks some had been found scattered in the
shoal area.
3. Numerical model
A numerical model for the sediment movement in the river mouth has been developed, which includes
three associated parts to deal with current, waves and sediment particles movement respectively. These
three parts are named as current module, wave module and sediment movement module respectively. Shortwaves are estimated based on the spectral action balance equation with the effect of current. The nonlinear
shallow water equation is then applied to calculate the flow due to tide, river discharge, and long waves.
Radiation stress is included to consider the effect from short waves. Following Tajima et al.(2007), themovement of sediment particles is associated with the bottom shear stress under combined waves-current
field.
3.1. Current module
Based on the shallow water assumption, the governing equations of current are expressed in the Cartesian
coordinates as follows.
∂η ∂p ∂q
+
+
=
0
(1)
∂t ∂x ∂y∂p ∂  p 2  ∂  pq ∂η τ bcx+ +− M x + Rx =0+  + gh∂t ∂x  h  ∂y  h 
∂x
ρ

(2)

∂q ∂  pq  ∂  q 2 ∂η τ bcy+ +− M y + Ry =0
 +   + gh∂t ∂x  h  ∂y  h 
∂y
ρ

(3)

where η is the surface elevation; p and q are the flux per unit width in x and y direction; h is the total water
depth, h= d + η , here d is the still water depth; g is the gravity acceleration; ρ is the water density. τ bcx
and τ bcy are the bottom shear stresses due to mean current component in x and y direction, considering as
the summation of the skin friction under combined wave-current field and the form drag due to sand ripples.
The skin friction for current is estimated by Madsen’s (1994) boundary layer model. Mx and My represent
the diffusion term, ∂  ∂  p  ∂  ∂  p  (4)=
M x h  ve    + ve     ∂x  ∂x  h   ∂y  ∂y  h    ∂  ∂  q  ∂  ∂  q  (5)=
M y h  ve    + ve     ∂x  ∂x  h   ∂y  ∂y  h   Here, ν e is the eddy viscosity. Rx and Ry represent the force due to wave motion, expressed by4

Coastal Dynamics 2009
Paper No.67=
Rx

1  ∂S xx ∂S xy +ρ  ∂x∂y (6)1  ∂S yx ∂S yy +ρ  ∂x∂y Here, S xx , S xy , S yy are wave radiation stress components, determined by
=
Ry

1

S xx = E  n (1 + cos 2 θ ) − 
2

1

S yy = E  n (1 + sin 2 θ ) − 2S xy = En sin θ cos θ

(7)

(8)
(9)
(10)

1
2kh 
1
n
ρ gH 2 ;=1 + is the shallowness
2  sinh 2kh 
8parameter. And H is the wave height; k is the magnitude of wave number; h is the water depth. Wave height,
wave direction, period can be estimated by the wave module.
Governing equations are discretized in a staggered mesh by finite volume method, and the discrete
equations are solved by ADI (Alternating Direction Implicit) method. This numerical scheme has been
proved efficient and of good stability.

Here, θ is the wave angle; E is the wave energy flux, E =3.2 Wave module
A steady spectral action balance equation is applied to model the random waves, which is expressed asfollows.
∂cx N ∂c y N ∂cθ Nκ ∂ 
∂N  1∂2 N 
2
2
(11)
cos
cos
+
+
=
−ε b N +
CC
θ
−
CC
θ
  g


g
∂x
∂y
∂θ
2σ  ∂y ∂y  2∂y 2 
where N is the wave action, N ( x, y, θ , f ) = E σ ; θ is the wave angle. The second term at right side is thediffraction effect proposed by Mase (2001) and Mase et al.(2004). Here, C is the wave phase velocity, Cg is
the wave group velocity, κ is a coefficient, κ = 2.5 was adopted by Mase (2001) .
The characteristic velocities cx, cy and cθ are defined as follows, considering the effect of current.
(12)=
cx Cg cos θ + U=
c y Cg sin θ + V

(13)

σ

 ∂h

∂h
 sin θ − cos θ ∂ysinh 2kh  ∂x

(14)
 ∂U

 ∂V

∂U
∂V
+
sin θ −cos θ  cos θ + 
sin θ −cos θ  sin θ
∂y
∂y
 ∂x

 ∂x

Here, U and V are the velocity in x and y direction respectively. σ is the intrinsic wave frequency; ω isthe absolute frequency relative to a stationary observer, which has a Doppler shift to the intrinsic wave
frequency. The dispersion relation of waves with uniform current is expressed as(15)σ=ω − k (U cos θ + V sin θ )
cθ
=

