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MEETING REPORT Rogue THE FOURTEENTH ‘AHA HULIKO’A HAWAIIAN WINTER WORKSHOP

BY PETER MÜLLER, CHRIS GARRETT, AND AL OSBORNE

“It came from nowhere, snapping giant of the Fourteenth ‘Aha Huliko’a Hawai- Shackleton (1919) gave a particularly in two. No one believed the survi- ian Winter Workshop convened January gripping account of an extreme en- vors … until now” screamed the cover of 25-28, 2005, at the University of Hawaii, countered during his epic 1300-km voy- New Scientist magazine on 30 June 2001, with the support of the Offi ce of Naval age in the 7-m whaler James Caird from introducing an article entitled “Monsters Research and the participation of 25 in- Elephant Island to South Georgia in May of the Deep.” The power and danger sug- vited speakers. 1916. During a day with tremendous gested by the term “rogue” to describe The practical importance of large cross- he recalls: extreme waves add to the public ocean waves (such as that in Figure 1) At midnight I was at the tiller and sud- fascination with these waves. They also is clear: they affect naval and civilian denly noticed a line of clear sky between presented important and challenging sci- shipping and can damage offshore oil the south and south-west. I called to the entifi c problems and provided the topic platforms and coastal structures. Ernest other men that the sky was clearing, and then a moment later I realized that what I had seen was not a rift in the clouds but the white crest of an enormous wave. Dur- ing twenty-six years’ experience of the ocean in all its moods I had not encoun- Figure 1. An extreme wave, a so called “white wall,” approach- ing a merchant vessel in the (from http: //www. tered a wave so gigantic. It was a mighty photolib.noaa.gov/historic/nws/wea00800.htm). Th e visual upheaval of the ocean, a thing quite apart classifi cation of extreme waves also includes “singular wave from the big white-capped seas that had towers” assumed to be generated by refraction and focusing in currents and the “Th ree Sisters” that bear some similarity been our tireless enemies for many days. to wave patterns created by a . I shouted, “For God’s sake, hold on! It’s got us!” Then came a moment of sus- pense that seemed drawn out into hours.

Peter Müller ([email protected]) is Professor of , University of Hawaii, Honolulu, HI, USA. Chris Garrett is Lansdowne Professor of Ocean Phys- ics, University of Victoria, Victoria, British Columbia, Canada. Al Osborne is Director, Nonlinear Physics Section, Physics Depart- ment, Università di Torino, Torino, Italy.

Th is article has been published in Oceanography, Volume 18, Number 3, a quarterly journal of Th e Oceanography Society. Copyright 2005 by Th e Oceanography Society. All rights reserved. Reproduction of any portion of this article by photo- 66 Oceanography Vol. 18, No. 3, Sept. 2005 copy machine, reposting, or other means without prior authorization of Th e Oceanography Society is strictly prohibited. Send all correspondence to: [email protected] or Th e Oceanography Society, PO Box 1931, Rockville, MD 20849-1931, USA. White surged the foam of the breaking 15 around us. We felt our boat lifted and fl ung forward like a cork in breaking surf. 10 We were in a seething chaos of tortured water; but somehow the boat lived through 5

