JTM Vol. XVI No. 1/2009
13
NEARSHORE CURRENT STUDY USING A QUASI 3D MODEL;
STUDY CASE : PERAIRAN PANTAI DADAP, INDRAMAYU
Engki A. Kisnarti1, Totok Suprijo
2
Sari
Sebuah model sirkulasi dekat pantai kuasi tiga dimensi, yaitu shorecirc, digunakan dalam studi ini untuk
memahami sirkulasi dekat pantai yang dihasilkan oleh gelombang pecah. Model ini sebelumnya dikembangkan
oleh Putrevu dan Svendsen (1993) di Center for Applied Coastal Research (CACR). Dalam upaya untuk
mengetahui sensitivitas parameter gelombang, yaitu sudut datang, tinggi dan periode gelombang terhadap hasil
perhitungan model berupa kecepatan arus sejajar pantai, maka model diterapkan untuk mensimulasikan arus
sejajar pantai yang terjadi pantai yang lurus dan kontur kedalamannya sejajar dengan garis pantai. Dari tes
sensitivitas ini dapat diketahui bahwa nilai magnitudo arus sejajar pantai akibat adanya gelombang pecah sangat
dipengaruhi oleh nilai sudut datang gelombang ke arah pantai. Secara umum hasil tes sensitivitas parameter
menunjukkan bahwa gelombang pecah yang arah datangnya membentuk sudut terhadap pantai akan
menghasilkan arus sejajar pantai yang magnitudonya lebih besar jika dibandingkan dengan gelombang
pecahyang hampir tegak lurus arah datangnya terhadap garis pantai. Selanjutnya, model kuasi tiga dimensi ini
diterapkan di perairan pantai Dadap yang terletak di Indramayu-Indonesia. Hasil simulasi model arus sejajar
pantai di perairan pantai Dadap selanjutnya diverifikasi dengan data pengukuran. Hasil verifikasi menunjukkan
bahwa hasil simulasi model cukup bersesuain dengan data observasi
Abstract A quasi three-dimensional nearshore circulation model, namely shorecirc, was applied in this study for
understanding nearshore circulation generated by breaking waves. The model was previously developed by
Putrevu and Svendsen (1993) in the Center for Applied Coastal Research (CACR). in order to do a sensitivity test
of wave parameters, i.e. wave breaker angle, height and period, to the magnitude of longshore current velocity, the
model was applied to synthetic, simple and plane beach. From the sensitivity test, it is known that the magnitude
of longshore current is significantly influenced by the wave angle. An Increasing in the breaking wave angle will
produce a bigger magnitude of longshore current than the one that generated breaking wave almost orthogonal to
the shore line. Further, The model was applied to the Dadap coastal waters located in Indramayu- Indonesia.
Model application the Dadap coastal waters is agreed with measurement data.
Keywords: alongshore current, three dimension quasi model.
1) Study Program of Oceanography, FTIK-University of Hang Tuah Surabaya, Indonesia. 2) Study Program of Earth Sains and Technology, FITB- Institute of Technology Bandung, Indonesia.
Email : [email protected]
1. INTRODUCTION
It is well known that nearshore processes
are strongly influenced by the propagation of
surface waves in the surf zone where intense
production of momentum transfer due to wave
breaking takes place. When surface waves
approach the shore obliquely, longshore
currents are generated near the breaker zone
which can cause substantial longshore
sediment transport. The accurate prediction of
longshore current is therefore of particular
importance in understanding nearshore
movement of sedimentary material by bed and
suspended transport mechanism, and hence
long-term morphological change (Fredsoe &
Deigaard, 1992).
