A FIELD STUDY OF WAVES
IN THE NEARSHORE ZONE
by
1
S. Hotta , M. Mizuguohi2 and M. Isobe3
ABSTRACT
Initial results are described of precise observations of waves
shoaling in the nearshore zone. The key technique of the experiments is
a 16 mm memo-motion camera system by which long term measurements of
waves can be made simultaneously at many locations. Six or seven pairs
of synchronized cameras were mounted on a research pier crossing the
surf zone. The cameras were focused on target poles mounted on sleds
which were towed about 200 m outside the breaker line, and on a line of
poles jetted into the sea bottom across the surf zone. Waves transforming in the nearshore zone were observed from about 400 m offshore to
the shoreline. At present only the characteristics of the statistical
waves, wave height distributions, wave period distributions, and the
joint distributions of wave height and period are described as part of
the initial analysis.
INTRODUCTION
The authors have been carrying out extensive field studies to
better understand the characteristics of waves in the nearshore zone.
As a method of measuring waves, we have developed and applied a remote
sensing photographic technique utilizing synchronized 16 mm memo-motion
cameras to record the water surface elevation at fixed time intervals at
poles installed in the nearshore zone. The basic function of this
system is to take continuous synchronized pictures over a broad area of
the nearshore zone. Some results with this method have been already
presented (Hotta and Mizuguohi, 1980; Hotta, Mizuguchi and Isobe, 1981;
Mizuguehi, 1982).
The observation time of a single camera is limited by the length of
the film.
Such a short length of time is insufficient for a
quantitative discussion of some subjects, especially the statistical
oharaoteristios of waves. This problem was overcome by employing
cameras in sets of two and running them alternately. Film changing can
1.
2.
3.
Research Associate, Department of Civil Engineering, Tokyo
Metropolitan University, Tokyo, 158, Japan.
Associate Professor, Department of Civil Engineering, Chuo
University, Tokyo, 112, Japan.
Associate Professor, Department of Civil Engineering, Yokohama
National University, Yokohama, 210, Japan.
38
WAVES STUDY IN NEARSHORE ZONES
39
be done for the camera not in current use, enabling a continuous record
without time limitation. Using this method, and poles mounted as
targets on sleds, three observation of waves in the nearshore zone were
conducted.
Data sets long enough to discuss the statistical wave
characteristics were obtained at several points from about 400 m
offshore and through the breaker zone to a point near the shoreline.
In
the present article, only the characteristics of the wave height and
period distributions and their joint distributions are described as part
of the initial analysis.
2.
FIELD OBSERVATION
2.1
Study site and observations
The field observation site was at Ajigaura beach facing the Pacific
Ocean, and located about 200 km north of Tokyo (Fig. 1). At this beach
there is a pier operated by the Public Works Research Institute,
Ministry of Construction, for facilitating field studies in the
nearshore zone.
Observations have been carried out utilizing the pier
as a platform for the 16 mm memo-motion camera system. The average
tidal range at this beach is about 1.2 m and the beach slope is about
1/60 to 1/70. The beach sand size is in the range of 0.2 to 0.5 mm.
Three observations were carried out. The first was done on Sep. 2,
1980 using six pairs of 16 mm cameras and six sleds. The second and
third observaions were done on Sep. 8 and 9, 1981.
In the second
observation, seven pairs of cameras, six sleds, and a single pole
(installed by water jet and positioned near the shoreline) were used.
The waves at seven locations from near the shoreline to a position about
400 m offshore were observed.
In the third observation, five pairs of
cameras were employed to record the shoaling deformation, and the
remaining two sets of cameras were used for the observation of wave runup in the swash zone.
The six sleds were linked together at about 50 m intervals and
pulled offshore by a tug boat. The wave conditions were relatively
rough and the breaking height of the larger waves was 1.8 to 2.2 m. The
width of the surf zone by visual observation was about 200 a, and two or
three broken waves existed in the surf zone.
Photo 1 shows the 16 mm camera system in operation on the pier for
Ex810908 [The notation is: Ex (beach experiment), 81 (year), 09 (month)
and 08 (day)].
Photo 2 shows the sleds before being pulled to sea.
Photo 3 shows the sea condition and target poles on the sleds in
Ex800902.
Figures 2 and 3 show the positions of the sleds and the beach
profiles for the first and second observations, respectively.
In Fig.
1
3, A to E' are the positions of the sleds for the third observation.
The average breaker line by visual observation was between Station C and
D for Ex800902 and Ex810908. All stations were positioned seaward of
the breaker line for Ex810909.
40
2.2
COASTAL ENGINEERING—1982
Instrumentation
The sleds on which the target poles (8 m high) were mounted are
constructed of steel pipe 50 mm in diameter. The sleds are 5.5 m long,
2.1 m wide, and 0.5 m high, and weigh about 200 kgf. The cameras were
mounted on the pier. Three kinds of zoom lenses were employed, 150 to
250 mm, 80 to 150 mm, and 17 to 85 mm. Each pair of cameras was
equipped with the same type of lens.
The cameras were synchronized by a main control unit and connected
by the same number of relay units in pairs. One camera of a set stops
operation at a certain frame as directed by the main control unit, and
the other camera of the set automatically begins to operate. This
procedure is repeated and an observation can continue without time
limitation. The sampling interval is variable between 0.1 to 10. In
the present observations, a sampling interval of 0.2 s was used. The
water surface variation photographed by the cameras is transferred to
paper tape using a 16 mm film analyzer and an ultrasonic digitizer graph
pen system. Records on the paper tapes are then transferred to magnetic
tapes or disk for analysis by computer.