(16)
σ 2 = gk tanh kh
In equation (11), ε b is the coefficient of wave energy dissipation. The energy dissipation can be

estimated by Tajima & Madsen’s (2006) model.
Kb
N
Cg exp ( −ξb 2 )  Etotal (1 + ξb 2 ) − Er  ⋅
=
εb N
h
E

(17)

total

where

ξb =

Hb
H rms

(18)

5

Coastal Dynamics 2009
Paper No.67

 5 γ s 2 tan β, 2 γ 2 − γ r2
Kb =  s5γ ,16 rγ=γ r + 4 tan βsγ r = 0.3

ξb =
Er =

tan β > 0(19)tan β ≤ 0
(20)
(21)

Hb
H rms

ρ g (γ r h )

(22)
2

(23)

8
And the breaking wave height Hb is estimated by1.5h  
kb H bh (24)=1.07 − 0.59 exp  −8.6 b  + 2.59 tan β 0 exp  −15.1 b  tanh kb hb
L0 
L0  

The incident wave is random in terms of both frequency and direction. The incident wave spectrum isgenerally expressed as the product of frequency spectrum and directional spreading function. The
Bretschneider-Mitsuyasu type frequency spectrum and the Mitsuyasu type directional spreading function
are used.
Governing equations are discretized by finite difference method. Considering waves are mainly
propagating in x direction, x directional derivative is approximated by explicit difference, and y directional
derivative and θ directional derivative are approximated by implicit difference. In this way, wave height
can be calculated step by step in x direction from offshore to onshore, and in each step wave spectrum is
calculated implicitly. This method is economical in memory and effective unless the wave direction departfar from x direction.

3.3 Sediment movement module
At first, sediment particles are assumed moving with the same velocity as currents if the local Shields
number is larger than the criterion for general movement. Using this assumption, the speed of sediment
movement was overestimated comparing with the field observation. Afterward, the model proposed by
Tajima et al. (2007) was applied with certain modifications. In their model, the movement of each sedimentparticle includes two components, a mean movement and a random walk.

 

(25)
xit +∆t = xit + us ,i ∆t + ri

 t + ∆t  twhere xi , xi are the location of i-th sediment particle at time t and t + ∆t ; us ,i is the mean velocity ofsediment movement and ri is the random walk step for one time step.
Tajima’s model followed Madsen’s (1991) bedload sediment transport model and presented theinstantaneous velocity of the moving particles, us , which is determined as a function of bottom shear stress,

τb .


  τ b′  τ b′(26)=
us max α 
− β s u*cr  , 0    ρ u*m
  τ b′
where u*cr is the critical bottom shear velocity corresponding to the shear stress just enough to initiate themovement of sand particle on a horizontal plane bed, u*m is the maximum shear velocity under wavecurrent coexisting field, α (=3.3) is a constant and β s is a coefficient accounting for the influence of thebottom slope.
1

1
2
(27)
=
β s  cos β (1 + tan β tan φm ) 2Here, β is the bottom slope in the flow direction and φm is the friction angle of moving sand grain.
The instantaneous bottom shear stress is expressed as a vector summation of two components due tomean current and waves.

6

Coastal Dynamics 2009
Paper No.67

f cw

(28)
ρ uwm uw ( t )2Here, τ bc′ is the skin friction shear stress due to mean current, f cw is wave friction factor under wave
current coexisting field. The shear stress τ bc′ and the friction factors f cw are estimated by Madsen’s (1994)

bottom boundary layer model under combined wave-current field. uw ( t ) and uwm are the wave orbital
velocity vector and its amplitude. To consider the nonlinear effect of nearshore wave, the 2nd order Stokes
wave theory was applied to estimate the wave orbital velocity.
To consider the dispersion characteristics of sediment movement, a random component based on
random walk theory is adopted. Tajima et al. (2007) considered that the sediment took a random walk onlyin the mean current direction and in the wave-propagation direction, and suggested two different dispersion
coefficients for wave and current. In their model, the sediment movement was averaged over one wave
period and the time step for calculating sediment movement was larger than several wave periods, so therandom walk in one time step was designed to display the orientation effect of wave oscillating motion andmean current. The present model computes the movement of each particle under wave-current coexisting
oscillating flow and thus already account for dispersive effects due to wave oscillating motion. Therefore,
the random walk in the present model should account for pure dispersive phenomena due to turbulence.
Here, the random walk is assumed to occur in arbitrary direction as follows.
 
