Journal of Coastal Research
SI 56
143 - 147
ICS2009 (Proceedings)
Portugal
ISSN 0749-0258
Large-Scale Circulation of Littoral Drift on Coast With Seasonal
Changes in Wave Direction and Amplitude
T. Uda†, T. Kumada‡ and M. Serizawa∞
†Public Works Research Center,
1-6-4 Taito, Taito,
Tokyo 110-0016, Japan
[email protected]
‡Laboratory of Aquatic Science Consultant Co., Ltd.,
1-14-1 Kami-ikedai, Ota,
Tokyo 145-0064, Japan
[email protected]
∞Coastal Engineering Laboratory Co., Ltd.,
301, 1-22 Wakaba, Shinjuku,
Tokyo 160-0011, Japan
[email protected]
ABSTRACT
UDA, T., KUMADA, T. and SERIZAWA, M., 2009. Large-scale circulation of littoral drift on coast with seasonal
changes in wave direction and amplitude. Journal of Coastal Research, SI 56 (Proceedings of the 10th
International Coastal Symposium), 143 – 147. Lisbon, Portugal, ISSN 0749-0258
In the long term, the direction of longshore sand transport in the shoreward zone is often reverse to that in the
offshore zone. This phenomenon has been observed at many coasts. Analysis using the contour-line-change
model proposed by SERIZAWA et al. (2003) has been applied to investigate this phenomenon, taking the
Kashimanada coast as an example. Its mechanism is explained by the large-scale circulation of littoral drift due
to the action of waves with different energy levels under seasonally changing wave conditions.
ADDITIONAL INDEX WORDS: Circulation of littoral drift, longshore and cross-shore sand transport,
change in wave direction, contour-line-change model
INTRODUCTION
When a groin is extended across the shoreline on coasts with
predominant longshore sand transport, the upcoast shoreline
advances, whereas it retreats downcoast. This is a well-known
fact, but is not always true on coasts with a seasonally changing
wave direction (KAMPHUIS, 2000). For example, on the
Kashimanada coast (Figure 1) facing the Pacific Ocean, waves
from the counterclockwise and clockwise directions relative to the
normal to the shoreline are predominant in winter and summer,
respectively, but the shoreline position on the south side of the
artificial headlands (HLs) on the coast always advances relative to
that on the north side, implying that the predominant direction of
longshore sand transport is northward. However, in reality,
southward longshore sand transport prevails on average and sand
has accumulated inside the wave shelter zone of Kashima Port
located south of the HLs owing to the wave-sheltering effect of
the breakwaters (MATSU-URA et al., 2008). KURIYAMA and
SAKAMOTO (2007) calculated the cross-shore distribution of the
mean longshore sand transport rate based on the long-term
observation of the velocity of longshore currents near the surf
zone at the Hasaki coast south of Kashima Port, and showed that
northward longshore sand transport dominates in the nearshore
zone, whereas in the offshore zone southward sand transport is
predominant. This observation suggests that the direction of mean
longshore sand transport is not necessarily uniform across the
nearshore zone, and that it may change over time. SATO (1996)
explained the fact that the predominant direction of longshore
sand transport differs in the nearshore and offshore zones as being
due to the effect of wind drift. This reversal of the direction of
longshore sand transport is considered to be very important in
predicting long-term beach changes, but the mechanism of the
phenomenon has not yet been clarified. The investigation of wave
observation data collected offshore of Kashima Port shows that
high energy waves are incident in winter, whereas in summer
relatively low-energy waves with a long duration are predominant.
Because the configuration of the overall coastline of the
Kashimanada coast has been in the equilibrium state, the total
wave energies in winter and summer must equal each other.
Figure 1. Location map.
Figure 2. Shoreline changes around HLs on Kashimanada coast
between 1986 and 1993
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Large-Scale Circulation of Littoral Drift
Otherwise, the overall shoreline would lose its equilibrium state.