it, half-full of water, sagging to the dead (m) Elevation 0 weight and shuddering under the blow. Other mariners have been less fortu- -5 nate. On 12 December 1978, the cargo 800 850 900 950 1000 ship München with 27 people on board Time (s) sent out a garbled May Day message, and Figure 2. Wave record of November 17, 1984 from the Gorm platform in the central (Sand et al., 1990). Th e wave that stands out, though only having a crest height of mere was never heard from again. Pieces of 11 m, clearly exceeds the signifi cant of the background by a factor of two. An- wreckage that were recovered included other famous wave record is the Draupner wave or “New Year’s Wave” where a an un-launched life boat with a pin that of 25.6-m height was measured in a 10.8-m sea on New Year’s Day 1995. had been twisted by an enormous force. The lifeboat was stored 20 m above the water line. There are many more ac- counts of extreme waves hitting cruise waves. Much of the scientifi c interest, if the wave is steep—immense forces ships, passenger liners, container ships, however, stems from evidence that un- can be exerted by a on tankers, and fi shing boats. The fate of the usually large waves occur more frequent- the side of a ship, or on an offshore or fi shing boat Andrea Gail was the basis for ly than would be expected from simple coastal structure (Figures 3 and 4 and, the movie The Perfect Storm. The bare statistics, sometimes appearing within a for example, Welch et al., 1999). statistics are that, over the last 20 years, group of very much smaller waves (Fig- We would also like to predict the per- 200 supertankers and container ships ure 2). More dynamically minded people sistence of an extreme wave or the wave longer than 200 m have sunk in severe often reserve the term rogue for these group in which it may occur. Can a “wall weather, extreme waves certainly being a waves that require more than mere sta- of water” be spotted enough in advance main suspect. The highest wave ever re- tistical superposition. Here we stay with to allow time for safety measures? Can corded—quoted in many oceanography the operational defi nition. one identify and track a group within textbooks—was the 34-m wave observed The quantity of interest depends on which a rogue wave might suddenly in the Pacifi c by the U.S. Navy-chartered the user. For bottom-fi xed structures appear? Do extreme waves appear in tanker Ramapo in the 1920s. The height used by the oil industry, it is the crest groups (the “Three Sisters” of mariners’ was obtained by lining up the wave crest height that matters, whereas for mari- lore)? Are there particular oceanograph- with a line from the top of the foremast ners the height from trough to crest ic conditions in which waves more than to the bridge. is more important. The direction of twice the signifi cant wave height are For operationally minded people, any propagation is a signifi cant factor; a more probable than suggested by simple large waves can be called rogues. More ship typically heads into large seas and statistics? precisely, the term rogue is sometimes uses its large pitch moment of inertia to Topics covered at the meeting included reserved for waves more than some mul- limit the response. A ship is vulnerable the basic physics (such as wave-current tiple (perhaps 2 or 2.2) times the signifi - to large waves coming from a different interactions) that leads to large waves, cant wave height, defi ned as the average direction as the roll moment of inertia is statistical considerations, and the nonlin- height of the highest one-third of the much less. This is particularly important ear physics that can provide surprises. We

Oceanography Vol. 18, No. 3, Sept. 2005 67 800

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-100 0 100 200 300 Time (s) Figure 4. Pressure measurement of an extreme wave recorded at the Admiralty Breakwater, Alderney, Channel Islands, which is exposed to waves from the Atlantic Ocean. Th e peak pressure 2 Figure 3. Th e Wilstar after being hit by a rogue wave in the . To devel- is 745 kPa, which corresponds to a weight of 74.5 tonnes/m . op standards for the design of ship hulls one must predict not only the likelihood of Many ocean-going ships are designed to withstand 15 tonnes/ 2 2 rogue waves but also the forces that they exert on the hull. Photo credit: DLR. m and may break at 30 tonnes/m . Figure courtesy of Howell Peregrine and Charlie Obhrai, University of Bristol, England.