At present, two different approaches have
been used for modelling the generation of
longshore currents by obliquely incident
surface waves progressing towards a shoreline
over a sloping beach. On the other hand, the
so-called short wave averaged models, which
are based on the concept of radiation stress
associated with incoming waves (Longuet-
Higgins & Stewart,1964), are characterized by
use of the depth integrated momentum
equations averaged over a short period surface
wave where components of the momentum
flux are separated into the wave-induced part
(i.e. radiation stress) and the depth-integrated
turbulent Reynolds stress.On the other hand,
‘shortwave-resolving’ models, which are
based on Boussinesq or Reynolds-averaged
non-linear shallow-water (NSW) equations,
resolve the short-wave motion during one
wave cycle. Using the radiation stress concept,
Longuet-Higgins (1970a,b) was one of the first
people to give a satisfactory theoretical
explanation of the longshore current
generation. Longuet-Higgins obtained an
analytical solution for the cross-beach profile
of the depth-uniform (time-mean) longshore
current in terms of the basic incoming short
surface-wave parameters. Bowen (1969) and
Thornton (1970) developed similar
expressions. Since the publication of these
pioneering works, progress was subsequently
made addressing and solving the shortcomings
of these earlier models. For example, an
extension of the Longuet-Higgins model to
Engki A. Kisnarti, Totok Suprijo
14
take account of large angles of wave incidence
was given by Liu and Dalrymple (1978). The
effect of lateral mixing on the longshore
current was investigated by Kraus and Sasaki
(1979). Although restricted to the case of a
plane sloping beach and with a substantial
empirical input, these analytical models can be
solved easily and must represent a baseline
against which improved modelling approach
could be judged.
Since then, short-wave-averaged models of
the longshore current have been further
developed and refined to include the case of a
barred beach, more realistic energy dissipation
in the surf zone and random wave incidence
(Wu et al., 1985; Baum & Basco, 1987;
Thornton & Guza, 1986; Wind & Vreugdenhil,
1986; Larson & Kraus, 1991; Church &
Thornton, 1993; Smith et al., 1993). Although
generally giving good predictions for the wave
height and the longshore current when
compared with field and laboratory
measurements, a feature of these models
(based on linear wave theory and the
application of turbulence closure schemes of
varying degrees of sophistication) is that they
are two-dimensional in character since they are
aimed to model the short-wave averaged
circulation. In the context of sediment
transport calculations, these models, in which
the short period surface-wave motion is
assumed known, are unable to represent the
potentially important contribution to the
suspended sediment transport rate that arises
from unsteadiness in the velocity and sediment
concentration fields during one wave cycle.
Similarly, bed load transport calculated by
such models represents only the tendency of
the mean transport because it is the
instantaneous bottom shear stress that
determines the threshold condition for
sediment motion.
More recently, so-called quasi three-
dimensional short-wave-averaged models of
the longshore current have been documented
(De Vriend & Stive, 1987; Svendsen &
Putrevu, 1994). Essentially, this type of
models obtains the three-dimensional short-
wave averaged velocity field without the use of
the fully three-dimensional equations. Garcez
Faria et al. (1996) presented a method of
combining a depth integrated two-dimensional
model with a one dimensional vertical model
to obtain the vertical profile of the longshore
current locally. A similar approach was given
earlier by Van Dongeren et al. (1994) in their
modelling of time-varying near-shore
circulation including the longshore current. In
addition to the necessity of a preliminary
separation of the flow field into wave and
mean components, models based on the
radiation stress approach (including those
referred to above) usually involve a number of
important assumptions some of which may not
be universally valid. For example, the
expression for the components of the radiation
stress, which is derived from small amplitude
non-breaking wave theory, has been extended
into the surf zone where wave height is further
assumed to be linearly related to local water
depth. The need for the prescription of the
position of the breaker line a priori may be
identified as another possible weakness in
these models. As mentioned earlier, short-
wave-resolving models involve solving
Boussinesq or Reynolds-averaged non-linear
shallow-water (NSW) equations so that the
short wave motion during one wave cycle is
modeled directly. This type of model, which
requires large computational time compared
with widely used shortwave-averaged models,
is relatively new and still under development.
The Boussinesq models have been presented
by Madsen et al. (1991), Wei and Kirby (1995)
among others, while the NSW models by
Hibberd and Peregrine (1979), Johns (1980),
Johns and Jefferson (1980), Kobayashi and
Karjadi (1996). Hibberd and Peregrine (1979)
developed a NSW model to describe the
progression of a uniform bore over a beach
towards a shoreline with some success.
However, it is noted that a highly dissipative
Lax-Wendroff scheme was incorporated in
their model in discretising the non-linear
advection terms in order to describe the steep
wave fronts numerically.
In this paper, the authors present an
application of the quasi 3D nearshore
circulation model to the Dadap coastal waters.
