Laboratory Observations of Green Water Over Topping a Fixed Deck

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Ocean Engineering 29 (2002) 1827–1840www.elsevier.com/locate/oceaneng

Technical Note

Laboratory observations of green waterovertopping a xed deck

Daniel T. Cox * , Jose Alberto OrtegaCoastal and Ocean Engineering Division, Department of Civil Engineering, Texas A&M University,

MS 3136, College Station, TX 77843-3136, USA

Received 25 July 2001; accepted 14 November 2001

Abstract

A small-scale laboratory experiment was conducted to quantify a transient wave overtoppinga horizontal, deck xed above the free surface. Detailed free surface and velocity measure-

ments were made for two cases with and without the deck structure to quantify the effect of the deck on the wave kinematics. The study showed that the structure increased the free surfaceabove the leading edge of the deck by 20%. The velocity prole at the leading edge was fairlyuniform, and the maximum horizontal velocity was similar to the maximum crest velocitymeasured without the deck. Immediately below the deck, the maximum velocity was 2.5 timesgreater than the corresponding velocity without the deck and 2.1 times greater than themaximum crest velocity without the deck. On the deck, the wave collapsed into a thin borewith velocities that exceeded 2.4 times the maximum crest velocity measured without the deck.

2002 Published by Elsevier Science Ltd.

Keywords: Wave overtapping; Wave kinematics; Extreme wave; Green water; Transient wave; Roguewave; Crest height; Offshore structures; Laboratory experiment

1. Introduction

Wave overtopping on the lower decks of offshore platforms and on the decks of ships can cause severe structural damage and increased safety risks due to the highforces generated by the wave (Bea et al., 1999; Gudmestad and Hansen, 2000). A

* Corresponding author. Tel.: + 1-979-862-3627; fax: + 1-979-862-8162. E-mail address: [email protected] (D.T. Cox).

0029-8018/02/$ - see front matter 2002 Published by Elsevier Science Ltd.PII: S 0029-8 018(02 )00011 -2



1828 D.T. Cox, J.A. Ortega / Ocean Engineering 29 (2002) 1827–1840

better understanding of green water overtopping is needed for more reliable design,particularly for vertical piles and other structural members that are typically designedusing the Morison equation. Moreover, green water can rush across the deck as ashallow water bore, resulting in high impact forces.

A number of researchers have studied extreme wave crest elevations, particularlywith regard to freak or rogue waves in the context of deck clearance (Forristall 1978,1997; Myrhaug and Kjeldsen, 1987; Kriebel and Dawson, 1993; Mori et al., 2000;Haver and Andersen, 2000). Relatively few studies have focused on the wave kin-ematics (Skjelbreia et al., 1991; Gudmestad, 1993) for extreme waves, and evenfewer studies have investigated green water overtopping in deep water. The topic,however, has been studied in the context of green water on the decks of ships (Grecoet al., 2000) and the overtopping of shallow water coastal structures (Franco andFranco, 1999). Recently, there has been interest in the green water phenomenonrelated to the slamming and overtopping of oating production storage and of oading(FPSO) systems. Leonhardsen et al. (2001) summarize the experience of ve FPSOsoperating in the North Sea, including two incidents which forced the shutdown of production and damaged safety equipment. Leonhardsen et al. (2001) concluded thatthe green water events are important considerations in the risk analysis of FPSOs.In addition to these eld observations, the number of experimental studies for FPSOsand oating offshore platforms is increasing (Buchner 1995, 1996; Hamoudi andVaryani, 1998; Berhault et al., 1998; Hellan et al., 2001; Stansberg and Nielsen,2001), although the complex uid–structure interactions are still not well understood.

Buchner (1995) found no direct relationship between the velocities of the incomingwaves and the velocities on the deck. Stansberg and Nielsen (2001) indicate thatgreen water is generally the combined effect of two mechanisms —extreme waveevents and negative pitch of the vessel —although a single steep wave is suf cientto cause overtopping in some cases (Hellan et al., 2001). In either case, the incomingwave kinematics should be regarded as important parameters (Stansberg andNielsen, 2001).