(29)
=
r r0 2ε cw ∆twhere r0 is the unit vectors in arbitrary direction randomly with each particle at each computational time
step. And the dispersion coefficient, ε cw is determined by ε cw = κ lu* . Here, κ is the Karman’s constant, l is
length scale of the near-bottom turbulence which is assumed equal to the boundary layer thickness of
combined wave-current field calculated from Madsen’s (1994) model and u* is the bottom shear velocity.
′ τ bc′ +τ=b

4. Observation and model application
4.1 Hydrodynamic factorsy (m)The computational domain is shown in Figure 5. The contour shows the topography of the basin. The
mesh size is 4m in both x and y direction. At landward boundary, x = 0m , a uniform velocity is used in thewhole section, and the measured current velocity at location ‘V1’ is adopted. At seaward boundary,x = 640m , the water level from Omaezaki station, which is located about 45km to east of the Magome
River mouth, is adopted as the boundary of current module. The measured wave height and period at theoutlet of river mouth are used as the seaward boundary for wave module. The discharge of sewage draining
into the basin is considered as a constant value of 1.75m3/s.
250

d (m)
2.5

200

2

150

1.5

100

1

50

0.5

0
0

100

200

300
400
x (m)

500

600

0

Figure 5. Magome River mouth topography

4.1.1 Tide
The calculated water surface elevation at different location is shown in Figure 6(a). Small difference
among each location can be found. It’s obvious that the difference during ebb tide is larger than that during
flood tide. The difference between the most seaward location ‘H1’ and most landward location ‘H3’ isillustrated in Figure 6(b). The solid line shows the numerical result and the dots show the measured data.
The elevation difference of the two meters is estimated as 1.84m, which was added to the measured data.
Tendency between the numerical result and the measurement agrees well.

7

Coastal Dynamics 2009
Paper No.67

0.5

0.1

-0.5

ηH1
ηH3

-1
0

20

10

t (h)

0
calculation
measurement(ηH1-ηH3+1.84)

-0.1
-0.2
10

50

40

30

H3

ηH2

H1

0

η -η (m)

0.2

η (m)

1

15

20

25
t (h)

30

35

40

(a) Water surface elevation(b) Difference between location ‘H1’ and ‘H3’
Figure 6. Water surface elevation
4.1.2. Current
The current in the Magome River mouth contains four components, river discharge, sewage discharge, tideflow and wave induced flow. Figure 7 shows the calculated velocity compared with the measured flow
velocity inside the river basin. Seaward flow during ebb tide is stronger than landward flow during floodtide. The simulated results acceptably agree with the measurements.
1

U (m/s)0.5
0calculated U
calculated V
measured V
measured U

-0.5
-1
0

5

10

15

20
25
t (h)

30

35

40

45

Figure 7. Current velocity inside the river mouth basin
Figure 8 presents the current field at each specified time. Waves induce a circulation in the river basin,
which can be observed when tide current is small, e.g., during low tide and high tide period as illustrated in
Figure 8(a) and (c). A simple average of the current velocity is made during one tide period shown in
Figure 9. The mean current is mainly contributed by the river discharge and the sewage discharge, and aweak circulation can be found near the sewage outlet.
250

250
0.6m/s

150
100

150
100
50

50
0
0

0.6m/s

200
y (m)

y (m)

200

100

200

300
x (m)

400

500

0
0

600

100

(a) Low tide (t = 10h)

400

500

600

(b) Flood tide (t = 14h)
0.1m/s200

0.6m/s

200

150

y (m)

y (m)

300
x (m)

250

250

100

150
100
50

50
0
0

200

100

200

300
x (m)

400

500

0
0

600

(c) High tide (t = 29h)

100

200

300
x (m)

400

(d) Ebb tide (t = 20h)

Figure 8. Current field at each specified time

8

500

600

Coastal Dynamics 2009
Paper No.67

2500.2m/s

y (m)

200
150
100
50
0
0

200

100

300
x (m)

