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BREAKWATER EFFECT OF A SUBMERGED HORIZONTAE7bø8ThFO1b.1813
Mikio Takaki
Department of Naval Architecture and Ocean Engineering Hiroshima University, Higashi-Hiroshima, JAPAN
Abs tract
The author has developed the breakwater using a submerged horizontal plate in
this paper. Firstly the extensive experiments have been carried out to
clarify the breakwater performance of a submerged horizontal plate. He has
found out a very interesting phenomenon in which two kinds of surface waves collide each other on the submerged horizontal plate and the total energy of
an incident wave reduces to less than approximately half due to the collision.
It has become clear from the experiments that a submerged horizontal plate is useful to reduce a wave height in low wave frequency, and it has an effect to
convert a long wave length into short ones. By applying these
characteris-tics, the author has proposed the new configuration of an efficient breakwater consisting of two submerged horizontal plates.
Introduction
The most popular facilities for control of ocean waves are fixed type wave barriers for harbors, which have been set up at comparatively shallow waters. While the water depth of 200 nautical miles offshore, which will be developed
in future, becomes deeper than 200 meters. Therefore it is impossible to
build up an usual fixed breakwaters, and "floating" breakwater has been
watched with keen interested in replace of it. Floating breakwaters have
some advantages comparing with fixed ones. They are a small building cost,
an easy interchange of sea water, no environmental destruction etc.
Con-sequently the construction of it in offshore has attracted a great deal of at-tention from the viewpoint of development of the marine resources.
Since it started to study regularly floating breakwaters in England more than
80 years ago, there has been a many kinds of floating breakwaters invented
un-der a many ideas, and some of them have been put into practical Let us
sort out the problems of the existing floating breakwaters. They are as
follows:
Difficult construction because of complicated configurations, Difficult positioning because of large drift forces,
Inefficient breakwater for long waves.
We have selected a horizontal submerged plate in order to find the solutions
of the above problems. It is because of a simple configuration and a small
drift force. So far there are a many studies 2-5) on the submerged plate.
Most of them are theoretical studies using potential theories, and there are
very few experimental studies. Therefore we have carried out the extensive
experiments to get the basic data concerning the wave transmission, reflection
and dissipation coefficients of a submerged plate and the effect of submerged
plate depths to them. We shall clarify the mechanism of wave breaking taking place on the submerged plate, and shall propose the new configuration of
effi-dent breakwater consisting of two submerged plates.
Experimental Condition
The general arrangement of the experimental conditions is shown in Fig. 1.
The experiments were carried out at Wave Making Tank (L * B * D * d = 42m *
l.2m * 2.5m * 2m) of the Department of Naval Architecture and Ocean
Engineer-ing, Hiroshima University. The two kinds of submerged plates were used in
this experiment, one was the length of 1 meter and another is 2 meters. By
adjusting the depth of the model, the submerged plate was set up to clarify the breakwater performance of a submerged plate in regular waves at six kinds
of submerged depths which were 0, 4.0, 9.0, 19.0 and 29.0 centimeters. The
regular waves with the wave slope of 1/40 were generated every 0.1 seconds
from 0.6 to 2.0 seconds. The reflection waves and the transmission waves
were measured by wave probes disposed as shown in Fig. 1.
Analysis of Wave Records
One example of the records of the regular incident, the reflection including
the incident, the reflection and the transmission waves is shown in Fig. 2.
The Incident wave were measured before a submerged plate was set up. The
reflection wave were obtained by deducting the incident wave from the
reflec-tion wave including the incident one at the same time. It is fair to say
that the reflection wave obtained by this method scarcely includes the
inci-dent wave. The reflection wave is almost a sine wave, while the transmission
wave is not sine. Therefore we have estimated wave energies by applying the
spectrum analysis method to these wave records in order to take the higher
or-der wave effect into account. We define the ratios of the reflection and
the transmission wave energy to the incident wave energy as the reflection and the transmission coefficient.
Let E1 be the incident wave energy per unit area. Then we can get the
fol-lowing equation,
E1 = ER + ET + EB (1)
where, ER : Reflection wave energy ET : Transmission wave energy
E3 dissipation wave energy due to wave breaking etc.