3.
RESULTS
3.1
Effective data
Ten rolls of films per set of cameras were taken for Ex800902.
Therefore 37,500 frames (7500 s) of data were completely obtained for
Stations A to F. During observation Ex810908, it rained after four
rolls of film were taken, and the observation had to be terminated
early. We had difficulty in handling the film in the rain, and a
portion of the data was lost. Effective data were 3800 s for Stations
A, B, C, D and E, 3599.4 s for Station F, and 3350 s for Station G.
Twelve rolls of film were taken for Ex810909. Data of 9120 s were
obtained for Stations A, B, C and D. However, the sled at Station E was
moved a few meters shoreward by large waves and went out of frame in the
sixth roll. The camera angle was adjusted, but the sled again went out
of frame in the twelfth roll. Thus a portion of the data at Station E
was also lost. The effective data at Station E was 3508.4 s for the
first part of the observation, and 4782 s for the latter part.
3.2
Number of waves defined by the zero-crossing method
Direct application of the zero-orossing methods creates a problem
for defining waves in the nearshore zone. That is, many small amplitude
short period waves are defined, especially in the surf zone. Figures 4
and 5 show the number of waves defined by the zero-up cross method for
the three observations. The number of waves given from limited data
were multiplied by the ratios of the total observaton time to the effective time. In Figs. 4 and 5, the number of waves defined with a minimum
wave height of 4, 6, 8, 12, 16 and 20 cm are also shown. D indicates
this minimum wave height (See also the number of waves defined in Table
1 and Fig. 7). A great number of small amplitude short period waves are
defined both inside and outside the surf zone. It does not seem reasonabale to take into consideration such small waves. However, no firm
physical criteria has yet been given for excluding small waves.
WAVES STUDY IN NEARSHORE ZONES
41
The problem of how to treat the small waves will not be discussed
further here. This and some related matters were treated by Hotta and
Mizuguchi (1980). In that reference, waves having a height smaller than
6 cm were ignored, based on accuracy limitations of the measurement
process. We further investigated the accuracy of this type of measurement of the sea water surface elevation, and have found that a maximum
error of +_ 2.6 cm should be expected. Therefore, we will continue our
discussion by ignoring waves lower than 6 cm. The treatment of the time
interval associated.with the omitted wave is also discussed by Hotta and
Mizuguchi. In the present paper, the time intervals of the omitted
waves were added to the trailing part of the preceding main wave,
referred to as the B-method in the previously-mentioned paper.
Viewing Figs, 4 and 5, it is seen that the number of waves'in the
surf zone defined by the zero-crossing method is larger than the number
in the offshore zone. The number of waves defined is constant in the
offshore, although some difference appears at Station E in EX8109O9
(attributed to missing data for that station). Therefore, the number of
waves is conserved in the offshore zone. The increase in the number of
waves defined in the surf zone is produced by the disturbance
accompanying wave breaking.
The symbol * in Figs. 4 and 5 is the number of waves defined after
applying a numerical filter which cuts waves lower than 0.04 Hz and
passes waves higher than 0.05 Hz. Due to filtering, 38O data points (76
s) were cut from the beginning and end of the time series. Because the
time periods of the defined waves with and without the filter are not
the same, we can not compare the absolute number of waves defined.
However, at Station A located near the shoreline in Ex800902 and
EX810908, the number of waves defined after applying the filter is
larger than the number defined without the filter. At other stations,
(more distant from the shoreline), the difference is small. This result
is interpreted as follows. The wave height in the neighborhood of the
shoreline is small, and anti-nodes of long period waves, such as edge
waves or two-dimensional on-offshore standing waves, can exist there.
The amplitudes of these long period waves rapidly decrease in the
offshore direction, and the effect of the long period waves on the
(ordinary) waves of period less than 20 s is small. We conclude that
the long period waves will have a proportionately larger effect on the
ordinary waves near the shoreline as compared to offshore.
3.3
Statistically representative waves
Values of the statistically representative waves, the wave grouping
parameters, statistics of the sea water surface elevation and spectral
parameters for each observation are listed in Tables 1 to 4. Table 2
gives the statistically representative waves defined without cutting the
small waves for Ex800902. Table 3(a) (not filtered) shows values
obtained by omitting waves lower than 6 cm and adding their time
durations to the front part of the following main wave. It can be seen
that the average wave heights and periods of the waves in Table 2 are
much smaller than those in Table 3, due to the effect of the many small
waves defined. However, the respective differences in the one-tenth and
significant waves are relatively small. This indicates that the large
waves in the wave distribution can be defined with little consideration
42
COASTAL ENGINEERING—1982
of the small waves. Table 3(b) gives the statistically representative
waves of Ex800902 after filtering. Concerning the mean wave, only the
values for Station A were altered by use of the filter.