The accurate prediction of longshore current in
this area is needed because an existing offshore
harbour has affected sediment transport in this
area. A salient sedimentary has been formed
surrounding the structures, therefore the
longshore current prediction is one of
particular importance in understanding
nearshore movement of sedimentary material
by bed and suspended transport mechanism,
and hence long-term morphological change in
this area.
II. MODEL EQUATIONS
2.1 Basic Equation
The model is based on the depth-integrated
equations which in complete form and in
tensor notation read:
Nearshore Current Study Using a Quasy 3D Model; Study Case: Perairan Pantai Dadap, Indramayu
15
0Q
t x
∂∂+ =
∂ ∂α
α
ζ
(1)
( ) 10
o t
o
d d w d w d
h
s B
o
h
V V dz u V u Vt x h x x
g h S dzx x
ζ ζβ α β
α β α β β α
α α α ζ
ζβ β
αβ αβ
β α
θ θθ
τ τζζ τ
ρ ρ ρ
∂ ∂ ∂ ∂+ + + +
∂ ∂ ∂ ∂
∂ ∂ + + − + + − = ∂ ∂
∫ ∫
∫
(2)
In this formulation the radiation stress
Sαβ is defined as
21( )
2o
w w
w w
h
Q QS p u u dz gh
h
ζα β
αβ αβ α β αβδ ρ δ ρ ρ≡ + − −∫ (3)
2.2 Numerical Solution
In the model, the instantaneous total fluid
velocity ( , , , )ααααu x y z t
is split into three
components:
'α α α αα α α αα α α αα α α α= + += + += + += + +w
u u u V
(4)
where 'ααααu
is turbulent velocity
component, ααααwu
is the wave component
difined so that 0====wu below through level,
and ααααV is the current velocity, which in
general is varying over depth. The overbar
denotes short wave averaging and the
subscripts x and y denote the directions in a
horizontal Cartesian coordinate system.
Figure 1.1. shows the definitions of the
coordinate system and components of
velocities used in the following. Thus ζζζζ
represents the mean surface elevation and 0his
the still water depth. The local water depth i
then determined as
(5)
represents the total volume flux
which is defined by
(6)
and is the volume flux due to the
short wave motion defined by
(7)
Hence we have
(8)
The currents velocity is devined into
a depth uniform part and a depth-varying
part by:
(9)
where is defined by
(10)
This implies that
(11)
From the current/IG-wave velocity profles
the current-current and current-wave
interactioterms (2) can be rewritten in terms of
a set of coefficients Mαβ, Dαβ, Bαβ dan Aαβγ
which are the 3D dispersion coefficients. The
3D-dispersion coefficients are defined by
0 ζζζζ= += += += +h h
ααααQ
0
ζζζζ
α αα αα αα α−−−−==== ∫∫∫∫ h
Q u dz
ααααwQ
0
ζ ζζ ζζ ζζ ζ
α α αα α αα α αα α αζζζζ−−−−= == == == =∫ ∫∫ ∫∫ ∫∫ ∫
tw w w
hQ u dz u dz
0w
hQ V dz Q
ζζζζ
α α αα α αα α αα α α−−−−= += += += +∫∫∫∫
ααααV
ααααmV
ααααdV
α α αα α αα α αα α α= += += += +m dV V V
ααααmV
0
α αα αα αα ααααα
ζζζζ
−−−−====
++++w
m
Q QV
h
0
0ζζζζ
αααα−−−−====∫∫∫∫ d
hV dz
Engki A. Kisnarti, Totok Suprijo
(12)
(13)
(14)
(15)
Using these coefficients the equations can then be written in terms of surface elevations and the
total volume flux components Qx and Qy as dependent unknowns. The result is
(16)
And
(17)
(0)(0)
(0)
(0)
1 1( ') ' '
( )
1( ') ' '
( )
o o o
o o o
wdo d
th h h
d wo d
th h h
QVB h z dz V dz dz
h v z h
V Qh z dz V dz dz
v z h
ζ ζ ζβα
αβ β
ζ ζ ζβ α
α
∂= − + − ∂
∂ + + − ∂
∫ ∫ ∫
∫ ∫ ∫
(0) (0)1 1' '
( )o o o
wwd d
th h h
QQD V dz V dz dz
h v h h
ζ ζ ζβα
αβ α β
= ∂ − −
∫ ∫ ∫
(0) (0) (0) (0)( ) ( )
o
d d d w d w
h
M V V dz V Q V Q
ζ
αβ α β β α α βζ ζ= + +∫
ζ
0yx
t x y
