Detection of wave groups from the motion behaviour of a discus buoy

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Journal of Hydro-environment Research 1 (2008) 195e205www.elsevier.com/locate/jher

Detection of wave groups from the motion behaviourof a discus buoy

R. Balaji a, S.A. Sannasiraj b, V. Sundar b,*

a Sogreah Gulf, Dubai, UAEb Department of Ocean Engineering, Indian Institute of Technology Madras, India

Received 8 March 2007; revised 7 November 2007; accepted 19 November 2007

Abstract

A scale modeled discus data buoy was tested for its motion characteristics under the action of wave groups of different frequencies in a wavetank. The wave groups were theoretically simulated based on the methodology of Xu et al., (1993, Statistical simulation of wave groups, AppliedOcean Research, 15, 217e226) and then converted to paddle displacement signals to drive the wave maker. The motion responses of the buoymodel were measured using potentiometers as well as with a non-contact motion tracking camera system. The details of the model, instrumen-tation, testing conditions and the analysis are presented. The displacement and wave elevation time histories were analysed through statistical,envelope, wavelet transform and phase-time approaches to detect the wave groupiness. The effect of groupiness parameters on the surge, heaveand pitch motions of the buoy are detailed in this paper.� 2007 International Association for Hydraulic Engineering and Research, Asia Pacific Division. Published by Elsevier Ltd. All rights reserved.

Keywords: Data buoy; Surge; Heave; Pitch; Wave group; Wavelet; Phase-time method

1. Introduction

Offshore and coastal structures are subjected to a variety ofwaves, of which, wave groups play an important role in exert-ing forces and moments on such structures and dictate thestability of floating structures and the stability of armour layerof breakwaters in an environment dominated by such waves.The failure of the Sines breakwater in Portugal in early 70’saccelerated the study on the characteristics of wave groupsand their effect on structures. Although, structures in the ma-rine environment are designed for a design wave height, theymay get exposed to waves that are greater in which case thestructure would still be safe as long as it occurs occasionally.However, the stability of structures becomes questionable ifthey are exposed to the action of wave heights higher thanthe design wave in quick successions as this would result inthe fatigue type of failure or sudden type failure like the totalcollapse of the armour layer of rubble mound breakwaters. In

* Corresponding author. Tel./fax: þ044 2257 4809.

E-mail address: [email protected] (V. Sundar).

1570-6443/$ - see front matter � 2007 International Association for Hydraulic Engineerin

doi:10.1016/j.jher.2007.11.002

the case of floating structures, the failure can be in form ofsnapping of the mooring lines. The successive waves exceed-ing the design wave height in quick succession are termed aswave groups.

Although, there are several methods for wave data collec-tion, acquiring the characteristics of ocean waves throughwave rider buoys still remain as one of the most popularmethod. The different types of buoys that are used to collectdata in the ocean are spar buoys, NOMAD buoys, sphericalbuoys and discus buoys. Worldwide, there are slightly morethan 200 buoys installed in the ocean, of which the mostwidely used are the 3 m diameter discus buoys.

The importance of the study on wave groups has beendescribed by Goda (1970, 1976 and 1983). Although, one ofthe primary purposes of any data buoy is to measure thewave characteristics that prevail in a particular site of interest,it can be well suited as a system to identify the groupiness in thewave field. In order to extract such information, the primary-requirement would be to have a thorough knowledge on themotion behavior of buoys subjected to the action of wavegroups. Though, the effects of wave grouping on the slow drift

g and Research, Asia Pacific Division. Published by Elsevier Ltd. All rights reserved.

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0 10 20 30 40 50

t (s)

-0.08

-0.04

0.00

0.04

0.08

(m)

Wave

Envelope

Fig. 1. Typical theoretically simulated wave groups and its envelope.