Table 4 gives results from Ex810900 and Ex810909. From Tables 3
and 4 it can be seen that in the surf zone, the maximum, one-tenth, and
one-third waves defined by the zero-down crossing method are slightly
larger than those given by the zero-up crossing method. The zero-down
crossing method defines one large wave and one small wave, while the
zero-up crossing method defines two waves of almost equal equal height
when a wave trails a relatively smaller wave (Hotta and Mizuguohi,
1980). This kind of wave behavior is seen primarily at the breaking
point and in the surf zone. This is also the reason why a bi-modal
distribution of the wave height, and a double-peaked distribution in
joint distribution of wave height and period, are found for waves in the
surf zone.
3.1)
Shoaling of the statistically representative waves
Figure 6 shows the shoaling deformation of the observed statistically representative waves. The shoaling deformation curve given by
linear wave theory is also drawn. The corresponding wave height in deep
water was calculated by linear wave theory using the wave period and
depth at the furthermost station (Station F for Ex800902, Station G for
Ex810908, and Station F for Ex8l0909). The shoaling coefficient was
defined as the ratio of the measured (or calculated) wave height at each
station to the wave height in deep water, assuming normal wave incidence. The reason why Station E for Ex810909 was not used is that the
periods of the significant, the mean, and the root mean square waves
differed somewhat from the respective quantities at the other stations,
in spite of the fact that a constant wave period was found for the
offshore zone. At present, we can not say why this happened. The onetenth wave period at Station E for Ex810909 was almost the same as at
other stations in the offshore zone.
As can be seen in Fig. 6, the prediction of linear theory agrees
well with the shoaling deformation of the statistical waves in this
limited distance of approximately 200 m. It is well known that the
shoaling deformation given by linear wave theory does not give good
agreement with the measured results regular waves in the laboratory and
for individual irregular waves on field beaches offshore and in the
neighborhood of the breaker line. However, the prediction by linear
wave theory agrees very well with the shoaling deformation of statistical waves in the present field observation.
3.5
Wave height and period distributions
The distribution of wave height and period and the marginal
distribution of wave height and period at each measuring station are
shown in Figs. 7 to 11. Figure 7 shows distributions for Ex800902
including the small waves. Equi-number lines of 10, 30 and 50 waves are
drawn respectively with dotted, broken, and solid lines. Figure 7 shows
the process of change of the distribution. Figure 8 shows the distributions for Ex800902 omitting waves lower than 6 cm, and applying the
filter. Figures 9, 10, and 11 show the distributions for Ex800902,
Ex810908 and Ex810909 omitting waves smaller than 6 cm. The distribu-
WAVES STUDY IN NEARSHORE ZONES
43
tions in Figs. 8, 9, 10 and 11 are normalized by the mean wave height
and the mean wave period for 1000 waves. Equi-probability density lines
of 0.1, 0.5 and 1.0 are drawn with dotted, broken, and solid lines,
respectively. The interval of (H/H) and (T/T) is 0.2. A probability
density of unity requires 40 waves.
From these figures, the following may be pointed out:
1.
There is a strong correlation between wave height and period for
the waves lower than the mean wave.
2.
The marginal distributions of the wave height and period becomes
bi-modal, and the joint distribution exhibits two maxima in the
neighborhood of the breaking point. This tendency is particularly
strong if waves are defined by the zero-down crossing method. The
marginal distributions of wave height and period in the offshore
approach a distribution similar to the Rayleigh distribution, but
one which has a peak on the smaller side of the mean.
3.
The range of wave height distribution is broad at the offshore side
of the breaking point, whereas the range of wave period
distribution is broad in the surf zone. These phenomena can be
interpreted from the shoaling and breaking deformation of waves.
That is, with approach to the breaking point, the waves increase in
height and broaden the range of the distribution. After breaking,
the disturbance accompanying the wave breaking generates many
secondary waves having small periods, and the range of the period
distribution thus broadens.
4.
The linear correlation coefficients between individual wave heights
and periods for the surf zone are smaller than those at the
seaward of the breaking point.
5.
From Figs. 8 and 9, it is seen that the long period waves have
little influence on the joint distributions.
4.
COMMENTS ON THE MEASUREMENT SYSTEM
The photographic technique as described here has the distinguishing
merit that the sea water surface elevation can be sampled directly and
at closely spaced points over a long observation of time. Also, because
the method is direct, the data can be easily reviewed and checked.
However, the method has the disadvantage that it takes a great deal of
time and much labor to transfer the sea surface elevation from the film
to a form suitable for calculation.
From the viewpoint of data
handling, the 16 mm camera should be replaced by video television in the
future. But at the present time, film gives higher resolution than
video TV.
We would like to suggest to researchers who intend to apply
similar methods that a heavier sled than our sled be used to avoid
movement as happened in Ex810909.
44
COASTAL ENGINEERING—1982
ACKNOWLEDGEMENTS
The field observations discussed in this paper were carried out
under the supervision of Professor K. Horikawa, Department of Civil
Engineering, University of Tokyo.
The authors would like to thank him
for his considerable assistance and advice.
We appreciate the permission of the Public Works Institute, Ministry of Construction for use of
the pier. We would also like to express our appreciation to our university students who supported the field work. Without their help we could
not have carried out these field observations. We would also like to
thank Dr. N. C. Kraus and Miss T. Kohno of the Nearshore Environment
Research Center for proofreading and typing of the manuscript.
REFERENCES
Ezraty, R., Laurent, M., and Arhan, M.: Comparison with observation at
sea of period or height dependent sea state parameters from a
theoretical model, OTC 2741, 9th Offshore Tech. Conf., 1977.