ζ ∂∂∂+ + =
∂ ∂ ∂
( )
2
(2 ) 2
( )
x yx xxx xy
yx xxx xx xy xx
y yx xxy xy xx xy xy
xxx
QQQ QM M
t x h y h
QQ Qh D B D B
x x h y h y h
Q QQ Qh D B Dyy D D B
y x h y h x h y h
Ax
∂ ∂ ∂+ + + +
∂ ∂ ∂
∂ ∂ ∂ ∂ − + + +
∂ ∂ ∂ ∂
∂ ∂ ∂ ∂ ∂ − + + + + +
∂ ∂ ∂ ∂ ∂
∂+
∂
1 1
o o
y yx xxxy xyx xyy
s Bxyxx x x
xx xy
h h
Q QQ QA A A
h h y h h
SSgh dz dz
x x y x y
ζ ζτ τζ
τ τρ ρ ρ
− −
∂+ + +
∂
∂ ∂ −∂ ∂ ∂ =− − + + + + ∂ ∂ ∂ ∂ ∂ ∫ ∫
( )
( )
(0) (0)(0)
(0) (0)
(0)
1'
1'
o o o
o o o
w
wd o dd
th h h
w
d do wd
th h h
QQV h VhA V dz dz
v x x x z h
Q
V Vh Qh V dz dzv x x x z h
αζ ζ ζ
βα ααβγ β
γ γ γ
βζ ζ ζ
β β αα
γ γ γ
∂ ∂ ∂ ∂
= − − − − ∂ ∂ ∂ ∂
∂ ∂ ∂∂
+ − − − ∂ ∂ ∂ ∂
∫ ∫ ∫
∫ ∫ ∫
Nearshore Current Study Using a Quasy 3D Model; Study Case: Perairan Pantai Dadap, Indramayu
17
(18)
The equations (16), (17), and (18) are the equations solved by the mode.
III. MODEL SENSITIVITY TEST In this research, some of simulations had
been done. The model was applied
synthetically and within simple areas, by using
the sensitivity test from wave parameters, i.e.
wave breaker angle, height and period, to the
magnitude of longshore current velocity.
These are the results of calculation velocity
of alongshore current for the changing of wave
breaker angle in the form of picture shown in
Figure 2. In the figure 2. (a) It can be seen that
the velocity of alongshore current increase by
the increasing of wave breaker angle until 510.
The minimum velocity of alongshore current
was happened at wave breaker angle equal to
300, meanwhile the maximum of alongshore
current happened at angle equal to 510.
So that more stand-out its difference, hence
in Figure 2. (b) showed by two data with wave
breaker angle 300 and 51
0. First data with wave
breaker angle 300, wave start to break at
distance 18 meter from coastline highly
waving equal to 0.682 meter. Second with
wave breaker angle 510 wave starts to break
happened at distance 17 meter from coastline
highly waving equal to 0.64466 meter. If
waving propagation in domain with constant
deepness and assume there no missing energy
(high of constant wave) obtained by of
momentum flux. Momentum flux instruct x
(normal style) is constant, momentum flux
instruct y (normal style) is constant, hence its
meaning there no change of momentum.
Gradient from momentum flux instruct x, y,
and by xy (tangential) referred by radiation
stress. With assumption above is, ever greater
of gradient instruct x momentum, hence
normal style of momentum flux instruct y
progressively make velocity of alongshore
current of ever greater coast.
The calculation of alongshore current
velocity for the wave breaker angle of waving
changing quantitatively shown in Tables 1.
Difference of biggest percentage of maximum
velocity happened at wave breaker angle
between 330 and 360, that is equal to 9.17 %.
Difference of smallest percentage of maximum
velocity happened at wave breaker angle
between 450 and 48
0, that is equal to 1.96 %.
The percentage mean from all incidence angle
waving equal to 4.33 %.
Results calculation of alongshore current
velocity for the changes of waves height in the
form of picture shown in Figure 3. (a) It can be
seen that in spite of the changing of assess
alongshore current velocity at height waving
from 0.610 meter until 1.037 meter, and also
can be seen the accretion distance of wave
break.