196 R. Balaji et al. / Journal of Hydro-environment Research 1 (2008) 195e205

oscillations of a rectangular floating vessel have been studied(Murray et al, 1987; Sawaragi et al, 1988), its interactionwith a data buoy has not been properly understood. In particu-lar, the effect of waves group of different frequency on themotion characteristics of data buoy is yet to be investigated.Liu (2000) identified the wave groups from the wave elevationtime histories measured by a wave-rider data buoy by using thewavelet transform. To collect the meteorological and oceanicparameters and to monitor the marine environment over IndianSeas, the Department of Ocean Development has establisheda National Data Buoy Programme (NDBP). Presently, underthe NDBP, 25 numbers of discus data buoys are deployed inBay of Bengal and Arabian Sea to measure and supply data soas to improve the weather and ocean state prediction. In an ear-lier experimental investigation, the authors measured the heaveand pitch motions of a scale modeled discus data buoy ofNDBP under the action of regular, random and bi-modal spectralwaves and also stated that the buoy predicts the wave spectrawell (Balaji et al., 2007). As a need for understanding of motionbehavior of the data buoy under the action of wave groups is felt,the present study was taken up in a laboratory wave flume. Theidentification of wave groups from the time histories of motionshas been sorted out using different approaches such as, statisti-cal, wavelet and phase-time method. The details of each of theapproaches and their importance are described.

2. Experimental program

2.1. Simulation of wave groups

Although several researchers have worked on the conceptof generating wave groups in the laboratory, the method usingSmooth Instantaneous Wave Energy History in which thegroupiness was specified by a characteristic wave height andreferred to as SIWEH as proposed by Funke and Mansard(1979) has been widely adopted. In a statistical simulation,Xu et al. (1993) considered the envelope approach, in whichthe group wave height factor, GHF (ratio of envelope andwave spectral moments) and group wave length factor, GLF(ratio of wave and envelope peak frequencies) were used forspecifying the effect of groupiness. In the present study, thetheoretical simulation of wave groups is based on the method-ology of Xu et al. (1993). Initially, the envelope time historywas simulated from the predefined Pierson-Moskowitz (PM)spectrum. The wave elevation time history was then simulatedfrom the PM spectrum in which the phases were constrainedby the prescribed envelope time history using the Hilberttransform technique. Different wave groups were simulatedby varying the ratio of peak frequencies of wave and the enve-lope spectra. A typical theoretically simulated wave groupalong with its envelope is shown in Fig. 1, which is then con-verted to first order wave paddle signals.

2.2. Model details and instrumentation

In the present study, a 2.2 m diameter discus shaped databuoy of NDBP was scale modeled by adopting a model scale

of 1:8. The diameter of the model discus data buoy is 0.275 mwith an overall height of 0.133 m and weighs 1.9 kg. Four con-ductive type wave gauges were used to measure the time his-tories of the water surface elevations at three locations, that is,on the seaward side of the buoy, two on either side in thevicinity of the buoy model and on the leeward side of themodel. The buoy motions were measured by using two preci-sion potentiometers with a range of 610 volts fixed on a fric-tionless pulley arrangement. The standard range of thepotentiometers is 20 k ohms with a total resistance toleranceof �5% and the independent linearity is about �0.25%.

In addition, two non-contact motion capturing infra-redcameras (Proreflex MCU) were used to measure the buoymotions. Each of the cameras emits infra-red light, which isreflected off low mass, retro-reflective markers and back tothe camera to generate a 2-dimensional image of the markerpositions. By triangulation with more than one camera,a three-dimensional recording of the marker positions can begenerated and in the present study, two MCUs were used to cal-culate the positions of the buoy model. The cameras use thereflected data to calculate the position of the targets witha high spatial resolution. There are different sizes and shapesof the passive markers; however for the present study flatbase spherical markers with a diameter of 19 mm were adop-ted. The spatial resolution of 19 mm diameter marker is lessthan 0.01 mm for a measurement distance of about 1 m. Prore-flex MCU uses a charge-coupled device (CCD) image sensor tocapture the markers movement with a resolution of 658� 500pixels and the maximum measuring frequency range of120 Hz. For the present study, eight numbers of passive reflec-tors were fixed on the model at different elevation, for the rigidbody definition. The two cameras were kept along one side ofthe wave flume with a distance of about 4 m in between them.The Proreflex MCU is calibrated using standard L-frame andwand system. The L-frame is fitted with four passive markersin a pre-defined locations, where as, the wand is fitted with twomarkers at the extreme ends. Using the corner of the L-frameas the co-ordinate of the measurement volume, the movementof the wand is captured and the measured and the actual dis-tance between the markers are compared for calibration. Forthe present study, eight numbers of passive reflectors werefixed on the model at different elevation, to define the rigidbody positions. The two cameras were kept along one side ofthe wave flume with a distance of about 4 m in between them.