Now let us define the reflection coefficient CR, the transmission coefficient
CT and the dissipation coefficient CB as follows,
CR _ ER / E1
CT = ET / E1 (2)
C3 EB / E1
The transmission wave records f(t) can be expressed by the following Fourier
Integral,
2
i i A( W )
= - f f(t)cos(
W )dt Tr BC W ) = EI,R = i 2 - f f(t)sin( w )dt Tr Ew =tan{B(w)/A(w)}
Let Gp(W ) be the energy density, we get
G( W) 1 AC W )2 + B( W )2}Aw
Therefore the total energy per unit area EA can be obtained by EA = f G
op
C w) dwWe analyzed wave spectra using the sampling time of 0.02 seconds and the
num-ber of date of 1024, which were limited by the tank end effect.
The regular incident wave and the reflection wave are almost sine as shown in
Fig. 2. It is, however, impossible to estimate the wave energy from a sine
wave by applying the spectrum analysis method. Therefore in our analyses, we define the wave energy of a sine form as follows,
2
aI,R
(4)
(7)
where, a1
R are the amplitudes of the incident and the reflection wave, and
g is omitted in the above equation.
Experimental Results in Regular Waves
Since the tendencies of the breakwater performance on the plate length of i meter and 2 meters are almost the same, we show only the results of the length
of 1 meter in this paper.
Fig. 3 shows CR CT and C3 for the plate on a free surface(d=0 cm). As the
wave length ratio CL/A, L:plate length, X:wave length) becomes larger, CR
in-creases, while CT decreases. These tendencies of CR and CT to LIA are proper to a floating type structure 6) The experimental results are the same
ten-dency as the the theoretical one by Stoker, but they are smaller than the
theoretical values. It is because of the wave energy dissipation which the
wave breaking took place on the plate in the experiments.
The most interesting fact in the results of submerged plate is that CT becomes
to minimum value nearby L/A = 0.3 as shown in Figs. 4 & 5. CT of the
sub-merged plate depth of d=9 cm decreases more than that of d0 cm in the long
wave range. On the contrary, CR increases more than that of d0 cm in the
short wave range. In addition to that, C3 of the submerged plate is generally more than 50 percentages of the incident wave energy, which is
larger than that of d=0 cm. Therefore it seems that the breakwater
perfor-mances are caused not by the wave reflection which Ijima et al.4 and
Patarapanich have insisted, but they are caused by the wave energy
dissipa-tion due to the wave breaking. C9 is larger than CR at most of all wave
length range in our experiment. Consequently it seems that the breakwater
performance of the submerged plate is mostly caused by the wave energy
dis-sipation.
Mechanism of Wave Energy Dissipation
Fig. 6 shows the effects of the submerged plate depth:d to C9 in case that the
plate length is 1.0 meter and the wave slope is the constant of 1/40. The
wave energy dissipation coefficients of d0 cm and d=4 cm are almost the same,
and are scarcely affected by the submerged plate depth. While C9 of d9 cm increases larger than ones of d=4 cm in the long wave range where L/X is smal-ler than 0.45. As the submerged depth increases moreover, C9 becomes smaller than ones of d=4 cm at all frequencies in the experiment. Therefore it seems
that the submerged depth of d4cm to 9 cm is the optimum condition to
dis-sipate wave energy efficiently.
Now let us assume that the incident wave energy E1 can be divided into the up-per and the lower region of the submerged plate. We get the following
equa-tion,
E
E +E
I u d (8)
where, E wave energy in the upper region of the plate Ed wave energy in the lower region of the plate.
Fig. 7 shows the effects of the submerged plate depth:d to EE/EU. It can be
seen that as the submerged plate approaches to the free surface, the case of
99 / E > 1 (g)
appears in the long wave range, while in case of d19 cm, the case of
EB / E < 1 (10)
appears in all wave frequencies in the experiment.
It can be seen as the result of the above considerations that the wave energy
dissipation which is more than the wave energy assumed to be existing in the
upper region of the plate takes place, as the submerged plate is brought
close to a free surface. Namely it means that the submerged plate does not
dissipate only the wave energy of the upper region but also some of the lower
region of it. So we carefully observed the experimental conditions by using
the video tape recording. We have found out a very interesting phenomenon as
follows.
