Dunes Growth Estimation for Coastal Protection
Muhammad Zikra
Department of Ocean Engineering, Faculty of Marine Technology, ITS,
Kampus ITS Keputih Sukolilo, Surabaya 60111
Abstract: This paper describes the investigation of dunes growth estimation caused by Aeolian
sand transport based on field survey and empirical model formulation. The empirical model is
based on considerations of the turbulent kinetic energy relationship as proposed by Coastal
Engineering Manual, 2000. The empirical method is then tested against field data collected on the
Espiguette spit, France. The result indicated that the winds blowing from the dunes or back beach
towards to the shoreline are not efficient in transporting sand. This is because of sheltering provided
by the dune itself or there is a limited supply of sand landward of the dunes.
Keywords: wind, dunes growth, sand transport
INTRODUCTION
The transport of sand by wind (Aeolian sand transport) is an important component part in
the dunes growth (Carter, 1988; Pye and Tsoar, 1990). These sand dunes are important for coastal
protection to provide protection from flooding due to high-water levels, shoreline erosion and
wave overtopping due to storm. These dunes often result from the natural accumulation of windblown sand originating on the beach face. However, they may also be man-made. Dunes can be
made artificially by: (a) beach nourishment, (b) grading existing sand available on the dry beach,
or (c) removing sand from below the high-water line during low tide and using it to construct a
protective dune (beach scraping).
In addition, sand transport under wind is known a continual and natural process that is often
bringing significant change on the beach area. Wind transport can cause the removal of sand or its
redistribution within the littoral zone and gives influence on dunes formation and evolution.
Onshore winds carry sand from the beach and deposit it in backshore marshes, in developed
backshore areas, or in natural or man-made dunes, while the offshore winds carry sand from the
beach into the sea or lake.
In Rhone Delta area, the wind-blown sands are responsible for big input and output of sand
on accretion beach called the Espiguette spit at Rhone Delta, Mediterranean Sea
(Sabatier, 2001). This condition must be controlled to protect the stability of dunes as coastal
protection structure for the area behind it. For that reason, it is important to be able to
quantitatively predict how much sand will be transported by wind at a given coastal site, which
direction the sand will be transported and where it will be deposited. In order to understand the
process, the procedures for calculating wind-blown sand transport in the Espiguette spit will be
derived in this paper. The use of empirical theoretical equation of Aeolian sediment transport is
one way to quantify and predict the sand movement under wind forcing.
181
METHODOLOGY
The research was performed using data collected at sandy spit on the eastern part of the Rhone
Delta, France (at Espiguette spit), which shows accretion and erosion since several decades (Figure 1).
Based on field measurement the characteristic of the beach is known as sandy beach with nominal
diameter, D50 = 0.20 mm and the astronomic tide amplitude is of +/- 0.30 m. Wind data were obtained
from Coungeron Station, France for interval period from 1961-1995 (Zikra et.al 2007). This wind
data were measured by anemometer located at 10 m above the ground. Percentages of average wind
speed and wind direction is given in table 1. Because there is a limitation on data especially moisture
content of sand (no available data on daily precipitation data and monthly evaporation data records)
then the sand transport will be calculated in dry condition and wet condition.