197R. Balaji et al. / Journal of Hydro-environment Research 1 (2008) 195e205

2.3. Test facility and wave conditions

Fig. 3. View of the experimental set-up.

The present experimental study was carried out in a 30 mlong, 2 m wide wave flume in the Department of Ocean Engi-neering, IITMadras. The model was installed in a constant wa-ter depth of 0.8 m at a distance of about 10.5 m from the wavepaddle. The cross sectional details of the wave flume includingthe position of the buoy model, fixing frame for the pulley sys-tem with potentiometers (P1and P2) and position of the wavegauges are shown in Fig. 2. A view of experimental set-up isshown Fig. 3. For the present study, the significant height ofwave (Hsw) was kept constant as 0.1 m, whereas, that of the en-velope (Hse) was 0.4 m. The peak frequencies of wave ( fpw)and the envelope ( fpe) spectra were varied such that a rangeof 0.49 to 0.9 for GHF and a range of 17.5 to 28.0 for GLFwere achieved. Each wave group simulation was repeated atleast twice in order to ensure the reproduction of groupinessin the flume. The signals from the potentiometers and thefour wave gauges were simultaneously acquired through anamplifier, with a sampling frequency of 40 Hz. Typical adoptedtime history of the wave elevation, h measured in the flume(W3) and its corresponding spectrum compared with the PMspectrum (source spectrum) described by a significant waveheight, Hs¼ 0.1 m and peak frequency, fpw¼ 0.7 Hz is shownin Fig. 4a. The measured wave elevation time history was sub-jected to Hilbert transformation to obtain the time history of thewave envelope, the spectrum of which has been compared withthe source wave envelope spectrum in Fig. 4b. The time histo-ries of surge,x, heave, z and pitch, q for the wave characteristicsmentioned as above and their corresponding spectra are pro-jected in Fig. 5. It can be observed that the natural periods insurge and pitch mode are 7.38 s ( fxn¼ 0.136 Hz) and 0.72 s( fqn¼ 1.34 Hz) respectively. The secondary peaks that appearin the surge response spectrum at the natural period of pitchare due to the coupling effect between them.

3. Analysis of results

3.1. Statistical and envelope approaches

The procedure started with the determination of the individ-ual wave heights, Hw (crest to trough) using the conventionalzero up-crossing analysis, from which (Hw)1/3 (average of thehighest one third) was evaluated which is the threshold valuefor wave height. In a similar way the threshold value was

30

1.7m

Rubble mound absorber

0.3m

weightCounter

PulleyW4 W2,W3

P2

B

Pote

Fig. 2. Cross sectional view of th

arrived for Hx, Hz and Hq with their respective time historyand are defined as (Hx)1/3, (Hz)1/3 and (Hq)1/3 respectively.The sequence of occurrence of Hw, Hx, Hz and Hq thus com-puted for typical wave elevation histories with GLF¼ 17.5and 28 are projected in Figs. 6 and 7 respectively. In orderto examine the effect of groupiness on the motion responsesof the buoy, two different envelope peak frequencies, fpe of0.025 and 0.04 Hz were employed maintaining the peak fre-quency of wave, fpw constant as 0.7 Hz. The significant valueof the time history of each of the variable aforesaid is markedin the respective plot of the above mentioned figures. It is clearfrom the results that at least two successive wave heights ex-ceed Hs in the wave elevation time histories for both thewave group characteristics, thus exhibiting the presence ofwave groupiness as per the claim of Ochi and Sahinoglou(1989). An increase in the GLF is observed to have resultedin an increase in the number of successive wave heights higherthan Hs due to an increase in the period of envelope (higherGLF). Although such a comparison has to be made by main-taining GHF constant for both the GLF adopted, it is difficultto fulfill this requirement in laboratory and hence the compar-isons are made for a closer value for GHF which are 0.6 and0.7. The magnitude in the heave mode is found to followclosely only with that for the wave elevation and not withthat for the surge and pitch mode of motion of buoy.

Further, the time histories of h, x, z and q were analyzed inthe frequency domain to arrive the wave and envelope spectra,

10.5m

.0mPerforated wave absorber

W1, W2, W3 & W4 are Wave gauges

Frame

uoy model 0.8m

Wave paddlentiometer(P1)

W1

e wave flume and the model.