Assuming that the upper region of the submerged plate is a sort of shallow
waters, we can get the phase velocities of shallow water waves as shown in
Fig. 8. The phase velocity becomes slower as the water depth decreases.
Therefore the incident wave is firstly propagated with a phase velocity of the
r
the upper and the lower region of the submerged plate. The wave on the upper region of the plate changes into shallow water, and the phase velocity becomes suddenly smaller. On the contrary, as the wave of the lower region of plate
is propagated with the same velocity as before, it gets to the back end of the plate faster than one of the upper region of plate. So the wave of the lower region generates the free surface elevation at the back end of plate, and some
of them are propagated to backward at the same time, and it collides against the wave with the forward speed of the upper region on the plate, and finally
a wave breaking takes place. We call this phenomenon "backward flow breaker" hereafter. It can be considered that even a simple form structure such as a
submerged plate can get the good breakwater performance due to backward flow
breaker. This wave dissipation mechanism is proper to a submerged plate in the vicinity of a free surface, but it never takes place in case of floating
structures which covers a free surface.
In addition to that, another interesting fact is that a submerged plate has an effect to convert a long wave length to short ones. Fig. 9 and Fig. 10 show the spectra of the transmission waves in the submerge plate of d=9 cm and 29
cm respectively. The arrows in these figures correspond to the frequencies
of the regular incident waves. It can be seen from these figures that the
submerged plate converts the incident wave into the different kinds of waves, and especially the waves in higher frequencies range rather than an incident
wave frequency are generated by it. These phenomena strongly comes out, as
the submerged plate depth become smaller. Therefore it seems that backward
flow breaker is strongly related with this phenomena.
As backward flow breaker is deferent from a wave energy dissipation occurred
in weather side of the usual floating structure 8), and it is a sort of wave
interaction on the submerged plate. Consequently it seems that this type of
breaker does not affect the wave drifting force on this plate. It is, however, necessary to check up on it with an experiment.
Finally the comparative studies of breakwater performance of the submerged
plate and the usual submerged mound are shown in Fig. li. The
experimen-tal values of the plates are smaller than the submerge mound, it is because
that the experimental values of plate is estimated by the first order of the
Fourier analysis, and it does not include the higher order wave heights. It
is very interesting that only one submerged plate has almost same performance
as the usual submerged mound.
New Configuration of Breakwater
THe submerged plate has two special advantages. The first one is an
effi-cient breakwater for long waves denoted by the white circle, while the plate on a free surface is efficient for short waves denoted by the white triangle
in Fig. 12. The second one is to convert long waves into short ones as shown in Figs. 9 & 10. This trend strongly comes out, as the submerged plate depth
becomes smaller.
The new breaker configuration has been developed by applying the above two ad-vantages of the submersible plate. The design policies of the breakwater are as follows:
(1) A part of a long incident wave height is firstly reduced by a
it.
(2) Furthermore, the short length wave heights are reduced by the plate on a free surface.
Consequently the new breakwater configuration consists of two kinds of plates.
One is a submerged plate arranged at the weather side, and another is arranged
on a free surface at lee side of the former plate as shown in Fig.l2. We
call this configuration "step type breakwater" hereafter. The performance of
step type breakwater is shown by black circle in Fig. 12. It become clear
from this figure that the step type breakwater is more efficient than the double deck type breakwater denoted by the black diamond shape which has been
said to be one of the most efficient breakwaters
U.
Especially thebreak-water performance in long wave range is better than any other type one.
Conclusions
From extensive experiments carried out in regular waves, the breakwater per-formance of a submerged horizontal plate and the mechanism of breaking waves
were made clear in this study. Especially the transmission coefficient of
the submerged plate of d=9 cm reduces to a minimum, and more than half of
in-cident wave energy is dissipated. This wave energy dissipation is caused by
breaking waves called "backward breaker".
Secondly it was made clear experimentally that a submerged plate has a effi-cient performance as a breakwater for a long wave, and has an effect to
con-vert a long wave into short waves.
Finally by applying the above advantages, the new breakwater configuration
having good performance was developed.