Figure 1. The coastline at Rhone Delta, France
(Adopted from Sabatier and Provansal, 2000)
Table 1. Wind Climate data from 1961-1995
Direction
Degree
0
20
40
60
80
100
120
140
160
180
200
220
182
F0=
0-1
0.229
0.212
0.221
0.237
0.271
0.334
0.371
0.088
0.185
0.132
0.186
0.255
F0=
24
2.397
1.936
1.912
2.120
3.067
3.026
3.084
0.599
1.066
0.901
0.936
1.517
F0=
5-7
2.258
1.363
0.812
0.818
1.569
1.758
2.559
0.427
0.625
0.403
0.328
0.550
F0=
F0= F0= F0=
8-1 11-13 14-16 17-19
1.093 0.361 0.173 0.036
0.387 0.054 0.022 0.008
0.185 0.077 0.013 0.001
0.293 0.105 0.030 0.003
0.869 0.408 0.132 0.027
1.182 0.481 0.253 0.078
1.957 1.043 0.454 0.098
0.187 0.059 0.075 0.004
0.245 0.075 0.013 0.003
0.120 0.028 0.005 0.001
0.080 0.028 0.007 0.000
0.133 0.038 0.005 0.004
F0=
20-22
0.016
0.000
0.001
0.003
0.012
0.018
0.042
0.004
0.001
0.000
0.000
0.000
F0=
23-24
0.001
0.000
0.000
0.000
0.000
0.004
0.011
0.001
0.000
0.000
0.000
0.000
F0=
25-27
0.000
0.000
0.000
0.000
0.001
0.004
0.009
0.000
0.000
0.000
0.000
0.000
F0=
28-30
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
F0=
30-33
0.001
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
F0>34
0.000
0.000
0.000
0.000
0.000
0.000
0.001
0.000
0.000
0.000
0.000
0.000
Total
(%)
6.556
3.981
3.222
3.609
6.357
7.139
9.632
1.445
2.215
1.591
1.564
2.502
Neptunus, Vol. 14, No. 2, Januari 2008: 181 - 188
Direction
Degree
240
260
280
300
320
240
Total (%)
F0=
F0= F0=
0-1
24
5-7
0.186 1.610 0.992
0.139 1.163 1.370
0.177 1.792 2.079
0.201 2.263 3.420
0.262 3.026 4.361
0.252 2.967 3.633
3.936 35.381 29.324
F0=
8-1
0.333
0.721
1.618
2.735
3.703
2.828
18.671
F0=
11-13
0.066
0.209
0.576
1.045
1.913
1.486
8.053
F0=
14-16
0.022
0.053
0.201
0.367
0.882
0.797
3.504
F0=
17-19
0.004
0.018
0.023
0.057
0.202
0.197
0.764
F0=
20-22
0.000
0.004
0.009
0.011
0.084
0.065
0.270
F0=
23-24
0.000
0.001
0.001
0.001
0.019
0.011
0.051
F0=
25-27
0.000
0.001
0.000
0.001
0.011
0.004
0.032
F0=
28-30
0.000
0.000
0.000
0.001
0.000
0.004
0.007
F0=
30-33
0.001
0.000
0.000
0.003
0.000
0.000
0.005
F0>34
0.000
0.000
0.000
0.000
0.000
0.000
0.001
Total
(%)
3.214
3.679
6.475
10.105
14.462
12.243
100.0
RESULT AND DISCUSSION
Aeolian sediment transport
Many models have been proposed to predict Aeolian sediment transport rates (Bagnold,
1941; Kawamura, 1951; Lettau and Lettau, 1977; White, 1979). In this paper, the equation as
proposed by Coastal Engineering Manual (CEM), 2002 is used to calculate Aeolian sediment
transport. This wind blown sediment transport equation is based on considerations of the turbulent
kinetic energy relationship which given by the formula
 u 
q = K * 
 g.D 
3
(1)
where q represents sand transport rate in gm/cm-s, u* shear velocity, g acceleration of gravity, D mean
sand grain diameter and K dimensional Aeolian sand transport coefficient. Value of K is a function of
sand grain diameter which can be expressed by
K = e -9.63 + 4.91 D
(2)
where D is in millimeter and K in grams per centimeter per second
Equations (1) can be used to estimate sand transport rates for given wind speeds and mean
sand-grain diameters. It is based on the data which include transport data for mean sand grain
diameters up to 1.0 mm; consequently, the equations should not be used to estimate transport on beaches
with mean grain diameters greater than about 1.0 mm. This equation can be recast into a dimensionless
form, which allows it to be used with any consistent set of units.
The revised equation is given by
 u 
q
= K'  * 
va ρa
 g.D 
3
(3)
in which νa represents the kinematics viscosity of the air and ρa the mass density of the air. The
dimensionless coefficient K' is given by
K’= e-1.00+4.91 D
(4)
in which D represents the median grain diameter in millimeters. Equation (3) reduces to original
equation (1) when νa = 0.147 cm2/sec and ρa = 0.00122 gm/cm3 are substituted into it.
The results of the Aeolian sediment transport analysis are tabulated in tables below. Table 2
presents the summary of the analysis results obtained by not considering moisture conditions
(precipitation or evaporation) and Table 3 shows analysis of sand transport with assumption that
Dunes Growth Estimation for Coastal Protection ………………………………..
183
the precipitation is higher than evaporation (wet condition). The result indicated that the total transport
is reduced from 44.61 m3/m-yr in dry condition become 14.54 m3/m-yr in wet condition. This result
indicated that moisture content conditions are very important in Aeolian transport calculations.