Fig. 4. Typical measured wave elevation histories and its spectrum (GLF¼ 17.5, GHF¼ 0.6).

Fig. 5. Typical measured buoy motion responses and their spectra (GLF¼ 17.5, GHF¼ 0.6).


Fig. 6. Zero up-crossing heights of wave elevation and motion responses (GLF¼ 17.5, GHF¼ 0.6).

Fig. 7. Zero up-crossing heights of wave elevation and motion responses (GLF¼ 28, GHF¼ 0.7).



in which the latter through the Hilbert transform technique asper the method of (Xu et al., 1993). Such spectra for the mea-sured time histories with characteristics stated earlier are pro-jected for GLF¼ 17.5 and 28 in Figs. 8 and 9 respectively.From the results, it is clearly seen that the peak energy of thewave and envelope spectra occur at two different frequencies,while that of the latter is essentially composed of low frequencycomponents. In addition, the envelope spectral peak increaseswith an increase in the GLF. However, the wave spectral ener-gies for the two values of GLF tested are nearly same.

3.2. Wavelet transformation

Both the above procedures provide only the frequency in-formation about the signals. In order to examine the physicalprocesses in both frequency and time domains, the applicationof the wavelet approach to the time histories was considered.The use of wavelet transformation technique in the analysis ofocean waves is an emerging topic in the recent years (Massel,2001., Balaji et al., 2006). The Continuous Wavelet Transfor-mation, CWT (Wx(a,t)) of a one-dimensional signal x(t) isgiven as,

Wxða;tÞ ¼1ffiffiffiffiffiffijaj

pZN

�N

xðtÞ,j��

t� t

a

�dt ð1Þ

in which, j* is the scaled and translated version of the basisfunction, j. The scaling and translations are governed by the

Fig. 8. Spectra derived from envelope a

parameters a and t, respectively. The Morlet wavelet functionis a Gaussian modulated complex-valued plane wave andhence, for the transformation of ocean wave signals, it iswidely adopted. The Morlet wavelet function is defined as,

jðtÞ ¼ p�ð1=4Þeiuote�ðt2=2Þ ð2Þ

Where, uo is the non-dimensional frequency, which is takenas 6.0 in the present study for satisfying the admissibility con-ditions (Farge, 1992). Using the above basis function, the timehistories were multiplied by j*, in which the parameters a andt are continuously varying, thus leading to a two-dimensionalrepresentation of the one-dimensional signal. For the Morletwavelet with uo of 6.0, the Fourier period (or inverse of fre-quency) corresponding to the wavelet scale is 1.03a (Torrenceand Compo, 1998). The measured time histories were thensubjected to CWT analysis. Upon application of CWT, the re-sulting wavelet contour plot reveals the energy density in thetimeefrequency domain. Typical wavelet contours for waveelevation, surge, heave and pitch are depicted in Fig. 10 forthe wave group with GLF of 17.5. The high concentration ofenergy of the wavelet contours clearly distinguishes the timeof occurrence of the wave group present in the time historiesof wave elevation and heave motion. Though, a similar trendis seen in the case of pitch and surge, the peaks are dominantfor t¼ 30 to 40secs which does not correspond to t¼ 20 to30 s around which the peaks are for the waves and the heavemode of motion. Within this range of time period, there are

pproach (GLF¼ 17.5, GHF¼ 0.6).

Fig. 9. Spectra derived from envelope approach (GLF¼ 28, GHF¼ 0.7).

Fig. 10. Wavelet energy contours of wave elevation and motion responses (GLF¼ 17.5, GHF¼ 0.6).


Fig. 11. Closer view of the wavelet contours (crests are numbered).


higher value wavelet contours present in the CWT of surge atthe level of the natural frequency of buoy model in the surgemode. However, because the buoy has a tendency to followthe wave, the CWT of the heave displacement very well distin-guish these high frequency components in the time-frequencyscale as can be seen in the figure. A closer view of the waveletcontours of wave elevation and heave motion, shown in Fig. 11reveals that there are three continuous wave crests followed bytroughs involved in the wave group formation, an observationnoticed in the statistical analysis.