also discussed wave breaking as a conse- dominant waves present but rather into Steady over large fetches are, quence of large waves and possibly as a short waves (Gemmrich et al., 1994). of course, rare, so models have been de- limiting factor on their amplitude. This energy is mostly lost by breaking, veloped to predict wave parameters in and this is how energy (and momentum) general conditions (Komen et al., 1994). BASIC PHYSICS is transferred to the current fi eld. The The forecasts are very valuable for deter- When the blows on a calm ocean remaining energy is passed by nonlinear mining safe and economical routes for it fi rst generates short ripples, which interactions to lower frequencies, caus- merchant shipping. The models allow are affected by surface tension as well ing the shift of the peak, and to higher for energy input by the wind, dissipation as gravity. Given suffi cient time and/or frequencies, where it is dissipated by by wave breaking, and the interactions distance offshore, longer waves become breaking (Komen et al., 1994). that shape the spectrum. In mathemati- dominant. The wave spectrum describes Various formulae have been fi tted to cal terms, these interactions rely on how wave energy is distributed with fre- the signifi cant wave height, the period of phase locking between different waves, quency, and the peak of this spectrum the dominant waves, and the frequency but this was traditionally thought to be gradually moves to a lower frequency at spectrum that are typically observed weak enough that it was reasonable to which waves propagate faster. In a “fully for a given wind speed and “fetch” (the think of a given as made up of developed” sea, waves at the peak propa- distance over which the wind has been a collection of independent waves that gate with a speed close to but slightly blowing). At 10 m/s and large fetch, the combine in a random manner to give faster than that of the wind. For a wind signifi cant wave height is 2 m, with the the sea state we observe. speed of 10 m/s, they propagate with a wave height defi ned as the distance from Extra physics that can clearly lead to speed of 11.4 m/s and have a period of trough to crest. This height increases as large waves includes refraction by cur- 7.3 s and a wavelength of 83 m. It seems the square of the wind speed, so that a rents (Figure 5). The simplest example is that, as the wave spectrum develops, the sustained 20 m/s wind can lead to a sig- when waves meet an opposing current; wind energy is not going directly into the nifi cant wave height of 8 m. waves with a phase speed c in still water

68 Oceanography Vol. 18, No. 3, Sept. 2005 can be stopped completely by an oppos- from the edges. This well-known physics large waves. Unfortunately, even these ing current of only c/4. One factor of two is surely the main reason for the extreme data can be corrupted by the effects of is a consequence of surface gravity waves waves frequently encountered in regions things like sea spray and the infl uence having a group speed (with which en- such as the Agulhas Current, though of the platform. ergy travels) that is half the phase speed. there is still more to be understood about Observations of waves from the back- The other factor of two comes from the the role of fi ne-scale gradients of the cur- scattered signal of short-wavelength reduction in wavelength, and hence in rent, its time dependence, and the way in radar, either shore- or ship-based, can speed, as the waves in front slow down which waves shed their increasing energy sometimes provide data on individual fi rst. If the energy fl ux is conserved, then via interactions and breaking during waves as well as the average wave height the wave height must increase as the their amplifi cation by currents. More- over many wavelengths. Accurate cali- group speed decreases. (In fact there is a over, in some locations the gradients of bration is, however, diffi cult. The inten- further increase in wave amplitude be- current (or topography in shallow water) sity of the backscattered radar signal de- cause the conserved quantity is actually are suffi ciently sharp that the waves can pends on the slope and amplitude of the the fl ux of “action,” or energy divided by be diffracted or partially refl ected as well scattering wave and the Doppler shift on intrinsic frequency; the converging cur- as gradually refracted. Although these its orbital velocity. The transformation rent puts more energy into the waves as mechanisms can cause large waves, there of these parameters to surface elevation it squeezes them.) In a sense, the waves is no obvious reason to expect that they is still a matter of active research. Infor- are four times more sensitive to opposing will lead to anomalous statistics. mation on fi elds over large currents than one might have expected. areas is also available from space-based More dramatic increases in wave en- OBSERVATIONS synthetic aperture radar (SAR) images ergy can occur in a two- rather than one- Measurements, such as those of Figure (Figure 6), though here too interpreta- dimensional situation. Waves meeting 2, made at offshore oil platforms appear tion and translation into wave heights an opposing current jet are slowed more to provide a basis for statistical analysis still present challenges. at the center of the jet, focusing energy and the identifi cation of unusually Altimeter measurements from aircraft are likely to be accurate, but are limited in number.

STATISTICS The histogram of wave amplitude (from mean to wave crest) or of wave height (from trough to crest) can be compared with theoretical expectations. More than fi fty years ago, Longuet-Hig- gins (1952) argued that, for a narrow- band frequency spectrum, the wave fi eld is a slowly modulated sinusoid with the histogram of wave amplitude being the same as the probability distribution of the wave envelope, and, within the con- Figure 5. Waves steepening and breaking in an adverse current. Th is example shows text of linear theory, the wave height is the Stuart Island tidal front in Haro Strait, Canada. It might also represent waves prop- just twice the amplitude. Longuet-Hig- agating from the Roaring Forties into the Agulhas current when wave heights of tens gins showed that, if the spectrum is of meters are imagined. Photo courtesy of Burkard Baschek, Woods Hole Oceano- graphic Institution. made up of many independent com-

