4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
THEORETICAL PAPER
THEORETICAL APPROACH OF LONGSHORE CURRENT
REDUCTION COEFFICIENT THROUGH PERMEABLE
GROIN
Hasdinar Umar1, Nur Yuwono2, Radianta Triatmadja2 and Nizam2*
1
2
Coastal Engineering Department, Universitas Hasanuddin
Civil and Environmental Engineering Department, Universitas Gajah Mada
*hasdinar.umar@gmail.com; +62812-2760-8658
Received: ….. (left blank)
Revised: ….. (left blank)
Accepted: ….. (left blank)
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 (dt), and number of the groin (n).
Reduction coefficient (Cr) 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 𝐶𝑟 =
⟨𝑣⟩𝑔𝑟𝑜𝑖𝑛
⟨𝑣⟩𝑡𝑎𝑛𝑝𝑎 𝑔𝑟𝑜𝑖𝑛
, where the reduction coefficient (Cr) describes the magnitude of
longshore currents reduction passing through the permeable groin.
Keywords: permeable groin, longshore current, current reduction coefficient
INTRODUCTION
General Background
Dynamic process in the form of wave forces, currents, wind, the movement of
sediment and so on as well as land use in coastal areas cause many problems such
as erosion, sedimentation, and siltation of the river mouth deflection, pollution
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4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
and salt water intrusion. To overcome those problems, the first step that must be
done is to find the cause of the erosion and sedimentation, so we can determine
how to handle it. Erosion and sedimentation are usually overcome by building
coastal protection structures; one of it is the permeable groins. 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.
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,
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4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
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 transport while still providing the supply of sediment to
without groin
with groin
Current velocity
the down drift groin.
Permeable pile groin
Terrace
Bar
Trough
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.
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4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
RESULTS AND DISCUSSION
Longshore Current without Permeable Groin
Longshore current equation of Longuet-Higgins, 1970 is the longshore current
caused by the difference in radiation stress, where Longuet-Higgins and Stewart,
1964 has reviewed the theory of radiation stress which excised current momentum
generated by the wave. In the development of longshore current equation,
Longuet-Higgins, 1970 using four (4) basic review,
1. Review of the waves approaching the shoreline
1
𝐹𝑥 =
8
𝜌𝑔𝐻 2 𝑐𝑔 cos 𝛼
(1)
2. Radiation stress theory
𝑆𝑥𝑦 = 𝐹𝑥
sin 𝛼𝑜
(2)
𝑐𝑜
3. Shear stress due to waves
5
𝜏𝑦 = 4 𝜌𝑢𝑚 2 tan 𝛽 sin 𝛼𝑏
(3)
4. Bottom shear stress
2
⟨𝜏𝑏 𝑦 ⟩ = 𝐶𝑓 𝜌𝑢𝑚 ⟨𝑣⟩
𝜋
(4)
Longshore current analysis without permeable groin developed by LonguetHiggins, 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,
𝑦 +
𝜕
𝜕𝑥
(𝑣𝑡 . ℎ.
𝜕 ⟨𝑣⟩
𝜕𝑥
) − ⟨𝜏𝑏 𝑦 ⟩ = 0
(5)
where
vt
⟨𝑣⟩
: mixed coefficient (eddy coefficient),
: longshore current velocity,
𝑦
: shear stress due to waves,
⟨𝜏𝑏 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
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4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
by the wave, making the shear stress due to waves (y) is only offset by the
average value of shear stress ⟨𝜏𝑏 𝑦 ⟩.
