THEORETICAL APPROACH OF LONG SHORE CURRENT REDUCTION COEFFICIENT THROUGH PERMEABLE GROIN

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THEORETICAL APPROACH OF LONG SHORE

CURRENT REDUCTION COEFFICIENT

THROUGH PERMEABLE GROIN

Hasdinar Umar1_{*, Nur Yuwono}2_{, Radianta Triatmadja}2_{, and Nizam}2

1_{Coastal Engineering Department, Universitas Hasanuddin}

2_{Civil and Environmental}_{Engineering Department, Universitas Gajah Mada}

*Email: hasdinar.umar@gmail.com; Phone: +62812-2760-8658

Abstract

Permeable groin is a coastal protection structure that is flexible and effective to

control the longshore current and hence longshore sediment transport. The ability to reduce both longshore currents and longshore sediment transport to a desired

extent can provide more control to avoid unwanted sudden changes of shoreline in

particular area.

The average longshore current velocity (v) through permeable groins can be developed theoretically based on Longuet-Higgins, 1970 equation by incorporating

structure parameters of permeable groin namely the distance between the piles (p),

diameter of the pile (d_t), and number of the groin (n). Reduction coefficient (C_r)

may be determined by comparison between longshore current through permeable

groin (<v>_groin) and longshore current without permeable groin (<v>_{without groin}).

The results showed that reduction coefficient (Cr) may be determined by

, where the reduction coefficient (C_r) describes the magnitude

of longshore currents reduction passing through the permeable groin.

Keywords: permeable groin, longshore current, current reduction coefficient

INTRODUCTION

General Background

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longshore sediment transport. The ability to reduce both longshore currents and

longshore sediment transport to a desired extent can provide more control to avoid unwanted sudden changes of shoreline in particular area.

Figure 1. Permeable groin at Teluk Penyu Coast, Cilacap

Design of permeable groins, especially pile groin requires basic theory in order to obtain results that support an effective design which is the reduction coefficient

(Cr) longshore current after the permeable groins.

Permeable Groin

Permeable groins have a porous structure that still allows the current through the structure so that the transport of sediment to the down drift groin could still occurred.

Longshore current and longshore sediment transport basically is controlled by

density of pile groin (p). Several researches related to permeable groin were done

by Hasdinar, et.al, (2011); Abdellah and Balah, (2001); Raudkivi, (1996); which were Hasdinar, et.al, (2011) studied the longshore current after permeable groin. Abdellah and Balah, (2001) has conducted research on the application of permeable pile groins as a coastal protection at Northwestern tourist beach, Egypt. Raudkivi, (1996) studied the application of permeable pile groin at the Baltic Sea coast.

Permeable pile groin structure can reduce longshore current and longshore sediment

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density of pile groin ( groin were done by

which were shore current after

on of coastal protection at Northwestern

studied the application of permeable pile groin

while still providing of sediment

thedown driftgroin.

Scheme of beach profile with permeable pile groins and current velocity without groins and with the groin

n this research was analytical the formula of

longshore current reduction coefficient through permeable groin. To derivate the reduction coefficient, two parameters were used. First, the longshore current without permeable groin and second the longshore current with permeable groin. Longshore current formula without permeable groin was derivate from

Higgins, 1970, which were used two parameters,

Figure 2. Scheme of beach profile with permeable pile groins and current velocity distribution without groins and with the groin (Raudkivi, 1996)

Methodology of Study

Method used in this research was analytical study regarding the formula of longshore current reduction coefficient through permeable groin. To derivate the reduction coefficient, two parameters were used. First, the longshore current without permeable groin and second the longshore current with permeable groin. Longshore current formula without permeable groin was derivate from Longuet Higgins, (1970), which were used two parameters, bottom shear stress and shear stress due to wave. Longshore current velocity with permeable groins was derived by assuming that the shear stress will increase as a result of shear stress due to groin piles. So that the longshore current velocity after a permeable groins will be using three parameters: the shear stress due to waves, bottom shear stress and shear stress

due to piles groin.

RESULTS AND DISCUSSION

Longshore Current without Permeable Groin

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1. Review of the waves approaching the shoreline

... (1)

2. Radiation stress theory

... (2)

3. Shear stress due to waves

... (3)

4. Bottom shear stress

... (4)

Longshore current analysis without permeable groin developed by Longuet-Higgins, (1970) using the assumption that the current is two-dimensional (no variation in the

vertical direction), steady and uniform in the y direction, so that the momentum

equation in the direction along the shore (longshore direction) using the equation,

... (5)

where

v_t : mixed coefficient (eddy coefficient),

‹

v

› : longshore current velocity,

τy : shear stress due to waves,

‹

τ_{b y}

_›

: bottom shear stress.