3.3. Phase-time method

The phase-time method (PTM), based on the Hilbert trans-formation, was introduced by Huang et al. (1992) to study the

Fig. 12. Hilbert frequencies of wave elevation and

frequency modulation, structure of the wave group and wavebreaking in the measured wave elevation time histories, whichwas later used by Griffin et al. (1996) to study the local prop-erties of the laboratory generated breaking waves. In PTM, ananalytical function is derived from the time histories (x(t)), asfollowing,

ZðtÞ ¼ xðtÞ þ ihðtÞ ð3ÞIn which h(t) is the Hilbert transform of the time history.

Then the phase function is obtained as,

fðtÞ ¼ tan�1

�hðtÞxðtÞ

�ð4Þ

The phase function is then decomposed into mean and timevarying component and conditional filtered, which is termed

motion responses (GLF¼ 17.5, GHF¼ 0.6).

Fig. 13. Hilbert frequencies of wave elevation and motion responses (GLF¼ 28, GHF¼ 0.7).


as the Hilbert frequency or local frequency. Zimmermann andSeymour (2002) adopted PTM to detect breaking waves inlarge-scale laboratory experiments, in which a threshold sur-face elevation (ht) value of 0.38Hsw was used to filter the ex-traneous large peaks in the frequency variation, in which, ht isthe level of wave elevation only above which the frequenciesare considered and where, Hsw is the significant wave height.The said relationship of ht¼ 0.38 Hsw was adopted for the pre-liminary studies, from which it was observed that severalpeaks within the envelope that should have been filtered outhad been included, thus misleading the information from theprediction. Hence the threshold value was increased by smallincrements and the analysis repeated. In doing so, a thresholdvalue of 0.42 times of the respective significant values of thevariables after several trials was arrived at for the purpose of

15 20 25 30

GLF

0

10

20

30

40

0

10

20

30

40

m0

/m0

m0

/m0

Fig. 14. Effect of GLF and GHF

filtering out the un-wanted localized frequencies. Upon apply-ing the PTM, the filtered local frequency variation for thewave elevation, surge, heave and pitch for the two differentwave groups depicted in Figs. 12 and 13. It is observed fromthe figures that the clusters of Hilbert/local frequencies appearfor the heave motion corresponding to the wave elevation thatexceeds the respective threshold values. It is also noted thatthe discrete frequency clusters of almost same magnitudes de-notes the number of crests existing within a wave group. Un-like in the statistical method, through which the prediction ofthe existence of wave groups could not be possible from themotion responses of the buoy is now seen to be possiblethrough PTM as one can observe that the surge and pitch mo-tion responses also exhibit the existence of the wave groups.The wide variations of local frequencies within a crest for

0.4 0.8 1.2

GHF

0

10

20

30

40

0

10

20

30

40

Surge

Pitch

m0

/m0

m0

/m0

on the motion characteristics.

0 5 10

Test number0 5 10

Test number

0

10

20

30

40

0

10

20

30

40

Group

Random

m0

/m0

m0

/m0

Fig. 15. Effect of groupiness on the motion characteristics.


the surge motion clearly indicate the drifting of the buoymodel due to the existence of the wave group. The abovesaid observations are seen for both the GLF tested.

The aforementioned four different methods to detect thepresence of group waves have been applied to the measuredtime histories of motion responses of a data buoy in a sequence.For example, though statistical method is a simple tool to find ifthe successive wave heights exceed threshold value, the time ofoccurrence of the event could not be derived. The envelope ap-proach through the Hilbert transform of the measured time his-tories yields good spectral information about the wavecharacteristics, namely, peak frequency and significant heightof waves and the groups. On the other hand, CWT and PTM ap-proach immediately reveal the time of incidence of wavegroups. It is emphasized that, a careful step by step approachin the analysis of the measured time histories of data buoy helpsin distinguishing the existence of wave groups.

3.4. Effect of groupiness

The influence of GLF and GHF on the surge and pitchmotions are shown in Fig. 14, where, the spectral momentsare represented in the form of non-dimensional parameters.It is to be noted that the heave motion is unaltered by the effectof wave groups and that shows the ability of the discus buoy tofollow the waves closely. In the above said figure, m0h, m0x

and m0q denote zeroth moment of the wave elevation, surgeand pitch spectra, respectively. Although the trend is domi-nated by scatter, in general, surge and pitch motion marginallydecrease with an increase in the GLF, due to the sluggishnessof the buoy motion for the low frequency wave groups. In con-trast, the motions marginally increase with an increase in theGHF, as the nonlinear low frequency wave forces increasewith the wave heights. In an attempt to understand the wavegroupiness, the buoy model was also tested under randomwaves (without groups) prescribed by the PM spectrum ofequivalent energy. The equivalent energy was achieved by firstconverting the wave groups into the frequency domain fromwhich random time histories were derived. The effect ofwave groups on the surge and pitch motions, shown inFig. 15, clearly describes that the buoy motions are higherfor wave propagating in groups. Quantitatively, the surge

motions are 80% higher than that for the random waves with-out wave groups, where as, the pitch motions are more by anaverage value of 35%.