Whereas research has included the deterministic modeling of a single green waterevent and the subsequent bore collapse and impact on the deck, another importantresearch area is to determine the exceedance probability for green water on the deck.

In this regard, efforts have been made to predict extreme crest elevations and runupheights on cylinders (Stansberg, 2001). For a xed structure, such as the lower deck of a platform, Cox and Scott (2001) conducted a small-scale hydrodynamic experi-ment to and applied statistical methods to study the likelihood of waves overtoppingthe structure. Cox and Scott (2001) analyzed over 3000 waves and developed empiri-cal relationships between the wave conditions and the likelihood of having largewaves overtopping the structure. The study showed that the exceedance probabilitiesfor the normalized maximum instantaneous overtopping rate and the normalizedovertopping volume could be predicted by a simple exponential curve, similar to thework of Kriebel and Dawson (1993) for crest height distributions. Individual waves

were not studied in detail in the Cox and Scott (2001) study.Buchner (1995) indicated that a number of assumptions concerning green water

overtopping that are currently in predictions methods are questionable, in particular



1829 D.T. Cox, J.A. Ortega / Ocean Engineering 29 (2002) 1827 –1840

that the water falls on the deck as a breaking wave and that the velocity of the wateron the deck is equal to the orbital wave velocity or phase velocity of the incomingwave. Although Cox and Scott (2001) found that free surface and volumetric over-topping exceedance probability curves followed exponential distributions, the hori-zontal velocity exceedance curves showed a curious behavior which could not beeasily predicted. In this regard, it is important to study the complex motion of anisolated wave. For the present paper, we used a transient wave condition and com-pared the water particle velocities on the deck with corresponding velocities meas-ured in the absence of the structure as well as the detailed velocities measured onthe deck.

2. Experiment

To simplify the overtopping process and measurement techniques, the experimentwas conducted in a narrow wave ume at Texas A&M University, restricting thestudy to two dimensions. The setup was similar to that of Cox and Scott (2001) andis repeated here brie y. The glass-walled ume was 36 m long by 0.95 m wide by1.5 m high and was equipped with a programmable wavemaker. The setup is shownschematically in Fig. 1, where x is the horizontal coordinate positive in the directionof wave propagation with x= 0 m at the wavemaker and z is the vertical coordinate,positive upward. The model deck consisted of a 93.5 cm wide by 61 cm long by

1.15 cm thick Plexiglas plate rigidly mounted to a steel frame and suspended fromthe top of the ume. The frame was constructed to minimize ow disturbance tothe overtopping wave. The leading edge of the deck was located at x= 8.0 m, andthe height from the still water level to the bottom of the deck was H dc = 5.25 cm. Thewater depth in the ume was d = 65.0 cm.

Fig. 2 shows the wavemaker signal to generate the transient wave for this study.Since our aim was to study the kinematics of one overtopping event which requireda large number of repeated runs, techniques developed to produce transient waves

Fig. 1. Elevation and plan view of experimental setup. Dots are schematic representation of LDV meas-uring elevations at each transect. A total of 54 measuring elevations were used for Case 1 and 103measuring elevations for Case 2.




Fig. 2. Wavemaker signal, WM, for transient wave generation.

from a long time series were not adopted (Stansberg, 1992; Kriebel and Alsina,2000). Instead, a short transient wave was chosen such that it produces one largeovertopping wave at the leading edge of the deck (at x= 8.0 m) similar to freak wavesobserved in the laboratory or nature. For our tests, the wavemaker signal wasdesigned to allow the preceding waves to pass under the deck without re ectionwhich would have interfered with the overtopping wave. The signal consisted of twocycles of a T = 1.0 s sinusoidal wave followed by two and a half cycles of a T = 1.5 ssinusoidal wave with larger amplitude. The ume was suf ciently long to preventinteractions resulting from re-re ection from the far wall. Two cases were run using

the same transient wave condition: Case 1 was run without the deck, and Case 2was run with the deck. Multiple measurements of the free surface and velocity weremade for each case by repeating the transient wave, and each measurement wassynchronized using the wavemaker signal.