Oceanography Vol. 18, No. 3, Sept. 2005 69 20 C

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-20 0 1000 2000 3000 4000 5000 Range (m) Figure 6. (A) Normalized SAR intensity in a 5 km X 10 km area at 48.45°S, 10.33° E, obtained by ERS-2 on August 27, 1996 at 2244 UTC. (B) Retrieved sea surface elevation, (C) transect along the white line inside the box in B. Figure courtesy of Susanne Lehner, University of Miami.

ponents, the probability distribution is (such as shown in Figure 2) may not for the non-stationary situation, as op- given by the Rayleigh formula, survive tests for statistical signifi cance posed to one in every 16,000 waves if the if it is buried in a longer data set and data were stationary. P this includes wave heights from a storm There are other diffi culties in evaluat- with larger waves in general. On the ing what are, after all, typically limited where σ is the rms elevation. (Note that other hand, as originally remarked by data. Even a time series of wave height for this probability distribution, the sig- Longuet-Higgins (1952), erroneous con- at a fi xed point really only samples the nifi cant wave height Hs is equal to 4σ.) clusions can be reached if a wave record equivalent of one horizontal dimension, The tendency of nonlinear waves to is treated as stationary (i.e., with statisti- and may not easily be related to the two- have sharper crests than troughs leads to cal properties that do not change with dimensional statistics of the sea surface. the Tayfun distribution (Tayfun, 1980), time), but is actually non-stationary. An Further, if one is interested in the to- which gives a higher probability of rogue example is shown in Figure 7. Here it is tal wave height, the measurement at a waves and which has been found to give assumed that a wave record is composed fi xed point of the height from a crest to an excellent fi t to computer simulations of two halves, with the variance in the the next trough may differ from what of many sea states. A further modifi ca- second half three times that in the fi rst a mariner at the crest would have seen; tion may come from relaxing the re- half. The probability of a large wave is the trough may shallow before it reaches quirement for a narrow band spectrum. considerably greater than would be pre- the fi xed sensor! A fi xed sensor is also There are clearly other major statisti- dicted with the assumption of station- clearly incapable of following the evo- cal issues that need to be resolved. An ary data. For this example, in fact, one in lution and persistence of an individual anomalously large wave in a short record every 1,300 waves would have H > 2.2 Hs wave or group.

70 Oceanography Vol. 18, No. 3, Sept. 2005 Just gathering reliable data on the oc- tion of large waves in terms of a “Benja- terms in the equations. The model equa- currence and statistics of extreme waves min-Feir Index” evaluated from the nar- tions are approximate, however, and it is clearly presents an ongoing challenge. rowness of the spectral peak; the more not yet known how directionally spread There are also signifi cant diffi culties in peaky the spectrum, the longer the basic a spectrum can be and still give rise to claiming statistical signifi cance for indi- groups and the more time for the insta- anomalous waves. A suspicion is that the vidual large waves while avoiding bury- bility to produce extreme waves. answer depends on where the spectral ing extreme events in long records. While Much of the existing theory is for uni- energy is with respect to a two-dimen- there are currently no clear answers, directional waves. The extension to al- sional instability diagram (Figure 8). there are reasonable grounds for suspect- low for the directional spreading that is On the (downwind) x axis, waves ing that more is going on than random always present is allowed for in some of close to the primary can interact as in superposition. the model equations and these can still the one-dimensional Benjamin-Feir show the emergence of more large waves mechanism, and we see, as discussed ear- NONLINEAR PHYSICS than would occur without the nonlinear lier, that the interaction will be strongest In the early 1960s, Cambridge fl uid dy- namicist Brooke Benjamin and his Ca- nadian graduate student Jim Feir found that they could not make a perfectly regular wave train in a simple wave tank. 1.0 This turned out not to be a consequence Non-stationary sea: wave height distribution, σ2 σ2 σ2 σ2 σ2 of faulty British technology, but rather 0.8 ( 1+ 2 )/2= , 2 =3 1 an unavoidable instability; a single fre- quency is unstable to sidebands that 0.6 ( ) grow and modulate the wave train. The P P H P(H1) total energy content is preserved, so 0.4 P(H2) some waves must now be larger than the 1/2(P(H )+P(H )) 0.2 1 2 average and so larger than in the expect- ed regular wavetrain. 0 The Benjamin-Feir instability occurs 100 most readily for waves of a single fre- quency initially, but a spectrum with a narrow peak will have long groups that resemble a regular wavetrain and so will 10-2 also tend to break up. The phenomenon P has been studied using the full inviscid (Euler) equations in x (along the tank), 10-4 z (vertical), and t (time) and also with approximate versions in the form of nonlinear equations involving only x and 0 1.0 2.0 3.0 H/Hs t. The models all show a tendency for Figure 7. Top: Th e blue curve shows a of wave height for groups of waves to evolve into sequences waves with signifi cant wave height Hs. Th e green and black dashed lines show of waves that look very like the Gorm the Rayleigh distributions for records with variance 1/2 and 3/2 that of the average. Th e red line is the average of these two distributions. Bottom: Th e event (Figure 2). One model (Janssen, same fi gure with the probability plotted logarithmically. Figure courtesy of 2003) even gives the probability distribu- Johannes Gemmrich and Chris Garrett, University of Victoria, Canada.