Taking these facts into account, the cause of the reversal in the
direction of net longshore sand transport is considered to be
closely related to these wave characteristics. We numerically
investigate this phenomenon on the Kashimanada coast using the
contour-line-change model proposed by SERIZAWA et al. (2003).
Figure 2 shows the shoreline changes between 1986 and 1993
around HLs on the Kashimanada coast (UDA, 1997). Examining
the shoreline configuration between the headlands, it can be seen
that the shoreline has retreated on the north side, resulting in the
narrowing of the beach, whereas the foreshore is as wide as 70 m
on the south side, where a steplike shoreline has formed. Taking
into consideration the fact that the occurrence probability of highenergy waves on this coast is larger from the counterclockwise
direction than from the clockwise direction, as mentioned in the
next section, it may be expected that the shoreline around the HLs
would advance on their north side, in contrast to the observed
changes. The observed shoreline configuration, therefore, suggests
the predominance of northward longshore sand transport.
On the Hasaki coast south of Kashima Port, five HLs were built
north of Hasaki fishing port. The analysis of beach changes
around this fishing port shows that southward longshore sand
transport is predominant, resulting in the accumulation of a large
amount of sand inside the fishing port (NAGAYAMA et al., 2008).
Nevertheless, the shoreline on the south side of the HLs has
advanced relative to that on the north side, suggesting that the
direction of longshore sand transport has reversed. This shoreline
configuration around the HLs leads to the question of what the
predominant direction of longshore sand transport is.
Wave conditions on the Kashimanada coast were investigated to
analyze the formation of the asymmetric shoreline configuration
on the basis of wave observation data collected offshore of
Kashima Port. Figure 3 shows the wave energy flux ratio for each
wave direction represented by the 16 points of the compass
relative to the total energy flux with the significant wave height at
1 m intervals. The ratio of the ENE component predominates in
the entire wave height range. However, for high-energy waves,
i.e., a wave height of 3 m or higher, the ratio of the NE component
is high, whereas for low-energy waves, i.e., a wave height of 2 m
or less, the ratio of the ENE component is high, enhancing its
contribution to the total wave energy flux. In the subdivision of
the wave direction into the 16 points of the compass, each wave
direction θ has a variation of ±11.25º, and the accuracy of the
expression of wave direction is inadequate. Therefore, the ratio of
wave energy flux to the total wave energy flux for groups with 1º
intervals was calculated for both high-energy and low-energy
waves, the heights of which are greater and smaller than the
energy-mean wave height (1.6 m) over a year, respectively (Figure
4). The peak of the wave energy flux ratio is at approximately
N45ºE and N67.5ºE for high-energy and low-energy waves,
respectively. In other words, the incident wave direction varies
with the wave height. Figure 5 shows the probability of
occurrence of high- and low-energy waves: the probability of
high-energy waves is low, whereas that of low-energy waves is
high. Figure 6 shows seasonal changes in the probability of
occurrence of incident waves. Winter waves with high energy, as
shown in Figure 5, are incident from approximately N59ºE, and in
contrast, summer waves with low energy are incident from N89ºE.
Thus, the seasonal variation in wave direction is important for the
prediction of beach changes on this coast. Therefore, in the
numerical simulation, consideration of the wave incidence from
the counterclockwise and clockwise directions relative to the
direction normal to the shoreline is taken into account.
METHOD
The contour-line-change model (SERIZAWA et al., 2003) is
applied to predict the beach changes. The fundamental equations
of the contour-line-change model are expressed in terms of the
Figure 3. Relative wave energy flux ratio for each wave direction
separated by 16 points of compass of wave direction relative to Figure 4. Wave energy flux ratio separated into groups with 1º
total energy flux with ranks of the significant wave height at 1 m intervals to total wave energy flux calculated separately for highand low-energy waves.
intervals between 1991 and 2006.
Figure 5. Probability of occurrence of high- and low-energy Figure 6. Seasonal change in probability of occurrence of incident
waves.
waves.
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Uda et al.
Table 1: Calculation conditions.