Completion of the longshore current equation simplified by ignoring the shear stress

due to turbulence so that the second term in Equation (5) can be neglected by the

wave, making the shear stress due to waves (τy ) is only offset by the average value

of shear stress

‹

τ_by

_›

.

τy =

‹

τb y

›

... (6)

If Equation (3) and (4) are substituted into Equation (6), then the longshore current equation of the conditions unhindered groin (Longuet-Higgins, 1970) as follows,

(5)

where , so that Equation (7) as a function of breaking wave

height (H_b) can be written as follows,

... (8)

If we assume that the shallow-water theory is applied, then the average of longshore current equation without the influence of lateral mixing can be written as,

... (9)

where,

... (10)

where

C_f : bottom friction coefficient,

H_b : wave height (m)

h_b : breaking wave depth (m),

tan β : beach slope,

a_b : breaking wave angle.

Hasdinar, 2012 used a no sinusoidal wave assumption of the orbital velocity which derived from mean orbital velocity equation written in Dean and Dalrymple, (1984).

... (11) So that the shear stress direction y (longshore direction) become,

... (12) Hence, longshore current equation can be simplified as,

... (13)

where

u_m : orbital maximum velocity (m/det),

tan β : beach slope,

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Figure 3. Longshore current without groin

LongShore Current with Permeable Groin

Development of longshore current equations with permeable groin based on the direction of longshore momentum equation without the influence of lateral mixing (Equation (10), Longuet-Higgins, 1970), with the basic assumption that the friction increased by the existence of permeable pile groins structure,

... (14)

where is shear stress due to permeable groin barrier that is a function of

the mean shear stress (shear stress between the water and the bottom) ( )

added the average shear stress between water and piles of groins ( ),

... (15)

Shear stress between water and piles of groins ( ) is considered equal to the

drag force of permeable groins (F_d) per unit area constraining groin area.

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Total shear stress equation after the barrier of permeable pile groins can be written as follows,

... (17) Longshore current velocity equation through the permeable pile groins developed

from the momentum equation y direction (parallel to the shoreline) after the groins,

as shown in Figure 4, which illustrates that there is a balance between the shear

stress due to waves (t_y) and the average shear stress due the permeable pile groin

groin (

_<

t

by

>

groin).

αb

Surf zone

Shoreline Breaker line

ty

y

x

(v)

Figure 4. Sketch of longshore current parameters after a permeable groin

t_y=

_<

t

by

>

groin ... (18)

where

_<

t

by

>

groin is the average shear stress due the permeable pile groin as a function

of the average shear stress (shear stress between the water and the bottom) (

_<

t

by

>

)

added the average shear stress between the water and the pile of groins (

_<

t_g

_>

),

(8)

If Equation (3) and Equation (20) is substituted into (18), the longshore current velocity equation through permeable groins structure can be written as follows,

... (21)

where

p : density of the groin (%),

h_r : the average depth of the submerged groin piles (m),

d_t : diameter of pile (m).

C_d : drag coefficient

Figure 5. Longshore current with permeable groin

Reduction Coefficient

Once known the magnitude of the average longshore current velocity after the groins then reduction coefficient can be determined. Longshore current velocity

reduction coefficient (Cr) is the ratio between the longshore current velocity after

groins ((v)_groin) with longshore current velocity without groins ((v)_{without groin)}). ... (22)

If the beach is used permeable pile groins as shoreline protection, then the magnitude of the longshore current coefficient reduction will be influenced by two roughness

parameters, bottom roughness coefficient (C_f) and drag coefficient (C_d). Based on

Equation (13) and (21), reduction coefficient (C_r) equation can be written as follows,

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If known π = 3.14 and g = 0.78, then Equation (23) can be written as follows,

... (24)

Relationship between the reduction coefficient (C_r) and groin density (p) is shown

in Figure 6.

Figure 6. The relationship between the reduction

coefficient (C_r) and groin density (p)

CONCLUSION AND RECOMMENDATION

Based on longshore current reduction coefficient, which is analytically calculated after the permeable groin (Equation (23) and (24)), the followings are the conclusions:

5. Longshore current reduction coefficient is influenced by two roughness

parameters, bottom roughness coefficient (C_f) and drag coefficient (C_d).

Besides the reduction coefficient is also influenced by groin structure

parameters as density of groin (p) and diameter of pile (d_t)

6. Finally a relationship of reduction coefficient (C_r) with a groin density (p)

may be constructed and is expected to be useful for designing a permeable groin that is more adaptable to the requirements of shore protection or reduction of longshore current and longshore sediment transport.

ACKNOWLEDGEMENTS

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