A Field Experiment on the Recurrence of Large Waves in Wind Seas

doi:10.4236/ojms.2011.13007

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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)

A Field Experiment on the Recurrence of Large Waves in

Wind Seas

Paolo Boccotti

NOEL Laboratory, Mediterranea University, Reggio Calabria, Italy

E-mail: [email protected]

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-

trary―see [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



the root-mean-square pres-

sure-head of the sea state); iv) belonging to two sea

P. BOCCOTTI

Table 1. The particulars of the three pairs of records with similar basic characteristics.

EW sea state

Dataset record time date

type i





(m)



(s)





1101 7 AM 5/17/10 U 17 8.908 0.064 2.58 -16.7

0.837

1 1276 11 PM 5/17/10 U 17 8.178 0.052 2.52 -18.3

0.831

1107 8 AM 5/17/10 U 13 8.357 0.050 2.44 -15.7

0.823

2 1280 0 AM 5/18/10 U 13 8.182 0.053 2.47 -19.3

0.832

2554 8 AM 5/25/10 D 2 9.601 0.037 2.47 -1.6

0.797

3 2854 10 AM 5/26/10 D 3 8.212 0.045 2.42 2.2

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-

P. BOCCOTTI 71

15.0

-2.0m

-5.0m

0.0

1.20m

135791113151719212325

246810 12 1416 1820 22 24 26

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 + 1 s

t + 2 s

t + 3 s

t + 4 s

t + 5 s

t + 6 s

t -1 s

t -5 s

t -4 s

t -3 s

t -2 s

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 + 1 s

t + 2 s

t + 3 s

t + 4 s

t + 5 s

t + 6 s

t -1 s

t -5 s

t -4 s

t -3 s

t -2 s

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).

P. BOCCOTTI

direction of wave advance

2554

2854

2554

2854

2554

2854

t + 1 s

t + 2 s

t + 3 s

t + 4 s

t + 5 s

t + 6 s

t -1 s

t -5 s

t -4 s

t -3 s

t -2 s

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.

4. References

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