Open Journal of Marine Science, 2011, 3, 69-72
doi:10.4236/ojms.2011.13007 Published Online October 2011 (http://www.SciRP.org/journal/ojms)
Copyright © 2011 SciRes. OJMS
A Field Experiment on the Recurrence of Large Waves in
Wind Seas
Paolo Boccotti
NOEL Laboratory, Mediterranea University, Reggio Calabria, Italy
E-mail: boccotti@unirc.it
Received May 10, 2011; revised July 18, 2011; accepted July 25, 2011
Abstract
Wind generated sea waves are generally regarded as an example of pure randomness in nature. Here we give
a proof that the matter is not exactly so: some identical sequences of relatively large waves were found many
hours apart from one another. This finding supports the theory of quasi determinism of sea waves.
Keywords: Experiment, Wave, Groups
1. Introduction
Waves generated on the sea surface by winds and associ-
ated stresses have a random nature. Strictly speaking,
this means it is nearly impossible that an observer taking
a sequence of snapshots of such waves will ever obtain
two identical scenes. However, the quasi-determinism
(QD) theory [1-14] suggests that an exceptionally large
wave belongs to a well-defined sequence of waves
whose configuration depends on the energy spectrum of
the sea state, and on the configuration of the solid
boundary (with the shape of the energy spectrum, and the
configuration of the solid boundary that may be arbi-
trarysee [9]). This in turn implies that two exception-
ally large waves in two sea states with the same spectrum,
and with the same configuration of the solid boundary
(and in particular with the same bottom topography),
should belong to two identical sequences of waves. This
is what our field experiment aimed to verify. The ex-
periment was performed on the sheet of sea of the NOEL
laboratory at Reggio Calabria (Italy).
2. The Field Experiment
A horizontal beam was placed 1.2 m beneath the mean
water level (see the scheme of Figure 1). The beam was
15 m long and placed orthogonally to the shoreline, ap-
proximately. It was mounted with 26 pressure transduc-
ers for measuring pressure head waves induced by
wind-generated waves on the sea surface, as schemati-
cally illustrated in figure 1. Each pressure transducer was
connected to a small vertical tube (0.40 m long) with a
bending section at the top (like a small periscope). The
opening at the top of this small tube was in a vertical
plane orthogonal to the shoreline. This tube was not
strictly necessary for our experiment, and it served only
to measure pressure head waves in the undisturbed wave
field. Thanks to the small tubes, the pressure head waves
were measured 0.40 m above the horizontal beam which
consisted of a truss of high stiffness and small section.
As to angle
of the dominant wave direction it was
estimated from the relative phase of point 26 and point
27. Pressure transducer 27 (not seen in fig.1) was 0.75 m
from transducer 26, and these two transducers were
aligned with the shoreline.
Obviously, the experiment could have been carried out
by measuring surface waves. The preference here for
pressure head waves is because they are not much af-
fected by a high-frequency noise and also because meas-
urements made by pressure transducers are in general
more precise and reliable than surface measurements
gathered with resistance gauges, buoys, radars and other
means.
In summarizing the experimental results, we will let
EW denote the largest pressure wave observed in a
five-minute recording of pressure fluctuations gathered
at the 26 transducers. The objective was to search if we
could find two EWs: i) being of the same type: zero
up-crossing (U) or zero down-crossing (D); ii) occurring
at the same location i (with I = 1, 2,..., 26 being the loca-
tions of the transducers); iii) having some very large
(with
being the ratio of a crest-to-trough height of a
pressure-head wave to
p
the root-mean-square pres-
sure-head of the sea state); iv) belonging to two sea
P. BOCCOTTI
70
Table 1. The particulars of the three pairs of records with similar basic characteristics.
EW sea state
Dataset record time date
type i
p
(m)
T
p
(s)
*
1101 7 AM 5/17/10 U 17 8.908 0.064 2.58 -16.7
o
0.837
1 1276 11 PM 5/17/10 U 17 8.178 0.052 2.52 -18.3
o
0.831
1107 8 AM 5/17/10 U 13 8.357 0.050 2.44 -15.7
o
0.823
2 1280 0 AM 5/18/10 U 13 8.182 0.053 2.47 -19.3
o
0.832
2554 8 AM 5/25/10 D 2 9.601 0.037 2.47 -1.6
o
0.797
3 2854 10 AM 5/26/10 D 3 8.212 0.045 2.42 2.2
o
0.793
states with essentially the same energy spectrum. Ac-
cording to the QD theory the essential parameters of the
spectrum are [9]: the peak frequency, the dominant di-
rection , and the bandwidth. So we have searched records
with some similar values of the triplet Tp,
,
*
where: Tp = period associated with the peak of the energy
spectrum;
= angle between the wave direction and the
beam axis,
= dominant angle
in the directional
spectrum;
*
= narrow-bandedness parameter (equal to
the absolute value of the quotient between the minimum
and the maximum of the autocovariance of pressure
fluctuations). We have found three pairs of records that
satisfied our search. The particulars of these are summa-
rized in Table 1 below.