In Figure 3. (b) showed two data height
waving 0.610 meter and 1.037 meter. First data
highly waving 0.610 meter, waving starting to
break at distance 18 meter from coastline
highly waving equal to 0.682 meter. Second,
highly waving 1.037 meter, waving starting to
break happened at distance 28 meter from
coastline highly waving equal to 1.0886 meter.
The comparison indicate that wave break
quicker happened at is height of wave 1.037
meter than height waving equal to 0.610 meter.
This matter happened because height waving
equal to this 1.037 meter of big energy, so that
cause the happening of mass transport. This
big energy cause velocity of particle in top
waving bigger than speed creep wave so that
happened wave and instability break. At height
waving equal to 0.610 meter, smaller wave
energy than is height of wave 1.037 meter.
Smaller energy need longer time to reach
( )
2
( ) ( )
2 (2 )
y x y y
xy yy
y yx xxy xy yy xx xy xy
y yxyy xy yy yy
Q QQ QM M
t x h y h
Q QQ Qh D B D D D B
x x h y h x h y h
Q QQh B D D B
y x h x h y h
∂ ∂ ∂+ + + + ∂ ∂ ∂
∂ ∂ ∂ ∂ ∂ − + + + + +
∂ ∂ ∂ ∂ ∂
∂ ∂ ∂ ∂ − + + +
∂ ∂ ∂ ∂
∂+
1 1
o o
y yx xxyx xyy yyx yyy
s B
xy yy y y
xy yy
h h
Q QQ QA A A A
x h h y h h
S Sgh dz dz
y x y x y
ζ ζ τ τζτ τ
ρ ρ ρ− −
∂+ + +
∂ ∂
∂ ∂ − ∂ ∂ ∂ =− − + + + + ∂ ∂ ∂ ∂ ∂ ∫ ∫
Engki A. Kisnarti, Totok Suprijo
18
instability and its of wave break. So that apart
the happening of wave break happened quicker
highly waving big.
The calculation of long shore current could
be done quantitatively in the form of tables
shown in Tables 2. It can be seen that at the
time of is height of wave boosted up
successively equal to 10 % that is from 0.610
meter till 1.037 meter, velocity maximum also
increase. Difference of biggest percentage of
velocity maximum happened at height waving
between 0.610 meter by 0.671 meter, that is
equal to 6.72 %.Difference of smallest
percentage of maximum speed happened at
height waving between 0.793 meter and 0.854
meter, that is equal to 0.20 %. The percentage
mean from all height waving equal to 3.10 %.
The results calculations of alongshore
current velocity for the period of wave
changing in the form of picture shown in
Figure 4. It can be seen that happened of
alongshore current velocity changing at period
waving from 4.0 second until 6.8 second,
although its changing was not very much.
The calculation of long shore current could
be done quantitatively for the period of waving
changing to be shown in Tables 3. It can be
seen that at the time of period waving boosted
up successively equal to 10 % that is from 4.0
second till 6.8 second, maximum speed also
increase. Difference of biggest percentage of
maximum velocity happened at period waving
between 4.0 second by 4.4 second, that is equal
to 1.79 %. Difference of smallest percentage of
maximum velocity happened at period waving
between 6.4 second and 6.8, that is equal to
0.41 %. The percentage mean from all period
waving equal to 1.33 %.
The alongshore current velocity could be
perform in the 3D shape, can be seen in Figure
5 – 7. Outside of break wave’s areas going to
the open sea, they have a very strong velocity
on the surface more than velocity near with
bottom. Area outside region waving breaking
(surf zone) represented by x = 21(m), 29(m),
37(m) for the wave breaker angle changing
each; every 10 %. While to be height and
period waving changing each; every 10 %,
area outside region waving breaking (surf
zone) represented by x = 4(m), 16(m), and
28(m). It was seen that the approximate of
component value u and v are zero, although
within vector velocity of alongshore current on
the surface less toward the deepness. For the
wave breaker angle changing each; every 10
%, area waving breaking (zone surf)
represented by x = 45(m) and 53(m). This
matter because of energy flux waving in x
direction is constant (dissipation by
disregarded elementary friction), so that its
activator style zero and no current in coastline
direction. Height and period waving changing
each; every 10 %, area waving breaking (zone
surf) represented by x = 40(m) and 52(m). In
the wave’s break area, the v velocity
component value bigger than zero, in the
meantime the u velocity component values still
around zero. It was seen that the v component
value has much effects for the alongshore
current forming. The velocity of alongshore
current in the surface was almost similar
within water bottom. It was happened because
of the waves start to break, so that the mixing
was happened from the surface to the waters
bottom and after it was passing the maximum
of alongshore current velocity, the velocity of
current in the surface being a little bit bigger
than in waters bottom.
