nearshore current study using a quasi 3d model; … 20090102.pdf · nearshore current study using a...

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


(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

QQ

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

∂ ∂ ∂ ∂

= − − − − ∂ ∂ ∂ ∂

∂ ∂ ∂∂

+ − − − ∂ ∂ ∂ ∂

∫ ∫ ∫

∫ ∫ ∫


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− −

∂+ + +

∂ ∂

∂ ∂ − ∂ ∂ ∂ =− − + + + + ∂ ∂ ∂ ∂ ∂ ∫ ∫


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.


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.


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


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


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


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


24

(a)

(b)

Picture 4. Snapshots of the 3D variation: (a) breaker wave angle 30

0, (b) 51

0.


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.


26

(a)

(b)

(b)

Figure 6. Snapshots of the 3D variation: (a) T = 4.0 second, (b) T = 6.8 second


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


28

Figure 9. Floating Movement

Picture 10. Direction movement

tracking 1 tracking

tracking

tracking 3

tracking 2


29

Figure 11. The velocity of alongshore current, observation vs numeric


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

nearshore current study using a quasi 3d model; … 20090102.pdf · nearshore current study using a...

Documents