Goda, Y.: The observed joint distribution of periods and heights of sea
waves, Proc. 16th ICCE, Vol. 1, 1978, pp. 227-246.
Hotta, S. and M Mizuguchi: A field study of waves in the surf zone,
Coastal Eng. in Japan, Vol. 23, JSCE, 1980. pp. 59-79.
Hotta, S., M. Mizuguchi and M. Isobe: Observations of long period waves
in the nearshore zone, Coastal Eng. in Japan, Vol. 2H, JSCE,
1981, pp. 1)1-76.
Mizuguchi, M.:
Individual wave analysis of irregular wave deformation
in the nearshore zone, Proc. 19th Coastal Eng. Conf. (in press),
1982.
SJ£" - so
DISTANCE FROM REFERENCE POINT
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Location map of the field
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Beach profile and positions
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45
WAVES STUDY IN NEARSHORE ZONES
1.5
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Linear Theory
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Fig. 6
Shoaling deformation of
statistically representative waves.
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Number of defined waves obtained by imposing a minimum wave
height (D) for EX810908 and EX810909.
0.1
COASTAL ENGINEERING—1982
46
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47
WAVES STUDY IN NEARSHORE ZONES
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Fig. 7
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1
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COASTAL ENGINEERING—1982
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Fig. 8
Normalized joint distribution after filtering for Ex800902.
49
WAVES STUDY IN NEARSHORE ZONES
H
1*
1
1
1
2
11) 101
1
1*
M
)9
11
2
1
T
1
1
!
|x
1
1113
11
1
I
)
i
I ,'»V
1 |ll
11
1
It
13
1
t
1,/0~«\1»
II
IT
1J
1
yi'.n i» i»\
IT
u i«
1*
»
10
/)/
•„J'''»
1
J
1
l
l
1
I*
111
/ 6 ,2*
1)
29
2J> 11
10
1
>
.»„-»--*-»" *\ 1
^-1— """
•
T 13
• "ft
1 '10 11
10 1> U 11 10
>|
1/
»
il) 11
1
1
1
i
M
1
H no ii 10 u y^'i* • i
h 1 ii i* ii ij/ii io *r"i
B,' II i» ai /i» i» > /i I
>
I
1
i
1
•i
A
B
r(H,T)=0.42
)
»t 1*1 11) 111 14*
I*
*4
M
1
it
i
*
r(H,T)=0.55
T
i
1«» 1»T l*t UT
41 1*9 1»
34
1
1
*
*
»
1
J
»
»
*
11
*
1
I
i
X
1 \1
U 1.
\
1
1
1
,
,
,
;
1
i
\j III 19 V> 1* 10
X , yfiy. U i
9
1
Ut
|*
1
»
1*
S
11/11
/7
J
"y i-> ti,-\i j*' «
i
i
1 'io
ii
/
I
IS/M
/4*19
M
I
17
10
I
2
)
i
i
//&*
ixiij/r
C
D
r(H,T)=0.46
r(H,T)=0.5e
T » i»o i»J is* 1ST m in
JO
II
E
r(H,T)=0.66
T/T
P
r(H,T)=0.68
Ex800902 UP-CROSS D=6
Fig. 9
Normalized joint distribution for Ex800902.
T/T
50
COASTAL ENGINEERING—1982
'
. ' ' '
10 N
1
v <•
/10
1)
10
-i
'
5
'
11
12
10
1
jyi>\i> i. *
(lj^n-^l£> xi io
l
x
:i;:A:
1
"\
*\
* ";
U
1J
13
1
J
10
11
4
)
'}
s
i
i
' * i^y
1
z''
ii
i
13
1
'
./, ../.. . . ,_p„ »
i
i
1
1
'
J
1)
11
11
I
»
t
10
f ••"'«-" 1
II
*
>•'
10
9)
1«
V
1
I
1
>" '
1
1
1
1
1
ilAn/-Ti A
1\TT-"T>-1
s
—•"
A
r(H,T)=0.58
1
»1 I'l !•» 10* 101 130
r(H,T)=0.59
T
ii
i
*
i
1*
i
11 103 141 191 13* 1*+ lot
Jl
13
*
1
1
.
i
11)1
1
1
i
3
1
1
i
i
i
\
)
i
1
i
'
i
!
V' 11
. ; .
tf;\::
II
\
X
u
13
1*
1
13
ir
is
i»
,ii
ii
i*
10
fll
—rtr
13
/&
s
t
*
l
-4
i
l
i
ii
ii'
10
1*
1
'/" V" ••)"
i
1/ 10 ^9
3
1
i
,l
IT/
I»
1
1
\ 1
1
i.
/
1«
31 l>»
I»
'»_i^ 1) /l
1
3
/lJ\A\ »» /fiTJ 10
i
1,
(di.3^'^-'rr
""A
') ' \'
/ ' \
/
i
3
Ai»,W
C
11
r(H,T)=0.57
D
60 1»T 131 111 1* 3 169 11*
»J
1
1
1
r (H,T)=0.58
} 1J0 137 13* 199
1
1
1 /
1
1
S
\
i ^/ ii a
IX
X
X
«
10
11/ 1* \»
!
i\
11 |
y'lyi^V
1
> •'» i/ )9 ft.