The free surface elevation was measured using a surface-piercing wave gage,beginning at x= 4.5 m from the wavemaker and continuing in increments of 0.5 m to x= 11.5 m for a total of 15 locations. The horizontal and vertical velocities ( u, w)were measured using a laser-Doppler velocimeter (LDV) at three transects x1 , x2 , x3

located at x= 4.5, 8.0, and 11.5 m. At each transect, the velocities were measured at20 elevations between the range 51.0 z 10 cm. For Case 2, additional measure-

ments of the horizontal velocity on the deck were measured from x= 8.0 to x= 8.24 min increments of 0.04 m for a total of seven transects along the slope. The numberof vertical elevations ranged from two locations in the thinnest portion of the over-topping wave at x= 8.24 m to 11 locations in the thickest portion at x= 8.04 m witha total of 49 locations measured on the deck. Velocity measurements were not madeon the trailing edge of the deck due to the presence of ume supports. The freesurface measurements were recorded at 25 Hz. The effective sampling rate of theLDV measurements varied because the transient nature of the experiments requiredan initially still water surface. For the initial few seconds of each run ( t 7 s), dro-pouts occurred regularly because the water was still. During the passage of the transi-

ent wave, dropouts were less frequent. One exception occurred during the over-topping event itself when air was entrained on the leading of the deck. This will bemade clear in later gures. For the portion of the record where the wave motion




was signi cant, the LDV sampling rate was approximately 200 Hz, and the velocitymeasurements were later reduced to 25 Hz by bin averaging.

3. Comparison of extreme wave kinematics with and without deck

Fig. 3 shows the measured free surface elevations at all 15 locations for Case 1and Case 2. The transient nature of the tests is evident in this gure: initially, twolarge waves exist at x= 4.5 m, which are then transformed into a single, larger waveat x= 8.0 m (location of deck), which then decomposes into two large waves at x= 11.5 m. The transient wave exhibits a behavior similarly observed in laboratorystudies on extreme wave evolution in random wave groups (Stansberg, 2000) andgreen water on FPSOs (Stansberg and Nielsen, 2001). The large wave at x= 8.0 mthat hits the structure is very similar to the extreme wave that impacted the DraupnerA Platform in January, 1995, (Haver and Andersen, 2000; Gudmestad and Hansen,2000). At x1 = 4.5 m, the incident wave is essentially the same for both cases. At x2 = 8.0 m the maximum wave height for Case 2 is H = 22.6 cm calculated using thecrest height h c = 14.6 cm occurring at t = 10.58 s and trough level h t= 8.0 cm att = 11.18 s. The zero-crossing prior to h c occurs at t = 10.22 s, and the zero-crossingafter h t occurs at t = 11.62, giving a characteristic wave period of T = 1.4 s. Using thisperiod, linear wave theory, and a depth of d = 65.0 cm, the wavelength is L= 2.76 m.The wave steepness is estimated as H / L= 0.0819 ( ak = 0.257 where a= H /2). There

is a small reduction in the wave heights in the lee of the structure from x=

9.0 mto x3 = 11.5 m.Fig. 4 shows the details of the large wave at x= 8.0 m for Cases 1 and 2. The dots

indicate the phases for which the detailed velocity measurements are shown in Fig.5. There is a small deviation in the wave heights (the wave height for Case 2 is1.06 times larger than Case 1), but the effect of the structure on the total wave heightis minimal. The deck in uence is more signi cant, however, if the portion of thewave that exceeds the deck height, h ex h c ( H dc H ), is considered. Here,

H = 1.15 cm is the thickness of the deck. With and without the structure, h ex = 8.23and 6.89 cm, respectively, so the water level relative to an observer on the deck is

actually increased by 20%.Fig. 5 shows the detailed vertical variation of the horizontal velocity between thecrest and trough levels at 12 phases of the large wave for Cases 1 and 2 at x= 8.0 m.The horizontal dash –dot lines correspond to h c = 14.6 cm and h t = 8.0 cm, the dottedline corresponds to H dc = 5.25 cm, and the long solid line corresponds to the still waterlevel z= 0 cm. The short, heavy solid line corresponds to the instantaneous free sur-face elevation at that phase for Case 1, and the short, light line depicts the same forCase 2. The lines indicate the same free surface elevations that were plotted in Figs.5 and 6. The maximum horizontal velocity for Case 1 is 0.72 m/s, occurring in phasewith the maximum crest elevation at t = 10.58 s.