Reference
Report of State of the Art on the Floating Breakwater, Japan National Committee for ECOR (1985).
Hino, M. and Yamasaki, T.,"Theory on Wave Reflection and Transmission to
Horizontal Plates", Technical Report, No. 9, Dept. of Civil Engineering,
Tokyo Institute of technology, (1970).
Hattori, S.,"Wave Height Transmission of Horizontal Plate Breakwater with Permeability", Proc. the 22th J. CONF. OF COASTAL ENG., JSCE, (1975). Ijima, T.,, Uwatoko, T., Ushifusa, Y. and Kojima, H.,"Experimental Study on
Improvement of Wave Interception by Sea-Balloon Breaker, Proc. of J. CONF.
OF COASTAL ENG., JSCE, (1986).
Patarapanich, N.,"FORCES AND MOMENT ON A HORIZONTAL PLATE DUE TO WAVE
SCATTERING", Coastal Engineering, 8, (1984).
Tasai, F.,"On the Drifting Force for Cylinders Floating on Waves", J. Kansai Society of Naval Architects, Japan, (1974).
Stoker, J.J.,"Water Waves", Interscience Publishers, Inc.,New York, (1957). Takagi, M.,"On Wave Drifting Force", 2nd Ocean Engineering Symposium, SNAJ, (1976).
Nagai, S., Kubo, N. and Kurata, K., 'Submerged Mound", Study on Control of
Waves on Coastline, Special Study Report on Natural Disaster, NO A-51-2
(1977).
LO 0.0 -LO -2.0 -3.0 = .0
Fig. i General arrangement of esoerimental conditie
r-i
j)
Wave4 WaveS Wave 6
a.5
(a> Incident wave )Tw1 aec, d4 cm, L2 si)
(C) Reflection wave
20
Fig. 2 Wave records
III
i,,, i
IlIIIttItTI
I,,
30 SEC If SECFIg. 4 Reflection, transmission and dissipation coeffjcjent of wave energy at submerged plate depth d4 cm
0 0.2 0.4 0.6 0.8 1.0 L2 1.4 1.6
Fig. 3 Reflection, transmission and dissipation coefficients
of wave energy at submerged plate depth d=0 cm
CR
10 15 20 25 30 35
Fig. 5 Reflection, transmission and dissipation coefficients of wave energy at submerged plate depth d-9 cm
7
Sua.P.Opth d - 0 Ct. P.L.ngt0i 0. - i Ct.by 5skr Ce C C.r _._V_.-C8 Sub.P.0.pth 4 - 4 P.L..nqth J. - i ¡ EpC...
CT __V__ C8 SsD.P.Septh 9 - 9 e. P.L.ngth t - i Cap C---Cr _._V_. C8 1.0 0.8 0.6 0.4 0.2 0I
U-U I-U--*
0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.0 0.8 0.6 0.4 0.2 0 U U U r01 / \ / v-v , 0.2 0.4 0.6 0.8, 1.0 1.2 1.4 1.6-J
4
20m 22v WavyWave J. Wave 2 Wave 3
10m I lv 7m r
-
-E(---o o CT L,'À
2.0 if i 0.0 -2.0 111 35 10 15 C 25 30r
1.0 0.8 0.6 0.4 0.2 L)-'I
0 0.2 0.4 0.6 0.8 LO 1.2 1.4 1.6Fig. 6 Comparisco of wave energy dissipation coefficients for Fig. 9 Spectra of transmission waves at the submerged plate
depth d.9 cm, length Lxi o various submerged plate depth
-L.a
OD
-
-....--0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Fig. 7 RatiOs of wave energy dissipation to inflow energy
on the submerged plates
/
Fig. a Phase velocity and breaking waves due to backward flow
on the submerged plates
0.04
0.0 2
T=1.2_
T=1.4
0 5.0 10.0 15.0 20.0 25.0
Fig. io Spectra of transmission waves at the submerged plate depth d.29 cm, length L-2m
Fig. TI Comparison of transmission coefficients between
the subaserged mound and the submerged plate
T=1.O sec.
-. w
Fig. 12 Comparison of transmission coefficients for various
types of breakwaters