1
»(
y' l*
A>''>2
ii/ 1
it
19
/ll
30
to
il 1
»N
i
• 11
1
V
30 u/
if'a
« ' i ,,-s
i
Iju-"-'
E
r(H,T)=0.68
T/T
F
r(H,T)=0.69
EX800902 DOWN-CROSS D=6
Fig. 9
Normalized joint distribution for Ex800902.
T/T
WAVES STUDY IN NEARSHORE ZONES
1
• i •
N
4
11
10
.*•"!
l'l 1 1»
r(H,T)=0.52
IS
39/u
10
i
|I
•
*
1
r-v)
/)
1
1
1
»
1
1
*J
t
r{H,T)=0.52
i
v*"^
^KT^ ;
,<»
° "•
11
;,-'f
?* 1CT 1*» 100 1»» 111 101
*
i
'^i.Vioi^s", 'i i'--
iVf.
A
*
'.
'; , '
'\.'._.'. > i •
,'i«/ 1>\ 11
SO/lt ,11
51
1 ,/•
,,'1
11
1J \
IV »\ 1*
*.,
__;.,•; ,,<:<&: . >
, ;
A
|l
is;y?y
/CI-TT-T
! 1
»
.
1
U
i> j 11
111 J.
fi\»_ n \£5
i* iu
II /(\
2
>
x
*
*
4
u
I'I
j
l
'
!. 1, .1 7j)., .1
f-
y.i©^ .. . i..v
C
r(H,T)=0.66
D
r(H,T)=0.64
in
*» 111 101 1
1* 20* 10* 111
1
n\
X
vrj®
r(H,T)=0.57
»
1
*
/^'--^ '
/
T/T
F
it
QQA\S\I/
11
j>-^o,yi
IT
10,-''l
ill
r(H,T)=0.60
Ex810908 UP-CROSS D=6
Fig. 10
t
V '
yy>
yyy-'y
E
»
Normalized joint distribution for Ex810908.
J
T/T
52
COASTAL ENGINEERING—1982
i
;^i
i'f»
ll/l
&
A
s
j
y
)
i«
*
ii
10
^1
ii'V*
10
10
10
M ill
12
10
*
*f)/1*
1
,*-' 1
1 „-<'
1
i2,.--r"T
r(H,T)=0.61
B
r(H,T)=0.68
1*1 32J 11
11)
21
It
2
2
1
'"A
1
2
•r' 10 ^UJ*1»
II
I
1
t'' u pi/to *f jyiy u
/•
fit
10 UlV^*T
**y^i*y^j.'''i
It
1»
10
U
|'i
-'•-"*»
-(^ i
!_,•'*!
f iy fSa z SU)
i
1
•i
y,
h
i"
i1'
1
1
\ 1
2
2
2
•
11
IT
1
) \21
It
1
•j
It' 11
*t
:J
'
-Ti'y* '/•'''
("Is^l7-.-'
C
-.1
r(H,T)=0.62
TO
*3 10* Itt 2*2 20*
D
tl
11
10
12
r(H,T)=0.63
MO*
•
It 2»* iU
1
1
J
/ » «
i\
1 /J /l«
II
\(
10
/• y&<
"1"
J1J1__11 / 10
/ 1J,'"2)
/
"»\
2
1
2*
\
ll! Ill >. \J \
1
•/» >l^>/ y •
1
,X
y''
12^-fl
i*y it i*x
J
2»
Jl/
J,''2
S
»»/
••V<Sl!yf.</'~~"
E
r(H,T)=0.58
T/T
F
r(H,T)=0.60
EX810908 DOWN-CROSS D=6
Fig. 10
Normalized joint distribution for
EX810908.
T/T
53
WAVES STUDY IN NEARSHORE ZONES
11
'* *' *'
lie Ml jJt
»D
J*
t
i
•
j
/f';\
•
1
li
,! 1. y ..... ,
,
.'T
*
11 1
1
/.^V-
.-*"* *
V, .
tfggk
1---''
\\i _1J.--'I
G
T/T
r(H,T)=0.57
G
r{H,T)=0.58
DOWN-CROSS
UP-CROSS
Fig. 10
Normalized joint distribution for Ex810908.
Photo 2
Photo 1
T/T
Sleds prior to being
pulled out.
16 mm camera system in operation
on pier for Ex810909.
Photo 3
Sea condition and target poles.
COASTAL ENGINEERING—1982
54
j
1
>
1
1
>
1
1
1
i y
i
n
it /St—to
U
1*^21
?l/ri
2J
<0
10
1)
I
1
1
it
i
>
i
1
.<'
l/ 3
y*
T
1)
i
1
*
* l( )
i)
n\i
u i) ii
if IS/*'
1*
i/m
)7
J*
JJ/Il
T\
/IJ
u
1
i
i
i
*) i
*/l
i
»__y »
i
n
i
x
/y*y%jr \-j''"" '
I
r(H,T)=0.65
17
i
)
i fa ii,Ai a ii ly u
lb
20/"lS
i
I
1
/•"" T\
19
/
i
1
r(H,T)=0.61
91 1»J 11* 1*1 1J» li*
tl
t
3
I
J*
32 103 ll« 1*3 1*3 1*» i*i
»•
i
i
i
i
i
1
1
2
1
1
1 AN 1
x
li
z
11
\
x
10
21
»\
i/io
1/ 7
U
'•
i> •HN 11
i
, , /, f.<
yy» »
/<?> 'V<V' '
.1)
C
u,---i
!