4. Summary

The motion characteristics of a scale modeled discus databuoy were studied under the action of wave groups of differentfrequencies. The existence of the groupiness was identified us-ing statistical, envelope, wavelet and phase-time approaches.The phase-time method can be used to predict the groupinessin the time histories of wave elevation and the buoy motions.The surge and pitch motions are more influenced by the groupparameters. Compared to the random waves of same energylevel, the existence of the wave groups affects greatly the mo-tion behavior of the buoy.

References

Balaji, R., Sannasiraj, SA., Sundar, V., 2007. ‘‘Physical model studies on dis-

cus buoy in regular, random and double peak spectral waves’’. Indian Jour-

nal of Marine Sciences 36 (1), 18e26.

Balaji, R., Sannasiraj, S.A. Sundar, V., 2006. Laboratory simulation and anal-

ysis of wave groups, 25th International Conference on Offshore Mechanics

and Arctic Engineering (OMAE), Hamburg, Germany, 4-9 June, CD-ROM

Proceedings, Paper No: 92144.

Farge, M., 1992. Wavelet transform and their applications to turbulence.

Annual Review of Fluid Mechanics 24, 395e457.

Funke, E.R., Mansard, E.P.D., 1979. On the synthesis of realistic sea states in

a laboratory flume, Report LTR-HY-66. National Research Council, Canada.

Goda, Y., 1970. Random seas and design of offshore structures. University of

Tokyo press, Tokyo.

Goda, Y., 1976. On wave groups, Behavior of offshore structures, BOSS. The

Norwegian Institute of Technology. 115e128.

Goda, Y., 1983. Analysis of wave grouping and spectra of long traveled swell.

Report of the Port and Harbour Research Institute 22 (1).

Griffin, O.M., Peltzer, R.D., Wang, H.T., Schultz, W.W., 1996. Kinematic and

dynamic evolution of deep water breaking waves. Journal of Geophysical

Research [Space Physics] 101 (No. 7), 16515e16531.

Huang, N., Long, S.R., Tung, C.C., Donelan, M.A., Yuan, Y., Lai, R.J., 1992.

The local properties of ocean surface waves by phase-time method.

Geophysical Research Letters 19 (No. 7), 685e688.

Liu, P.C., 2000. Wave grouping characteristics in near shore Great Lakes.

Ocean Engineering 27, 1221e1230.

Massel, S.R., 2001. Wavelet analysis for processing of ocean surface wave

records. Ocean Engineering 28, 957e987.


Murray, J.J., Wilkie, B.P., Muggeridge, D.B., 1987. An experimental and

analytical study of the effects of wave grouping on the slowly varying drift

oscillation of a floating rectangular barge. Ocean Engineering 14 (No 4),

255e274.

Ochi, M.K., Sahinoglou, I.I., 1989. Stochastic characteristics of wave groups

in random seas, Part 1: Time duration of and number of waves in

a wave group. Journal of Applied Ocean Research 11 (No.1).

Sawaragi, T., Aoki, S., Takada, M., 1988. Effects of wave grouping on the low-

frequency motion of a moored rectangular vessel and the characteristics of

nonlinear hydrodynamic forces. Coastal Engineering in Japan 31 (No.1),

167e182.

Torrence, C., Compo, G.P., 1998. A practical guide to wavelet analysis.

Bulletin of the American Meteorological Society 79, 61e78.

Xu, D., Hou, W., Zhao, M., Wu, J., 1993. Statistical simulation of wave

groups. Applied Ocean Research 15, 217e226.

Zimmermann, C.A., Seymour, R., 2002. Detection of Breaking in a Deep

Water Wave Record. Journal of Waterway, Port, Coastal, and Ocean

Engineering 128 (No. 2), 72e78.

Detection of wave groups from the motion behaviour of a discus buoy

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