The effect of the structure on the velocity magnitude and phases is interesting.Fig. 5d –g, for example, shows that u in the absence of the deck is large(approximately 0.7 m/s) near deck level and decreases monotonically with depth as




Fig. 3. Free surface measurements for Case 1 (solid) and Case 2 (dash –dot) at 15 locations. The freesurface was not measured at x= 8.5 m for Case 2 because of the presence of the deck.




Fig. 4. Details of surface measurements from Fig. 3 for Case 1 (solid) and Case 2 (dash –dot) at x= 8.0 m.The labeled dots correspond to the 12 phases plotted in Fig. 5.

expected. With the deck in place, u is approximately as large (0.7 m/s) above thedeck, but the variation is not monotonic. At t = 10.46 s, the wave is located at theleading edge of the deck and has not propagated across it (as can be seen in Fig.7). Also at this time, a wall of water was observed on the deck with higher velocitynearer the deck than at the free surface. This higher velocity presumably preventsthe free surface from breaking. Below the deck, the horizontal velocity is clearlyless than and lags both the velocity above the deck (for the same case) and thevelocity at the same elevation for Case 1. At t = 10.54 s, the horizontal velocity is ata maximum and is fairly uniform with depth above the deck. The wave has propa-

gated onto the deck but has not collapsed (also see Fig. 6). At t = 10.58 s, the horizon-tal velocity is decreasing at the leading edge, and the wave is collapsing and shootingrapidly across the deck. Below the deck, the horizontal velocities are still lower thanthose measured without the deck. The velocities continue to decrease above the deck,and at t = 10.70 s, the ow near the deck has reversed as some of the water drainsoff the leading edge. Below the deck, however, the horizontal velocities are reachingtheir maximum values, exceeding those measured above the deck level by 14% andthose measured at the same elevation for Case 1 by 40% (Table 1). After the over-topping event has passed, the phase discrepancy is quickly resolved and the horizon-tal velocities are nearly equal under the trough at t = 11.18 s. The minimum horizontal

velocity is approximately half of the maximum horizontal velocity for this transientwave. Fig. 6 compares the velocity vectors at t = 10.74 s for Cases 1 and 2. Themagnitude of the velocity near the deck for Case 2 is 2.5 times greater than the




Fig. 5. Vertical variation of horizontal velocity, u (m/s), for Case 1 ( •) and Case 2 ( ° ) at the leadingedge of the deck ( x= 8.0 m) for the 12 phases shown in Fig. 4.




Fig. 6. Velocity vectors at t = 10.74 s for Case 1 (a) and Case 2 (b). The horizontal and vertical velocitiesare scaled the same. The maximum velocity show in (a) is 0.59 m/s, and the maximum velocity shownin (b) is 1.48 m/s.

velocity at the same elevation without the deck and 2.1 times greater than themaximum velocity measured for Case 1 under the wave crest.

4. Quanitication of green water on the deck

Following Buchner (1995), an overtopping event can be described in four phases:(1) the relative wave motions come above the freeboard; (2) the water ows ontothe deck; (3) the wave ows over the deck; and (4) the wave hits a structure. For

Phase 1, it was shown that the presence of the xed deck had little in uence on thetotal wave height but that the height relative to an observer on the deck is increasedsigni cantly. For Phase 2, high speed video observations revealed that the water




Fig. 7. Horizontal velocity measured at seven locations on top of deck from 8.0 x 8.24 m duringovertopping event for 10.46 t 10.70 s. Velocity scale indicated by thick horizontal line. Instantaneousfree surface, h , measured seaward of the deck indicated by shorter horizontal line.

ows onto the deck by collapsing rather than breaking, consistent with observationsby Buchner (1995) for a oating body. There was, however, observable entrainmentof air by cavitation on the leading edge of the plate. For Phase 3, the water was

observed to ow over the deck as a shallow water bore. As discussed by Buchner(1995) the problem is similar to the dam break problem (Stoker, 1957), althoughthe horizontal velocity of the wall of water is clearly not zero. Phase 4 (wave impact)




Table 1Maximum horizontal and minimum vertical velocities at x= 8.0 m

Case no. Above deck ( z= 10.0 cm) Below deck ( z= 4.0 cm)

umax (m/s) t (s) umax (m/s) t (s) vmin (m/s) t (s)

1 0.72 10.58 0.60 10.58 – –2 0.74 10.54 0.84 10.74 1.22 10.74

was not studied, and, for future tests, the scale effects of air entrainment cannotbe neglected.