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,
⟨𝑣⟩ =
5𝜋
8𝐶𝑓
𝑢𝑚 tan 𝛽 sin 𝛼
where 𝑢𝑚 =
𝛾𝑏
2
√𝑔ℎ𝑏 =
(7)
𝐻𝑏
2
𝑔
√ℎ , so that Equation (7) as a function of
𝑏
breaking wave height (Hb) can be written as follows,
⟨𝑣⟩ =
5𝜋
16𝐶𝑓
𝑔
𝐻𝑏 √ℎ tan 𝛽 sin 𝛼
𝑏
(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,
𝑣 ℎ < ℎ𝑏
ℎ
⟨𝑣⟩ = ( ) × { 𝑏
ℎ𝑏
0 ℎ > ℎ𝑏
(9)
where,
𝑣𝑏 =
5𝜋
16𝐶𝑓
𝑔
𝐻𝑏 √ℎ tan 𝛽 sin 𝛼𝑏
𝑏
(10)
where
Cf
Hb
hb
tan β
b
: bottom friction coefficient,
: wave height (m)
: breaking wave depth (m),
: beach slope,
: 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,
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4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
2
𝛾
⟨𝑢𝑜𝑟𝑏 ⟩ = ( + )𝑢𝑚
𝜋
4
(11)
So that the shear stress direction y (longshore direction) become,
2
𝛾
⟨𝜏𝑏 𝑦 ⟩ = ( + )𝐶𝑓 𝜌𝑢𝑚 ⟨𝑣⟩
𝜋
4
(12)
Hence, longshore current equation can be simplified as,
5
⟨𝑣⟩ = 4
𝑢𝑚 (tan 𝛽 sin 𝛼𝑏 )
2 𝛾
𝜋 4
( + )𝐶𝑓
(13)
where
um
: orbital maximum velocity (m/det),
tan β : beach slope,
b
: breaking waves angle,

: ratio between breaking wave height (Hb) with a depth of a
breaking wave (hb),
hb
: depth of a breaking wave (m).
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,
𝜏𝑦 = ⟨𝜏𝑏 𝑦 ⟩𝑔𝑟𝑜𝑖𝑛
(14)
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4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
where ⟨𝜏𝑏 𝑦 ⟩𝑔𝑟𝑜𝑖𝑛 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) (⟨𝜏𝑏 𝑦 ⟩)
added the average shear stress between water and piles of groins (⟨𝜏𝑔 ⟩),
⟨𝜏𝑏 𝑦 ⟩𝑔𝑟𝑜𝑖𝑛 = ⟨𝜏𝑏 𝑦 ⟩ + ⟨𝜏𝑔 ⟩
(15)
Shear stress between water and piles of groins (⟨𝜏𝑔 ⟩) is considered equal to the
drag force of permeable groins (Fd) per unit area constraining groin area.
1
⟨𝜏𝑔 ⟩ = 𝐶𝑑 𝜌(
2
𝐿
𝑁
𝑔 𝑑𝑡
)ℎ𝑟 𝑑𝑡 𝑢𝑚 ⟨𝑣⟩
(16)
Total shear stress equation after the barrier of permeable pile groins can be written
as follows,
2
𝛾
1
⟨𝜏𝑏 𝑦 ⟩𝑔𝑟𝑜𝑖𝑛 = ( + )𝐶𝑓 𝜌𝑢𝑚 ⟨𝑣⟩ + 𝐶𝑑 𝜌(
𝜋
4
2
𝐿
𝑁
𝑔 𝑑𝑡
)ℎ𝑟 𝑑𝑡 𝑢𝑚 ⟨𝑣⟩
(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 (y) and the average shear stress due the permeable pile
groin (⟨𝜏𝑏 𝑦 ⟩𝑔𝑟𝑜𝑖𝑛 ),
αb
Breaker line
(v)
⟨𝜏𝑏 𝑦 ⟩
⟨𝜏𝑏 𝑦 ⟩𝑔𝑟𝑜𝑖𝑛
y
y
x
Surf zone
⟨𝜏𝑔 ⟩
Shoreline
Figure 4. Sketch of longshore current parameters after a permeable groin
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4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
𝜏𝑦 = ⟨𝜏𝑏 𝑦 ⟩𝑔𝑟𝑜𝑖𝑛
(18)
where ⟨𝜏𝑏 𝑦 ⟩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) (⟨𝜏𝑏 𝑦 ⟩) added the average shear stress between the water and the pile of
groins (⟨𝜏𝑔 ⟩),
⟨𝜏𝑏 𝑦 ⟩𝑔𝑟𝑜𝑖𝑛 = ⟨𝜏𝑏 𝑦 ⟩ + ⟨𝜏𝑔 ⟩
2
𝛾
(19)
1
⟨𝜏𝑏 𝑦 ⟩𝑔𝑟𝑜𝑖𝑛 = ( + )𝐶𝑓 𝜌𝑢𝑚 ⟨𝑣⟩ + 𝐶𝑑 𝜌(
𝜋
4
2
𝐿
𝑁
𝑔 𝑑𝑡
)ℎ𝑟 𝑑𝑡 𝑢𝑚 ⟨𝑣⟩
(20)