The shorecirc three dimensional quasi
model is also compared with Longuet-Higgins
analytic model . Wave breaker angle which is
used: 100, 200, 300, 400, and 500. Other
parameter which used is high of wave, H =
0.61 meter and period waving, T = 4 second.
Quantitatively, the calculation result of
numerical velocity and analytical of
alongshore current shown in table 4. It was
seen that the biggest differences between
numerical velocity and alongshore current
analytical are at wave breaker angle 40 as
much 8.42%. The difference of the smallest
percentage between numeric and alongshore
current analytical are at wave breaker angle 20,
equal to 0.90%.the difference average equal
with 5,67%.
IV. MODEL APPLICATION
4.1 The Dadap Coastal Waters
The Dadap Coastal water is situated by
existing of offshore harbor that has been
developed in 1999 by Ministry of Public
Work. Situation map is shown in Figure 7.
For to detect the pattern of current and
moving the water mass, have done floating
tracking at 16 September 2007. The floater
released at location. The floater released have
done on boat. When the floater detached to
sea, the location recorded with GPS and its
time. When operation of float tracking have
finish, the floater take away. The construction
of floater is shown in figure 8.
Nearshore Current Study Using a Quasy 3D Model; Study Case: Perairan Pantai Dadap, Indramayu
19
4.2. Simulation Design The validity had done to apply the 3D
shorecirc quasi 3D in Dadap waters Juntinyuat,
Indramayu. Desain model to used in the
simulation (initial condition) showed in Figure
8. In the simulation assumed water territory in
a state of peace without existence of horizontal
and also vertical movement, causing appliesu
= v = w = ζ = 0
Boundary condition therefore need to be
specified along three different types of
boundaries. At the seaward boundary, an open
boundary condition needs to be specified that
can generate incoming (long) waves and
currents and at the same time allow the
outgoing waves to leave the calculation
domain with minimal reflection. This kind of
(absorbing-generating) boundary condition is
available in model.
At the cross-shore boundaries, in the
present version of the model, there are several
ways of specifying the lateral boundary
conditions which represent the conditions
along the upstream and downstream cross-
shore boundaries (in the sense of the
dominating alongshore current). The following
options are available: a periodic boundary
condition can be used. This means that the
instantaneous flow at each point of one of the
cross-shore boundaries is mirrored at the
equivalent point of the other cross-shore
boundary.
The other option is to place a vertical wall
at a very small depth (a few cm) along the
shoreline. Only the cross-shore volume flux is
set to zero, no constraint is required on
and in general the model computes
along the shoreline.
4.3 Measurement Campaign at Dadap
Coastal Waters Figure 9 show movement objek in Dadap
waters. During measuring, objek (float)
moving go along on shore. This moving
coused side effect from tide. To disappear side
effect from tide, have done computation v
direction and velocity alongshore current. This
result showed in Figure 10.
V. DISCUSSION The velocity of alongshore current
vertically, can be seen in Figure 12. The
outside surf zone area, representatives by x= 4,
22, 40. The alongshore current velocity on the
surface similar with water’s bottom for energy
flux was decreased in x direction, meanwhile
the radiation stress worked in y positive
direction.The surf zone representatives by x =
58, 76, and 94. The alongshore current velocity
on the surface similar within water’s bottom. It
was happened since waves begin break around
at 400.2 meter, therefore become a mixing
from the surface to the water’s bottom.
From figure 11, was seen in the tracking 1
and 3, relation between observation in the field
and simulation model show that observation
result in the field more dominant than
simulation model. Otherwise, in the tracking 2
the relation between observation in the field
and simulation model show that simulation
model bigger than observation in the field.
Therefore, generally the relation between
observation in the field and simulation model
show that observation in the field bigger than
compare with simulation model. It has shown
with deviation standard as much 0.051 m/sec.