Fig. 7 shows the details of the horizontal velocities measured for several phasesand at several locations along the deck. The vertical velocity was not measuredbecause of restrictions in the LDV lens geometry. The duration of the overtoppingevent, from when the wave hit the deck to when the water receded from the leadingedge, was 0.34 s. At the leading edge, the horizontal velocity is fairly uniform, exceptfor the development of a thin boundary layer near the deck. The maximum horizontalvelocity is 0.74 m/s occurring at t = 10.54 s. As the wave moves across the deck, asigni cant air pocket is entrained, resulting in the signal dropout near the deck. Thevelocities increase with increasing distance from the leading edge of the deck andare always largest in the front of the wave. The maximum velocities recorded in the

front are summarized in Table 2. The horizontal velocities are generally larger thanthe maximum crest velocity recorded in the absence of the structure. The largestvelocity recorded on the deck is 1.70 m/s which is 2.4 times greater than themaximum crest velocity measured in Case 1.

5. Summary

A small-scale laboratory experiment was conducted to quantify the overtoppingof a transient wave on a horizontal deck xed above the free surface. To simplify

Table 2Maximum horizontal velocities on deck (note: uc = 0.72 m/s is maximum horizontal crest velocity inabsence of deck at x= 8.0 m)

t (s) x (m) umax (m/s) umax /uc

10.46 8.00 0.49 0.710.50 8.04 1.04 1.410.54 8.04 1.00 1.4

10.58 8.16 1.64 2.310.62 8.20 1.69 2.310.66 8.24 1.70 2.4




the overtopping phenomenon, the study was restricted to two-dimensional wavepropagation. A transient wave condition was chosen to allow only one large waveto overtop the structure and to prevent interference from re ections of precedingwaves. The transient wave generated at the structure was similar to the extremewaves observed in nature. Detailed free surface and velocity measurements weremade for two cases (with and without the structure) to quantify the effect of thedeck structure on the wave kinematics. The study showed that:

1. The effect of the structure on the free surface at the leading edge increased thetotal wave height by 6% and the free surface height relative to an observer onthe deck by 20%.

2. Above the deck and at its leading edge, the horizontal velocity pro le was fairlyuniform and the maximum horizontal velocity was similar to the maximum crestvelocity measured without the deck.

3. Immediately below the deck, the maximum velocity was 2.5 times greater thanthe corresponding velocity without the deck and 2.1 times larger than themaximum crest velocity measured without the deck.

4. On the deck, the wave collapsed into a thin bore with velocities that exceeded2.4 times the maximum crest velocity measured without the deck.

This study shows that for a thin, xed deck, it may be reasonable to assume aninitial condition at the leading edge (i.e. initial free surface and velocity) based onthe free surface and crest velocities in the absence of the deck. However, the detailsare different. For example, the velocity pro le is more uniform with the deck thanwithout it. The wave does not break on the deck, consistent with studies of greenwater on oating structures (Buchner, 1995), instead, the wave collapses into a bore.The wave collapse and bore propagation is similar to the dam break problem butwith a non-zero initial horizontal velocity. Below the deck and along the deck, thepresence of the structure signi cantly affects the velocity magnitudes and phases.Calculations derived simply from the maximum crest velocities in the absence of the deck would lead to an underdesigned structure. Further research is needed toquantify the effect of the structure on the uid accelerations.

Acknowledgements

This work was sponsored by the National Science Foundation Career Award CTS-9734109 and by the National Science Foundation Research Experience for Under-

graduates Program. The authors thank the Offshore Technology Research Center atTexas A&M University for the use of the laser-Doppler velocimeter and John Reedand Haejin Choi for technical support in conducting the experiments.




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Laboratory Observations of Green Water Over Topping a Fixed Deck

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