The pressure-waves observed in the datasets of Table
1 are plotted in Figures 2, 3 and 4, respectively. Each of
these figures comprises a sequence of 24 pairs of profiles
plotted over an interval of time including to when the
crest or the trough of an EW occurs at transducer i. We
note first in Figure 2 that the waves of record 1101 are
very similar to the waves of record 1276 during an inter-
val including time instant to wherein the crest of the zero
up-crossing EW occurs. As the time lag |t - to| grows also
the differences between the waves of the two records,
gradually, grow. On the interval (to - 3s, to + 4s) the like-
ness between the waves of record 1101 and the waves of
record 1276 seems amazing. Essentially the same com-
ment holds for the waves of the pair of records 1107 and
1280 (Figure 3) , and for the waves of the pair of records
2554 and 2854 (Figure 4). The time interval of the great
likeness is (to - 3s, to + 1.5s), and (to-1.5s, to + 3s), re-
spectively, in fig.3 and in fig.4. Note that waves of all the
pictures are irregular (not regular in shape and size).
However, on the above specified time intervals including
instant to, these irregular waves appear to be not random.
Indeed, the same movie of the waves on the beam is re-
peated at least twice on these intervals.
3. Conclusive Remarks
The experiment described in this paper requires that one
assembles an array of gauges and find two sea states A
and B with the following characteristics:
i) A and B must have essentially the same spectrum (if
the experiment is performed with wind waves with a
unimodal spectrum, like JONSWAP, and one dominant
wave direction, it is sufficient that A and B have the
same triplet Tp,
,
*
);
ii) the wave with the largest
of sea state A and the
wave with the largest
of sea state B must occur at
the same location, and these
must be very large (
> 8);
iii) the wave with the largest
of sea state A and
the wave with the largest
of sea state B must be of
the same type (zero up-crossing, or zero down-crossing).
Then, from the QD theory it is expected that there is a
time interval in which the wave profiles recorded by the
gauge array in sea state A are very close to the wave pro-
files recorded by the gauge array in sea state B. The ex-
periment consists in verifying whether this is true or not.
For the experiment described in this paper, we assem-
bled an array of 26 gauges, and we found three pairs of
sea states (out of about 3000 sea states examined)
wherein the conditions (i), (ii), and (iii) were fulfilled. In
all these three pairs of sea states the expectancy based on
the QD theory was confirmed, and this fact supports the
validity of this theory quite effectively, albeit based on
limited observations.
Since large waves induce larger wave loads, they are
of principal interest in designing fixed or floating struc-
tures in the oceans. Thus, the QD theory has theoretical
and practical significance in ocean engineering and naval
architecture because it suggests that extreme wave loads,
far from being random, tend to be deterministic. This is
why some independent repetitions of the experiment are
crucial for ocean engineering and naval architecture.
The experiment may be performed everywhere, even
on shallow water, wherein waves may be subject to
shoaling and refraction. The experiment may be very
well performed with a part of the gauges on deep water
and a part on shallow water. This is because the QD the-
ory must be verified to hold for an arbitrary solid bound-
Copyright © 2011 SciRes. OJMS
P. BOCCOTTI 71
15.0
m
-2.0m
-5.0m
0.0
1.20m
135791113151719212325
246810 12 1416 1820 22 24 26
y
Figure 1. Schematic of the field experiment. The variation of water depths due to the astronomical tides was within ±0.15 m.
direction of wave advance
1101
1276
t
o
t + 1 s
o
t + 2 s
o
t + 3 s
o
t + 4 s
o
t + 5 s
o
t + 6 s
o
t -1 s
o
t -5 s
o
t -4 s
o
t -3 s
o
t -2 s
o
1101
1276
1101
1276
Figure 2. Profiles of pressure-head waves on the horizontal beam in records 1101 of May 17, 2010 (morning) and 1276 of May
17, 2010 (night). Vertical ordinates refer to the pressure-head variations scaled with the root-mean-square pressure-head.
direction of wave advance
1107
1280
t
o
t + 1 s
o
t + 2 s
o
t + 3 s
o
t + 4 s
o
t + 5 s
o
t + 6 s
o
t -1 s
o
t -5 s
o
t -4 s
o
t -3 s
o
t -2 s
o
1107
1280
1107
1280
Figure 3. Same as Figure 2 but for pressure-head waves in records 1107 of May 17, 2010 (morning), and record 1280 of May
18, 2010 (night).
Copyright © 2011 SciRes. OJMS
P. BOCCOTTI
Copyright © 2011 SciRes. OJMS
72
direction of wave advance
2554
2854
t
o
2554
2854
2554
2854
t + 1 s
o
t + 2 s
o
t + 3 s
o
t + 4 s
o
t + 5 s
o
t + 6 s
o
t -1 s
o
t -5 s
o
t -4 s
o
t -3 s
o
t -2 s
o
Figure 4. Same as Figure 2 but for pressure-head waves in records 2554 of May 25, 2010 and 2854 of May 26, 2010.
ary. The experiment may be very well performed in a
wave flume.
The fact that the fluctuating pressure head at some
given depth is the same in two distinct sea states does not
imply that the free surface displacement be the same in
these sea states. Thus some repetitions of the experiment
should be made with surface waves, even though meas-
uring surface waves in the field is more expensive than
measuring pressure head waves.
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