Relation picture between observation in model
simulation and field showed in Figure 13.
VI. CONCLUSSIONS
The result of simulation and discussion
which had been done, could be obtained some
of conclusion. In the sensitivity test,
alongshore current velocity more significant in
the increasing of wave breaker angle (4.33%)
compare with the increasing of height waves
(3.10%) and waves period (1.33%). The
increasing of height waves, in spite of to
increase alongshore current velocity, it was
also increase the distance of waves breaker
happening. The big of height wave has a big
energy more than the small height waves. The
bigger energy was faster to achieve instability,
therefore break first than energy that it has by
the small height waves. The outside of surf
zone, the velocity on the surface bigger than in
the bottom. It was happened since the energy
that belongs to the waves was not reach yet to
the bottom. When the waves begin break, the v
component within breakers waves areas more
dominate than u component.
The validation result between observation
in the field and simulation model show of
deviation standard as much as 0.051 m/sec.
REFERENCES
1. Fredsoe, J. & Deigaard, R. 1992 Mechanics
of Coastal Sediment Transport, World
Scientific, Singapore, 369 pp.
2. Haas, K. A, I. A. Svendsen, M. C. Haller,
and , Q. Zhao, 2003, ”Quasi-Three-
Dimensional Modeling of Rip Current
Systems”, Journal of Geophysical Research,
Vol. 108.
Engki A. Kisnarti, Totok Suprijo
20
3. Haas, K. A, I. A. Svendsen, R. W. Brander,
and , P. Nielsen, 2002, ”Modeling of a Rip
Current System on Moreton Island,
Australia”, International Conference on
Coastal Engineering.
4. Haas, K. A, I. A. Svendsen, and Q. Zhao,
2000, “3-D Modeling of Rip Currents”,
International Conference on Coastal
Engineering.
5. Horikawa, K., ”Nearshore Dynamics and
Coastal Processes”, University of Tokyo
Press, 1988.
6. Komar, P.D., 1976, “Beach Processes and
Sedimentation”, Prentile Hall Inc., New
Jersey.
7. Li, Z and B. Johns, 1998, “A Three-
Dimensional Numerical Model of Surface
Waves in the Surf Zone and Longshore
Current Generation over a Plane Beach”,
Estuarine, Coastal and Shelf Science,395-
413.
8. Putrevu, U. and I. A. Svendsen, 1999,
“Three-dimensional Dispersion of
Momentum in Wave-induced Nearshore
Currents”, Eur.J.Mech. B/Fluids, 83-101.
9. Svendsen, I. A. and U. Putrevu, 1994,
“Nearshore Mixing and Dispersion”, Proc.
Roy. Soc. Lond, A, 445,561-576.
10. Zhao, Q., I. A. Svendsen, and K. Haas,
2003, “Three-Dimensional Effects in Shear
Waves”, J. Geophys. Res.,
108(C8),3270,doi:10.1029/2002JC001306.
Table 1. The result of maximum calculation of alongshore current of its change percentage and
coast with wave breaker angle changing every 10 %.
Angle (0) Max Velocity (
m/sec) Percent (%)
30 0.92846
6.03
33 0.98802
9.17
36 1.0878
4.24
39 1.136
3.55
42 1.1778
2.94
45 1.2135
2.42
48 1.2436
1.96
51 1.2685
Average 4.33
Nearshore Current Study Using a Quasy 3D Model; Study Case: Perairan Pantai Dadap, Indramayu
21
Table 2.The result of maximum velocity of alongshore current of its change percentage and coast highly waving
changing every 10 %.
High of wave (H) Max Velocity (m
/sec) Percent (%)
0.61 0.92846
6.72
0.671 0.99539
0.73
0.732 1.0027
5.46
0.793 1.0606
0.20
0.854 1.0627
4.48
0.915 1.1125
1.29
0.976 1.1270
2.84
1.037 1.1600
0.81
1.098 1.1695
3.58
1.159 1.2129
3.28
1.22 1.2540
Average 3.10
Table 3.The result of maximum calculation of alongshore current of its change percentage and coast with period
waving changing every 10 %.