Initial slope and equilibrium slope
Depth of closure hC
Berm height hR
Coefficient of longshore sand transport
Coefficient of OZASA and BRAMPTON (1980)
Coefficient of cross-shore sand transport relative to
longshore sand transport
Critical slope on land and seabed
1/50
10 and 6 m in winter and summer, respectively
3.3 and 2 m in winter and summer, respectively
A=0.5
ζ=0.0
Kz/Kx=0.2
Calculation domain
Mesh intervals, Time step
longshore and cross-shore sand transport rates, qx and qz, given
their depth distributions in the depth zone between the depth of
closure hC and the berm height hR, and the equilibrium slope of
sand, tanC. The contour line changes are calculated from the
continuity equation in the x-z domain using the longshore and
cross-shore sand transport rates qx and qz at each point on each
contour line.
In the calculation, a scale model of the Hasaki coast
(NAGAYAMA et al., 2008) south of Kashima Port is considered as
an example. In the calculation domain with fixed boundaries at
both ends, the wave conditions were assumed to be as follows: the
wave direction has a seasonal variation, as is the case offshore of
the Kashimanada coast, and winter waves have a high energy but
short duration (energy-mean significant wave height: Hw =1.85 m),
whereas summer waves have a relatively low energy but long
duration (Hs =1.49 m), so that the total wave energy in winter (Ew)
is equal to that in summer (Es). The duration of the winter and
summer waves was determined to be inversely proportional to the
power of 5/2 of the wave height (tw : ts = 37 : 63) because of the
equivalence of the total wave energy in winter and summer. This
assumption was made because the overall shoreline configuration
has been maintained in the long term. Regarding the time scale, tw
in winter and ts in summer are 135 and 230 days, respectively.
Since the time step is Δt=1 hr, one year corresponds to 8,760
steps: 3,240 steps in winter and 5,520 steps in summer.
Owing to the wave observation at a depth of 20 m offshore of
Kashima Port, the peak of the wave energy flux ratio is
approximately at N45ºE and N67.5ºE for high-energy waves in
winter and low-energy waves in summer, respectively, as shown
in Figure 4. These wave directions respectively make angles of
15º and -7.5º with the direction (N60ºE) normal to the contour line
of -20 m near the wave observatory. On the other hand, the
shoreline of the Hasaki coast extends parallel to the -20 m contour
line, except in the area offshore of the Tone River mouth, and the
direction of this offshore contour line is 3.6º counterclockwise
compared with that at the wave observatory offshore of Kashima
Port. Taking this difference between the directions of the offshore
contour line into account, the predominant wave direction can be
assumed to be 11.4º in winter and -11.1º in summer relative to the
mean direction of the normal to the shoreline of N56.4ºE on the
Hasaki coast. Finally, the breaker angle becomes 4.2º in winter
and -4.2º in summer by Snell’s law given the observed
predominant wave directions of 11.4º in winter and -11.1º in
summer.
Five calculations were carried out for different arrangements of
coastal structures: no structure in case 1, a groin with point depths
of 3 and 6 m is built at the center of the coast in cases 2 and 3,
respectively, and three groins with point depths of 3 and 6 m are
installed in cases 4 and 5, respectively. Table 1 shows the
1/2 and 1/3, respectively
X=0 to 16 km alongshore
Z=5 m to -15 m
x=400 m and z=1 m, t=1 hr
calculation conditions. The important point of this calculation is
that not only the wave direction seasonally changes, but also the
depth of closure hC and the berm height hR vary in response to
wave conditions. In winter, hC is larger because of higher waves,
whereas in summer, hC is smaller due to the incidence of calm
waves. When the wave direction seasonally changes under these
conditions, at a location in the offshore zone, the depth of which is
between the values of hC in summer and winter, sand can only
move in winter and not in summer. If sand is transported only by
longshore sand transport, the back and forth movement of sand
occurs every season, and sand that sinks in the zone deeper than
hC is left as it is. In this model, sand is first transported to near the
south end of the coast in the winter, and in the subsequent summer
nearshore sand is transported northward, with the result that the
local slope in the offshore zone becomes gentler than the
equilibrium slope of the sand. This causes onshore sand transport
due to the stability mechanism of the longitudinal profile based on
the relationship between the equilibrium slope and the local slope,
which is the most fundamental characteristic of the contour-linechange model.