1!
/
">N
^•.
T
10
*"\
IT
±7
,\
»
IT/ 11
I
1 \
j 10
Ij/ll
/ ll/Sl
2«
I*/lT
jl
I
10/1
/yiyanfu „ ./,
/" " ^' » »
,-r".
i /VOy !j/^*" jo.'--r
i
1
I
(a/iC^'""
i
r{H,T>=0.65
D
r(H,T)=0.68
T/T
S3 10) !•* 13» 1*2 IT* lit
Fig. 11
Normalized joint
distribution for
E
r(H,T)=0.67
T/T
Ex810909 UP-CROSS D=6
EX810909.
55
WAVES STUDY IN NEARSHORE ZONES
'
, , ,
^ :j
>
.... ,
yi
X
/'/" ^ y
A
r(H,T)=0.62
B
r(H,T)=0.59
" "
l01 l
" l" "°l,i
1
1
1
V
ViV,
.'10/fl
A
C
,'* /4*
r(H,T)=0.65
D
10
/*
U
1
1
-V 1
1
,1
1
1
1
x
13
,.
^.'
Violi 1
Jl
il
IT
JJ/n
i/ *
__A--''i 1
r(H,T)=0.72
Fig. 11
1)7
i
T/T
Normalized joint
distribution for Ex810909.
<• \2 1"!!£ .I
E
r(H,T)=0.70
T/T
Ex810909 DOWN-CROSS D=6
56
COASTAL ENGINEERING—1982
0=0)
EX800902
Ex81O908
UP
DOWN
A
8
C
D
E
F
A
B
C
0
E
F
d
1.81 1.B4 3.22 2.79 4.93 5.14
1.81 1.84 3.22 2.79 4.93 5.14
N
1737 1597 1657 1308 1319 1282
1738 1597 1667 1308 1318 1283
H max
T max
166
K 1/10
T 1/10
I
T
217
243
217
242
119
137
140
167
135
139
6.53 6.89 6.71 8.18 8.89 9.20
H 1/3
T 1/3
189
2.94 7.51 9.29 8.21 9.66 12.0
98
114
107
123
105
109
6.36 6.73 6.37 8.04 8.34 8,66
56
65
64
69
61
64
4.31 4.69 4.52 5.73 5.68 5.84
H rms
66
78
74
84
72
75
173
186
208
241
228
208
3.17 12.5 10.3 10.2 10.8 9.40
112
131
138
160
135
138
6.11 7.25 5.89 8.36 8.93 9.05
92
108
107
119
104
0
/ffl
&!
4.08
319
B
C
D
19
22
36
.02 0.96 1.37
E
34
F
35
G
35
.98 0,68 0.89
.43 4.06 5.14
.45 3.56 4.34
344
160 1228 1215
462 1305
n
40
e
v
0.95
.95 0.96 0,97
.98 0.99 0.99
1.22
.17 1.16 1,00
.96 1.22 1.08
A
6
r.
0
E
F
A
23
27
28
30
28
30
41
1.26 1.25 0.93 1.16 0.64
.51
1.37 1,09 0.88 0.81 0.52
6.05 4.89 4.36 5.43 3.73 3.43
528 74B 960 926 777 872
5.05 4.64 4,16 4.03 3,53
11
18
-2
-11
-30
-6
108
6.50 6.22 5.95 7.88 8.12 8.63
56
65
64
69
61
64
4.31 4.68 4.52 5.73 5.68 5.84
64
75
74
82
72
74
Ex800902
T rms
5.02 5.37 5.11 6.47 6.43 6.57
4.94 5.34 5.05 6.43 6.39 6.55
0.68 0.69 0.66 0,70 0.78 0.82
0.47 0.58 0.58 0.66 0.76 0.80
o
r(H)
r(T)
-.13 -.14 0.02 0.11 0.25 0,30
0.01 0.00 0.08 0.26 0.29 0.32
/el
-.04 -.04 -.05 0.13 0.22 0,24
0.05 0.01 0.05 0.21 0.24 0.28
WG 1/3
217 198 201 131 116 119
1.14 1.11 1.13 1.30 1.47 1,48
1.19 1.20 1.14 1.36 1.46 1.49
n1
n
WG a
7.95 8.06 8.24 10.0 11.3 10.8
511 464 421 314 292 365
8.47 8.97 8.32 10.9 11.3 10.8
480 430 407 279 285 248
U
Ta
1.58 1.66 1.75 1.88 2.03 2.25
1.72 1,83 1.80 2.04 2.12 2,31
Ta
3.40 3.44 3.94 4.17 4.51 4.84
3.6? 3.71 4.08 4.69 4,62 5.19
Table 2
0.72
"P
r(M)
T 1/3
Tl/3
A
18
206
178
199
121
117
120
Si
e
27
0
-2
13
24
0.94 0.94 0.97 0.97 0.98 0.98
0.86 0.86 0.85 0.83 0.85 0.86
Table 1
Statistically representative
waves for Ex800902 including
small waves.