Period Wave (T) Max Velocity(m
/sec) Persent (%)
4.0 0.8014
1.79
4.4 0.8161
1.39
4.8 0.8276
0.73
5.2 0.8336
0.73
5.6 0.8398
0.59
6.0 0.8448
0.49
6.4 0.8494
0.41
6.8 0.8524
Average 1.33
Engki A. Kisnarti, Totok Suprijo
22
Figure 1.Definition sketch
(a) (b)
Picture 2. The velocity of alongshore current increase by increasing wave breaker angle. (a) The velocity of
alongshore current increase by the increasing of wave breaker angle until 510. (b) The velocity of
alongshore current increase by increasing wave breaker angle 300 and 51
0.
H = 0.610 m, T = 4 sec
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
0 10 20 30 40 50 60
distance (m)
current (m/sec), a=30current (m/sec), a=51High of break water (m), a=30
high of break w ater (m), a = 51breaker line, a = 30
breaker line, a = 51Series7
H = 0.610 m, T = 4 sec
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
0 10 20 30 40 50 60
distance (m)
velo
cit
y o
f lo
ng
sh
ore
cu
rren
t (m
/s) alpha 30
alpha 33
alpha 36
alpha 39
alpha 42
alpha 45
alpha 48
alpha 51
Nearshore Current Study Using a Quasy 3D Model; Study Case: Perairan Pantai Dadap, Indramayu
23
(a) (b)
Figure 3. The velocity of alongshore current for height change waving. (a) The velocity of alongshore current at
height waving from 0.610 meter until 1.037 meter. (b) two data highly waving 0.610 meter and 1.037
meter
Figure 4. The velocity of alongshore current at period waving from 4.0 second till 6.8 second
T = 4 detik, a = 30 0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 10 20 30 40 50 60distance (m)
current (m/sec), H = 0.610 mcurrent (m/sec), H = 1.037 mhigh of breaker w ave (m), H = 0.610 mhigh of breaker w ave (m), H = 1.037 mbreaker line, H = 0.610 mbreaker line, H = 1.037 mSeries7
T = 4 detik, a = 30 0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 10 20 30 40 50 60
distance (m)
velo
cit
y o
f lo
ng
sh
ore
cu
rren
t (m
/s)
H = 0.610 m
H = 0.671 m
H = 0.732 m
H = 0.793 m
H = 0.854 m
H = 0.915 m
H = 0.976 m
H = 1.037 m
ve
loc
ity o
f lo
ng
sh
ore
cu
rre
nt
(m/s
)
distance (m)
T = 4 sec, a = 30 degre
T = 4.0 sec
T= 4.4 sec
T = 4.8 sec
Engki A. Kisnarti, Totok Suprijo
24
(a)
(b)
Picture 4. Snapshots of the 3D variation: (a) breaker wave angle 30
0, (b) 51
0.
Nearshore Current Study Using a Quasy 3D Model; Study Case: Perairan Pantai Dadap, Indramayu
25
(a)
(b)
Figure 5. Snapshots of the 3D variation: (a) H = 0.61 m, (b) H = 1.037 m.
Figure 5. Snapshots of the 3D variation: (a) H = 0.61 m, (b) H = 1.037 m.
Engki A. Kisnarti, Totok Suprijo
26
(a)
(b)
(b)
Figure 6. Snapshots of the 3D variation: (a) T = 4.0 second, (b) T = 6.8 second
Nearshore Current Study Using a Quasy 3D Model; Study Case: Perairan Pantai Dadap, Indramayu
27
Figure 7.Location of tracking and design of model
Figure 7. Location of tracking and design of model
Figure 8. Construction of floater
Location of Tracking
Engki A. Kisnarti, Totok Suprijo
28
Figure 9. Floating Movement
Picture 10. Direction movement
tracking 1 tracking
tracking
tracking 3
tracking 2
Nearshore Current Study Using a Quasy 3D Model; Study Case: Perairan Pantai Dadap, Indramayu
29
Figure 11. The velocity of alongshore current, observation vs numeric
Engki A. Kisnarti, Totok Suprijo
30
Figure 12. Snapshots of the 3D variation.
Figure 13. Relation picture between observation in model simulation and field.
0.05
0.10
0.15
0.20
0.25
0.30
0.05 0.10 0.15 0.20 0.25 0.30
Simulation Model (m/sec)
Ob
serv
ati
on
(m
/sec)
Tracking 1
Tracking 2
Tracking 3
Linear