Table 2. Summary of wind blown sediment transport for dry condition
Wind Direction
Direction in which sand is transported (m3/m)
North
North East
East
South East
South
South West
West
North West
Total S =
Total SW =
Total W =
Total NW =
Total N =
Total NE =
Total E =
Total SE =
TOTAL
12.77
0.82
3.75
5.54
0.33
0.33
4.08
17.01
44.61
Table 3 Summary of wind blown sediment transport for wet condition
Wind Direction
Direction in which sand is transported (m3/m)
North
North East
East
South East
South
South West
West
North West
Total S =
Total SW =
Total W =
Total NW =
Total N =
Total NE =
Total E =
Total SE =
TOTAL
5.31
0.00
0.78
1.56
0.00
0.00
0.78
6.10
14.54
(a)
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Neptunus, Vol. 14, No. 2, Januari 2008: 181 - 188
(b)
Figure 2. (a) Wind-blown sand transport rose at dry condition,
(b) Wind-blown sand transport rose at wet condition
The results of the potential sand transport by wind at Rhone Delta beach (at Espiguette spit)
are also shown in the form of a transport rose as shown on Figure 2. The transport rose shows the
direction from which the sand is transported with the most being transported to the South and South
East (seaward direction)
Dune growth prediction
The efficiency of sand transport on dunes growth is depending on the proportional to the square
of the cosine of the angle between the wind direction and a vector perpendicular to the shoreline
(CEM, 2002). Sand transport rates in the offshore direction, perpendicular to the general orientation
of the dune toe, are given by equation
q⊥ = q cosα cos2β,
180o < β < 360o
where β is the angle the wind makes with the shoreline and α is the angle the wind makes with a vector
perpendicular to the shoreline. Therefore, α = β – 90o and
cos (α) = cos (β - 90o) = - sin (β)
Therefore,
q ⊥ = - q sinβ cos2β, 180o < β < 360o
The sin β term in the equation corrects the transport from the wind direction to a direction
perpendicular to the shore, while the cos2 β term is the efficiency term introduced to consider the
sheltering effects of the dune.
The result of dune growth estimation is presented in Tables 4. The table shows that winds
blowing seaward from the dunes are not very efficient in transporting sand from the dunes back onto the
beach (dune growth = 2.45 m3/m/year). This condition prevails at Espiguette spit, where much of the
area landward of the beach is wetlands. In this case, we need stabilization of dune to control the
landward movement of wind-blown sand into developed areas. Stabilization can be achieved using
vegetation or sand fencing. The best type of stabilizing methods varies with geographical area,
location on the dune, exposure of the site, whether the water body is salt or fresh water, etc.
Dunes Growth Estimation for Coastal Protection ………………………………..
185
In present conditions at the Espiguette spit, the “Ganivelles” stabilisation method (Figure 3)
can be improved and combined using vegetations method as sand trapping to stabilize the dunes and
coastlines. In addition, when designing a dune system as coastal protection structure, the dunes should
be set back ( ± 70m) from the shoreline (Figure 4) so that there is sufficient dry beach to provide a
source of sand.
Table 4. Estimated annual dune growth at rhone delta (Espiguette spit)
Wind Direction
North
North East
East
South East
South
South West
West
North West
Annual
Transport
(m3/m)
12.77
0.82
3.75
5.54
0.33
0.33
4.08
17.01
Wind
Angle
β
318
3
48
93
138
183
228
273
TOTAL
Cos (a)
Efficiency
Dune growth
sin β
-0.6691
0.0523
0.7431
0.9986
0.6691
-0.0523
-0.7431
-0.9986
cos2 β
0.552
1.000
1.000
1.000
1.000
0.997
0.447
0.003
(m3/m/year)
-4.72
0.04
2.79
5.54
0.22
-0.02
-1.35
-0.05
2.45
Figure 3. Dune conditions at Espiguette spit
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Neptunus, Vol. 14, No. 2, Januari 2008: 181 - 188
Figure 4. Reconstructing the dune using “ganivelles”
and vegetation
CONCLUSION
The result indicated that strong seasonal winds are responsible for big inputs and outputs
of sand on the Espigette spit, Southern France which known as “Tramontane” and “Mistral”. The
winds blowing from the dunes or back beach towards the shoreline which this winds blowing are
not efficient in transporting sand. This is because of sheltering provided by the dune itself or there is a
limited supply of sand landward of the dunes.
In addition, the predictions of aeolian sediment transport could be significantly improved
by implementing the models with environmental conditions such as moisture content, grain size
distribution, micro-topography, salt cementation, shells remains, on the shear velocity, the
threshold velocity and the roughness length.
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