23
3 a
1 a
a
02
ectral width parameter defined by
E=
40
0
E
43
46
3
-3
-17
18
15
0,97 0.98 0.98 0.99 0.99
1.03 0.86 0.92 1,0" 0.99
Statistical parameters of sea
water surface elevation, and
spectral parameters.
number of waves defined by zero-crossing method
maximum wave height (cm)
maximum wave period (s)
one-theth wave height (cm)
one-tenth wave period (s)
significant wave height (cm)
significant wave period (s)
mean wave height (cm)
mean wave period (s)
root mean square wave height (cm)
root mean square wave period (s)
correlation coefficient between individual wave height and period
correlation coefficient between successive two wave height
correlation coefficient between successive two wave period
number of run exceeding significant wave height
mean length of run for WG 1/3
mean length of total run for WG 1/3
number of run exceeding mean wave height
mean length of run for WG a
mean length of total run for WG a
standard deviation of sea water surface variation
skewness of sea water surface variation
kurtosis of sea water surface variation
mean root square of sea water surface variation (variance) (cm2)
mean water level from reference elevation (Cm)
spectral width parameter defined by
40
1692 1594 1631 1861 176B
LIST OF SYMBOLS
water depth (m)
H max
T max
H 1/10
I 1/10
H 1/3
T 1/3
H
T
H rms
T rms
r(H,T)
KH)
r(I)
WO 1/3
J 1/3
I 1/3
WG a
Ex810909
B
C
I'l-m^/imQia^)} '
l/3
y=
v= [m
[is]0
m^/ai^-]
QDi
2/m^-1]]''3
nn=nofnS(r,df
57
WAVES STUDY IN NEARSHORE ZONES
EXB0090?
(D-8)
EX800902
UP
DOWN
A
R
C
D
E
A
F
1
P
E
1.81
.84 3.22 2.79 4.93 5.14
1.81 1.84 3.22 2.79 4.93 5.14
N
1434
348 1445 1118 1142 1082
1435 1348 1445 1118 1141 1083
T max
H 1/10
T 1/10
H 1/3
T 1/3
i?
T
H rms
T rms
r(H,T)
166
189
217
243
217
242
2.94 7.51 9.29 8.21 9.56 12.0
m
140
144
173
139
119
112
130
110
65
75
71
79
69
73
85
79
91
78
B2
5,90 6.16 5.74 7.28 7.14 7.46
r(H)
0.58 0.59 0.57 0.58 0.68 0.69
-.15 -.14 -.03 0.17 0.24 0.29
r(T)
0.00 0.02 -.03 0.12 0.15 0,20
228
139
98
115
142
112
168
127
139
109
65
75
71
FILTERED
UP
79
69
173
142
F
188
223
244
216
121
141
101
118
144
111
172
130
139
110
75
70
79
70
84
70
79
91
78
172
115
95
E
F
178
201
236
222
217
135
113
140
110
165
126
138
109
140
112
6.01 7.03 6.05 8.38 8.52 8.96
62
75
70
79
70
72
4.87 5.(6 5.10 6.72 6.69 6.72
81
0.00 0,06 -.09 0.14 0.18 0.22
D
6.31 7.95 5.86 8.89 9.04 9.15
72
5.50 6.06 5,63 7.24 7.23 7.27
0.60 0.60 0.57 0.60 0.66 0.73
-.14 -.14 -.06 0,18 0.26 0.32
C
3.14 11.1 10.2 10.2 11,1 10.1
113
4.87 5.46 5.10 6.72 6.69 6.72
B
1508 1344 1440 1084 1097 1091
141
6.62 7.22 6.66 8.44 8.68 8.94
62
A
229
6.69 7.30 7,16 8.73 9.13 9,36
74
0.42 0.55 0,46 0.58 0.66 0,68
-.01 -.03 0.04 0.29 0.29 0.32
0.04 0.30 0,08 0.18 0.21 0.23
E
5.62 7.41 9.57 9.15 9.29 10.9
114
5.22 5.60 5.18 6.71 6,56 6.92
71
79
B9
83
78
82
5.87 6.18 5,69 7.27 7.11 7,45
0
1508 1344 1440 1093 1098 1092
208
6.53 7.19 6.35 8.40 8.49 8.96
C
68
82
78
89
78
80
5.44 6.06 5.56 7.24 7.19 7.25
0.40 0.S2 0.43 0.59 0,63 0.72
0.01 -.01 0.02 0.29 0.32 0.36
0.06 0.06 0.05 0.18 0.26 0.26
182
163
170
99
158
148
163
107
T 1/3
1.12
.14
.19 1.35 1.48 1.52
1.25
.20
.20
.35
.48 1.48
1.15 1.13
.13 1.29 1.47 1.57
1.24 1.19 1.16 1.3B 1.53 1.60
Tl/3
7.B4 8.27 8.51 10.2 1!,0 11.0
8.98 9.10 8.88
0.5
1.6 11.7
8.05 8,33 8.44 10.0 10,9 11.5