If Equation (3) and Equation (20) is substituted into (18), the longshore current
velocity equation through permeable groins structure can be written as follows,
⟨𝑣⟩𝑔𝑟𝑜𝑖𝑛 =
where
p
hr
dt
Cd
5
𝑔
(tan 𝛽
𝐻
8 𝑏 √ℎ𝑏
2 𝛾
𝜋 4
((( + )𝐶𝑓 )+
sin𝛼𝑏 )
4𝐶𝑑 𝑝ℎ𝑟
)
2𝜋𝑑𝑡
(21)
: density of the groin (%),
: the average depth of the submerged groin piles (m),
: diameter of pile (m).
: 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
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4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
reduction coefficient (Cr) is the ratio between the longshore current velocity after
groins ((v)groin) with longshore current velocity without groins ((v)without groin)).
𝐶𝑟 = ⟨𝑣⟩
⟨𝑣⟩𝑔𝑟𝑜𝑖𝑛
(22)
𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑔𝑟𝑜𝑖𝑛
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 (Cf) and drag coefficient (Cd).
Based on Equation (13) and (21), reduction coefficient (Cr) equation can be
written as follows,
𝐶𝑟 =
2 𝛾
𝜋 4
( + )𝐶𝑓
2 𝛾
𝜋 4
( + )𝐶𝑓 +
(23)
2𝐶𝑑 𝑝ℎ𝑟
𝜋𝑑𝑡
If known π = 3.14 and  = 0.78, then Equation (23) can be written as follows,
𝐶𝑟 =
1.3𝐶𝑓
𝐶 𝑝ℎ𝑟
1.3𝐶𝑓 + 𝑑
𝑑𝑡
=
1
𝐶 𝑝ℎ𝑟
1+ 𝑑
(24)
1.3𝐶𝑓 𝑑𝑡
Relationship between the reduction coefficient (Cr) and groin density (p) is
shown in Figure 6.
Redution coefficient, Cr
1
0.8
0.6
0.4
0.2
0
0%
20%
40%
60%
Groin density, p (%)
80%
100%
Figure 6. The relationship between the reduction coefficient (Cr) and groin density
(p)
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4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
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:
1. Longshore current reduction coefficient is influenced by two roughness
parameters, bottom roughness coefficient (Cf) and drag coefficient (Cd).
Besides the reduction coefficient is also influenced by groin structure
parameters as density of groin (p) and diameter of pile (dt)
2. Finally a relationship of reduction coefficient (Cr) 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
The authors would like to express their sincere gratitude to the Hydraulics
Laboratory, Department of Civil Engineering and Environmental Engineering,
Gadjah Mada University. Appreciation also extended to the entire academic staffs
of Department of Coastal Engineering, Hasanuddin University.
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4th International Seminar of HATHI, 6-8 September 2013, Yogyakarta
Dean dan Dalrymple, 1984,Water Wave Mechanics for Engineers and Scientists,
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Yogyakarta
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