400

500

600

Figure 9. Mean current field during one tide period
4.1.3. Waves
The calculated wave height is compared with the other two measurements inside the river mouth, shown in
Figure 10. Points represent the measurement, lines represent calculation results. Computational results
agree well with the measurement.
0.8

H (m)

0.6
H3

0.4
0.2
0
0

H2
H1

10

5

15

20

25
t (h)

35

30

40

45

50

Figure 10. Wave height at different time

250

250

200

200

150

y (m)

y (m)

Figure 11 shows the distribution of wave inside the river mouth basin, in which the contour shows thewave height and the vectors show the direction of wave. Waves are obviously deflected inside the river
basin due to refraction and diffraction. Figure 11(a) and (b) show the wave height distribution at the hightide and the low tide respectively. Obviously, waves during high tide invade much further inside of theriver basin comparing to that during low tide. It means that waves can reach further upstream which makes
the sediment movement inside river mouth more active, while the water depth is larger.
H (m)

0.5
0.4

150

0.3

100

0.2

50

50

0.1

0
0

0
0

100

100

200

300
x (m)

400

(a) High tide

500

600

100

200

Figure 11. Wave height distribution

300
x (m)

400

500

600

(b) Low tide

Considering that wave period vary due to the effect of current, the intrinsic wave period is calculated
by numerical iteration before using the measured wave data as the seaward boundary. It is also found thatwave height has periodical alteration even when the wave condition is almost uniform at offshore. That is
because waves are affected by the oscillating tidal current in the jetty channel. The present model has thecapability to model the interaction between waves and current. The computation results of a wider
computational domain show clear periodical variation of wave height in the channel of the river mouth, by

9Coastal Dynamics 2009
Paper No.67
using an almost uniform incident wave height, as shown in Figure 12. The dashed line shows the incident
wave height and the solid line shows the calculated wave height in the jetty channel. The observation also
shows a clear tendency that wave height is amplified by the ebb current. Peaks appear in the measured
wave height at the channel around time 20h and 32h without visible peaks of offshore wave height.
1.2
1

H (m)

0.8
0.6
0.4

Measured
Offshore data
Calculated
Offshore input

0.2
0
0

10

20

30

t (h)

40

50

Figure 12. Periodic variation of wave height
4.1.4. Long waves
From the field observation, long wave component inside the river mouth basin was found. Long waves canpropagate further into the shallow area with less energy dissipation. The mean wave height of long wave
components and short wave components is evaluated by spectral analysis. Figure 13 (a) is the result at themost seaward location ‘H3’, and Figure 13 (b) is the result at the most landward location ‘H1’. It showsthat the short waves significantly decay inside the river mouth basin, whereas the long waves survive.
Figure 14 shows the transfer function and the phase lag between velocity and water surface elevation.
The phase lag of high frequency components is around zero, but the lag of low components is around 0.5 π
or -0.5 π . That characteristic of the low frequency indicates the existence of standing wave, which is theresult of interference of the incident wave and the reflected wave due to river bank.
0.4

Transfer function

1

H (m)

0.3
0.2
0.1
0
10

15

20

25
t (h)

30

35

40

0.5

0
-3
10

(a) ‘H3’phase lag (π)

0.3
H (m)

1

Short wave
Long wave

0.2
0.1
15

20

25
t (h)

-1

10

(a) Transfer function

0.4

0
10

-2

10 f (Hz)3035(b) ‘H1’
Figure 13. The long wave component

40

0.5
0
-0.5
-1
-3
10

10

-2

f (Hz)-110(b) Phase lag to velocity
Figure14. Relation between velocity and water surface

A representative wave with the period of 100s is chosen to study the feature of long wave numericallyby shallow water model. A sinusoidal wave with amplitude of 5cm is applied to the seaward boundary.
Figure 15 shows the calculated wave height distribution under the condition that initial water level is 0m
and current is absent. Standing wave characteristic can be clearly found, and this agrees well with theobservation.