Designating the depths of closure in winter and summer as hC1
and hC2, respectively, the relation between hC1, hC2 and the point
depth of the groin becomes important in terms of the passage of
part of the longshore sand transport offshore of the tip of the
groins. Here, we assumed that hC1 =10 m and hC2= 6 m, and the
point depths were assumed to be 3 and 6 m. In the case that the
point depth of the groin is 3 m, longshore sand transport can pass
over the groin in both winter and summer, but in the case that the
point depth is 6 m, longshore sand transport can partly pass
offshore of the groin in winter but not in summer. In the
calculation, the wave direction was periodically altered, and the
results after ten cycles of wave action were obtained.
RESULTS
Figures 7(a) and 7(b) respectively show the mean sand transport
flux in winter and summer after ten cycles of wave action under
the conditions of a periodically changing wave direction. In the
closed calculation domain, rightward sand transport flux is
generated in winter, in which sand movement occurs even in the
offshore zone. In contrast, in summer, sand movement does not
occur in the offshore zone because of the lower wave height, and
instead, leftward sand transport flux concentrated near the
shoreline was generated. Although the direction of the sand
transport flux is opposite in winter and summer, the cross-shore
width where sand transport occurs is wide in winter and narrow in
summer, during which sand transport flux is concentrated near the
shoreline.
Figure 8 shows the sand transport flux averaged over a year
after ten cycles of wave action. Although leftward longshore sand
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Large-Scale Circulation of Littoral Drift
transport prevails near the shoreline, the direction of longshore
sand transport reverses in the offshore zone, causing the largescale circulation of littoral drift. Rightward sand transport flux in
the wave run-up zone was generated by the difference between the
berm heights, hR1 and hR2, in winter and summer, respectively; hR1
is larger than hR2; thus, only the beach changes in winter remained
in the run-up zone between hR1 and hR2.
Without structures obstructing longshore sand transport in the
calculation domain (case 1), only the circulation of littoral drift
occurs as shown in Figure 8. When structures affecting longshore
sand transport such as groins or detached breakwaters are added to
the calculation domain, a large change is caused in sand transport
flux. Figures 9(a), 9(b) and 9(c) show the predicted contours in
winter and summer, and the bathymetry averaged over a year,
respectively, under the conditions that a groin with a point depth
of 3 m was constructed at the center of the beach (case 2). In
winter (Figure 9(a)), rightward longshore sand transport develops,
and part of the sand flows into the zone to the right of the groin
after turning around the tip of the groin. Simultaneously, the
Figure 9. Predicted contours under conditions that a groin with
a point depth of 3 m was constructed at the center of the beach:
(a) winter, (b) summer and (c) the bathymetry averaged over a
year (case 2).
Figure 7. Mean sand transport flux after ten cycles of wave
action (case 1): (a) winter and (b) summer.
Figure 8. Sand transport flux averaged over a year after ten
cycles of wave action (case 1).
contour lines advance on the left side of the groin, recede on the
right side of the groin and meander offshore of the groin. In
Figure 10. Sand transport flux averaged over a year after ten
cycles of wave action (case 2).
summer (Figure 9(b)), bathymetric changes opposite those in
Figure 9(a) take place, but the bathymetric changes on both sides
of the groin and the meandering of the contours offshore of the
groin become significant because of the concentration of sand
transport flux in the shallow zone. With regard to the bathymetry
averaged over a year, there appeared to be no changes in the
contour lines in the vicinity of the shoreline, but examining the
contour line changes in detail, it was found that the contour lines
near the shoreline advance to the right of the groin compared with
those to the left of the groin.
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Uda et al.
Figure 10 shows the sand transport flux averaged over a year
after ten cycles of wave action corresponding to the bathymetry in
Figure 9(c). Similar to the mean sand transport flux in case 1
without groins, as shown in Figure 8, the circulation of littoral
drift is generated, but is separated by the groin, resulting in the
generation of two clockwise circulations.