8.67 B.60 8.09 10.4 10.7 11.7
227
231
412
j a
Ta
1.75
37B
379
250
104
241
B
'JG 1/3
WG a
110
117
74
5.22 5.55 5.18 6.70 6.57 6.92
208
7.02 8.33 6.17 9.01 9.07 9.16
115
6.90 7.21 6,76 8.34 8.71 8.97
191
3.17 16,2 1.26 9.92 10.8 10.5
143
7.00 7.26 7.02 8.50 9.13 9.36
103
173
A
F
d
H max
(D-S)
DOWN
C
233
206
.83 1.70 2.02 2.21 2.39
3,48 3.56 3.82 4.48 4.91 5.26
381
357
363
99
136
93
439
211
1.85 1.90
.73 2.13 2.14 2.35
3.77 3.78 3.98 4.93 4.95 5.15
159
37B
170
385
109
242
101
218
95
207
d
H
H max
T max
H 1/10
T 1/10
H 1/3
T 1/3
R
T
H rms
T rms
C
0
691
117
[0F
C,
515
530
516
422
460
145
253
265
218
247
)
EX810909
A
B
C
D
E
F
G
0.95 1.31 1.19 1.95 3.28 4.22 4.34
899 691 615 530 616 421 461
114
136
137
242
268
241
255
7.37 9.81 10.5 9.62 9.25 9.80 B.69
64
75
92 160 149 139 137
5.93 7.72 9.B5 9.04 8.93 9.37 8,83
116
106
98
98
5.09 6.54 8.01 7.72 7.98 8.13 7.81
r(H,T)
0.61 0.68 0.62 0.63 0.56 C.60 0.58
r(H)
r(T)
-.11 0.11 -.07 0.12 0.30 0.33 0.27
-.03 -.02 0.09 0.10 0.12 0.20 0.10
A
R
C
UP
0
E
9.53 8.75 8.80 8.92 9.20
8.79 8.49 8.53 8.73 9.11
B7
4.23 5.47 7.36 7.15 7.35 7.19 7.26
6.65 6.68 6,69 6.74 7.17
43
47
50
55
66
70
102
114
94
106
88
99
98
5.08 6.57 8.00 7.71 7.95 B.16 7.82
0.52 0.52 0,66 0.64 0.57 0.60 0.57
-.00 O.05 0,03 0.22 0.36 0.28 0.29
0,02 -.02 0.15 1.12 n.20 0.21 0.13
5*
fl
40
*o
45
106
78
128
121 115 118 114
7.26 7,23 7.22 7.32 7.71
0.62 0,59 0.65 0.72 0.70
0.05 0,14 0.27 0.24 0.29
41
48
.31 1.31 1,43 1.39
.31
1,10 1.24 l.lfi 1.30
.55 1.47
.36
8,40 8.B3 ?.27 9.P2
C.-i 10.3
0.3
9.20 9,98 10.8 10.9
Ta
249 198 131 121
94
76
92
1 .59 1.72 2.26 2.25 2.59 2.76 2.30
1.80 1.8? ?.?i 7.33 2.61 2.68 2.29
Ta
3,59 3.50 3.92 4.39 5.4B 5.53 4.9B
4.06 4.OR 4.3= *,75 5.59 5.45 4.92
WG a
Table 4
288 335 328 32B 336
12.4 9.34 8.63 8.72 8.37
213 219 207 207 200
181 173 162 167 161
8.20 B.23 8,56 8.94 9.29
112 106 102 104 101
0.4 8.06 9.79 10.4 9.62
53
E
8.46 8.13 8,78 9,23 9.82
1.10 1.17
64
0
1370 1364 1362 1363 1164
7,67 8.57
49
C
1370 13G5 1362 1353 1163
278 323 316 322 345
8.00 5.44 7.60 9.66 10.6
212 221 206 213 207
Tl/3
80
B
2.28 3.52 4,73 5.08 5.45
3" 1/3
116
A
2.2B 3.52 4.73 5.08 5,45
0.12 0.16 0.23 0,19 0.20
146 136 126 124 112
1.31 ,29 1.45 1.3B .35
WG 1/3
(D-M
DOWN
7.29 9.32 9.67 8.61 8.70 9.3! B.56
68
79
99 162 150 138 138
6,29 8.32 8.90 8.53 8,74 9.29 9.02
43
50
66 102
94
88
87
4.22 5.46 7.35 7.16 7.35 7.19 7.27
7!
200
3.76 3.83 3.87 5.04 5.28 5.47
5.40 15.1 10.0 9.87 9,40 8.74 10.8
81
93 108 IBB IBB 169 174
56
208
89
1.B1 1.91 1.69 2.19 2.30 2.46
8.66 4,12 11.3 10.1 10.8 7.75 B.89
86
93 103 186 189 170 175
46
216
97
3.44 3.55 3.72 4,49 5.05 5.28
UP
E
0.95 1.31 1.19 1.95 3.28 4,22 4.34
B98
122
372
105
Statistical representative waves for Ex8009O2.
EX810908
B
351
176
(b)
DOWN
A
401
154
1.68 1.81 1.64 2.02 2.31 2.43
(a)
Table 3
174
220
170
118
112
92
77
93
0,1
325 320 283 283 231
2.14 2.02 2.23 2.24 2.31
4.20 4,26 4.87 4.78 5.02
Statistical representative waves for Ex810908 and
178
113
170
106
163
102
165
104
159
101
5.66 6.68 6.69 6.73 7.17
126 120 115 117 113
7.26 7.24 7.24 7.30 7.73
0.65 0.51 0.65 0.68 0.67
0.15 0.22 0.28 0.29 0.33
0.14 0.19 0.24 0.23 0.22
1.30 1.36 1.45
.40 1.39
9.13 9.76 10.6
0.7 10.9
150
310
140
299
126
274
126
266
104
224
2.21 2.16 2.27 2.35 2,43
4.42 4.54 4.97 5.08 5,21
EX810909.