10

Coastal Dynamics 2009
Paper No.67
H (m)

250

0.25

y (m)

200

0.2

150

0.15

100

0.1

50

0.05

0

100

200

300
x (m)

400

500

600

Figure 15. Long wave height distribution
4.2 Sediment movement
The color sand movement in the first day of the field measurements was modeled. The number of particles
used in the model is 105 for each color sand, which is large enough to capture the feature of sandmovement. The critical Shields number adopted is 0.06. In order to represent the mixture of surface sandparticles with bed sediments, half of color sand particles is assumed to be moved when the local Shields
number exceeds the critical value. Figure 16 shows the spatial distribution of the color sand by tracing
large number of particles at each specified time. The yellow dots represent yellow sand particles and theblue dots represent blue sand particles.
The blue particles move landwards during flood tide and seawards during ebb tide mainly along theleft bank. Some of blue particles remain at the shoal area after ebb tide, so during low tide there are stillsome particles found landward to the original location of blue sand, as shown in Figure 16(e) and (i). The
sewage flow plays an important role to transport sediment to main flow channel. It is clearly shown in
Figure 16 (f) and (k) that some blue sand particles are transported by the sewage flow. The simulated
sediment movement agrees well with the observation (Figure 3).
The injection location of the blue particles is near the outlet of sewage flow, as shown in Figure 16(a),where water depth is small. Here waves are relatively intensive, as shown in Figure 11, which offer themain driving force of sediment movement. It is known that wave could induce more intensive bottom shear
stress than current, and under the wave condition sediment particles are easy to be picked up. Although theoscillatory wave motion does not induce great net sediment transport, waves still play a very important rolein sediment transport under coexisting field of waves and tide current. Under the imaginary situation
without waves, the numerical result shows that the blue particles barely move.
In contrast, the original location of yellow sand is further close to the river flow route, as shown in
Figure 16(a), where the flow of river and tide is dominant and the effect of waves is weak. At the beginning,
the yellow particles are mainly moving along the main flow channel, where the water depth is relatively
large. The preceding numerical analysis of hydrodynamic environment in the river mouth shows that along
the main flow channel current velocity is large. Consequently sediment particles at main flow channel aredominantly carried by the current and generally tend to move seawards due to the seaward residual current
during one tide period. When the yellow particles move into the contraction part of the jetty, where theeffect of waves becomes notable, sediment would be transported to the shoal area at the left bank by waves
during flood tide and be flushed back to main flow channel during ebb tide, as shown in Figure 16(k) and(l). This is the reason why some yellow particles spread at the shoal. The numerical simulation of yellow
sand movement is therefore reasonable with the observation.
The numerical result also shows that sand particles spread in broader area with time. The simulation is
performed only for one day, so the distribution of color sand is more concentrated. Generally the color
sands will scatter after the longer period as is confirmed in the observed results.
It is noted that some yellow sand is found around its injection location and along the mean flow
channel in the field survey, as shown in Figure 4. Because some color sand particles might be covered by
the bed sand and remain there until the color sand is exposed again on the surface. It means that some color
sand might be found along their tracks. However, in the present model, the topography is assumed to be
fixed, and only the mixing percentage is introduced at 50%. Further improvement is required to include
topography change and parameter tuning for the mixing layer.

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Figure 16. Spatial distribution of color sand12

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5. Conclusion and discussion
Hydrodynamic environment in the Magome River mouth is quite complex owing to the contribution ofwaves, river discharge and tide, as well as a sewage discharge into the river mouth basin. Field survey
inside the Magome River mouth was carried out. Long waves were observed more significantly inside theriver mouth in contrast with short waves. Waves invading through the jetty channel were found to begreatly interacted with the tide current.
A numerical model was developed to simulate the complex hydrodynamic environment, including tidecurrent, river discharge, sewage flow, long waves and short waves. Short waves are estimated by the wave
energy balance, considering the influence of current. All the other components are simulated by the shallow
water equation including the nearshore current induced by shore waves. Reasonable agreement was foundbetween field observation and numerical estimation.
Two kinds of color sand were introduced at two different locations in order to investigate themechanism of sediment movement. By surface sand sampling in the succedent three month, spatial
distributions of color sand inside the river basin were obtained. The sediment movement pattern was
evaluated. A numerical model to track the color sand transport was also applied to reveal detailed featuresof sediment movement in a couple of tide periods. The simulation result reproduced the observed color
sand moving characteristics.
Acknowledgements
This study is a part of Tenryu-Enshu project, “Dynamic sediment management and coastal disasterprevention by advanced technologies”, which is supported by the Special Coordination Funds forpromoting Science and Technology of Ministry of Education, Culture, Sports, Science and Technology.
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