Figure 11(a) shows the shoreline configuration averaged over
the winter, summer and the whole year after 10 cycles of wave
action when a groin with a point depth of 3 m was built at the
center of the coastline. Although the shoreline periodically
changes on both sides of the groin, the shoreline averaged over a
year advances to the right of the groin. When the groin is extended
to a point depth of 6 m (case 3), the shoreline averaged over a year
further advances, as shown in Figure 11(b). This is because the
obstruction of rightward longshore sand transport in winter due to
the groin was enhanced by the extension of the groin. In case 4,
where three groins with the same depth as the groin in case 2
(shown in Figure 11(a)) were built, the difference between the
shoreline position on both sides of each groin further increases, as
shown in Figure 11(c). Figure 11(d) shows the mean shoreline
configuration in winter and summer, and that averaged over a year
when three groins with a point depth of 6 m were built (case 5).
Although the shoreline exhibits seasonal variation, the shoreline
configuration averaged over a year becomes steplike; the shoreline
to the right of each groin advances relative to that to the left. The
formation of an asymmetric shoreline on both sides of each groin
convincingly explains shoreline formed around the HLs on the
Kashimanada coast, as shown in Figure 2.
CONCLUSION
The general understanding that the predominant direction of
longshore sand transport is from the side of a groin on which the
shoreline advances to its opposite side is not always true, as
typically shown in Figure 11(d). KAMPHUIS (2000) qualitatively
discussed the same problem, but such mechanism was
quantitatively clarified in this study. On coasts where the wave
direction seasonally changes, sand transport flux circulates with
no net sand transport. This implies that judging the predominant
direction of longshore sand transport based on only the asymmetry
of the shoreline configuration may lead to an incorrect conclusion.
Furthermore, it should be noted that the asymmetry of the
shoreline configuration increases with the number of groins or by
the enhancement of the blocking effect of longshore sand transport
due to the increase in the depth (extension of the length) of groins.
LITERATURE CITED
KAMPHUIS, J., 2000. Introduction to coastal engineering and
management. Canada: World Scientific, pp. 275-277.
KURIYAMA, Y. and SAKAMOTO, H., 2007. Cross-shore distribution
of longshore sand transport averaged over a long period. Jour.
Japanese Coastal Eng., Vol. 54, pp. 696-700. (in Japanese)
MATSU-URA, T.; UDA, T.; KUMADA, T., and NAGAYAMA, H., 2008.
Evaluation of stabilization effect of artificial headlands built
on Kashimanada coast using model for predicting changes in
contour lines and grain sizes. Proc. 31st ICCE. (in press)
NAGAYAMA, H.; UDA, T.; MATSU-URA, T., and KUMADA, T.,
2008. Prediction of bathymetric and grain size changes around
port subject to active supply of sand from large river. Proc.
31st ICCE. (in press)
OZASA, H. and BRAMPTON, A.H., 1980. Model for predicting the
shoreline evolution of beaches backed by seawalls. Coastal
Engineering, Vol. 4, pp. 47-64.
SATO, S., 1996. Effects of winds and breaking waves on largescale coastal currents developed by winter storms in Japan Sea.
Coastal Eng. in Japan, Vol. 39, No. 2, pp. 129-144.
SERIZAWA, M.; UDA, T.; SAN-NAMI, T.; FURUIKE, K., and
KUMADA, T., 2003. Improvement of contour line change
model in terms of stabilization mechanism of longitudinal
profile. Coastal Sediments ’03, pp. 1-15.
UDA, T., 1997. Beach erosion in Japan. Tokyo: Sankaido Press,
p. 442. (in Japanese).
Fig. 11. Mean shoreline configurations after ten cycles of wave
action for (a) a groin with a point depth of 3 m, (b) a groin with
a point depth of 6 m, (c) three groins with a point depth of 3 m
and (d) three groins with a point depth of 6 m.
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