Oceanography Vol. 18, No. 3, Sept. 2005 71 Directional fi ve wave interactions may need to be k y Spectrum included, but then wave breaking may be Contours a bigger issue. As suggestive and exciting as all these theoretical results on the Benjamin- Feir instability (and its generalizations) are, it is not yet clear how this mecha- nism might actually operate in the open ocean. How is a slightly modulated kx kp regular wave train set up? Or in spectral terms, how is a narrow band spectrum possible in the fi rst place, since the Ben- jamin-Feir instability destabilizes and broadens a narrow band spectrum on a time scale faster than, say, the synoptic wind time scale? Establishing favorable initial conditions is certainly a problem. Figure 8. Wavenumber space, with the origin taken at (kp, 0), the peak wave- number of a directional spectrum (thin lines) propagating primarily in the We have remarked that anomalous x-direction. Waves within the black region can interact with (kp, 0) to produce of groups. Figure courtesy of Al Osborne. statistics are associated with the wave- wave interactions causing fi xed phase relations between different waves. One type of phase locking that seems strong is between a wave and its fi rst harmonic. if the spectral peak is narrow enough in crossing seas. We also need further This has the familiar consequence that to have most of the wave energy in this analysis to predict the persistence of indi- a regular train of surface waves (called region. Off-axis waves are less likely to vidual rogue waves and the groups within Stokes waves) has broad troughs and interact and do so more weakly; waves which they may spring up. narrow peaks, as mentioned earlier, propagating at more than 35 degrees off One way of looking at the Benjamin- with the peaks thus being higher than the central axis do not contribute at all. Feir instability is as a four-wave interac- the troughs are deep. This asymmetry It is not yet known how much of the en- tion. A primary wave with frequency ω seems to carry over into irregular wave ergy of the directional spectrum needs to enters twice to interact with a sideband trains (Figure 2). Theoretically, it can be be within the black region of Figure 8 in frequency ω−δ to produce a wave with shown that using Stokes waves, rather order to produce modulational instabil- frequency 2ω − (ω − δ) = ω + δ. This than sinusoids, as building blocks re- ity and associated rogue waves. second sideband interacts in a similar duces the degree of nonlinearity in the Nonetheless, if further work shows this way with the primary to reinforce the governing equations. picture to be correct, it implies that cross- fi rst sideband and so on. Of course, for ing seas may not have anomalous statis- to occur, the wavenumbers WAVE BREAKING tics, but may be hazardous just because must match too, and this is what deter- The topic of rogue waves cannot be sepa- they can catch ships on their beams. mines the region of instability. rated from a discussion of wave break- However, Shackleton’s observation, and Resonant nonlinear interactions may ing. Do rogue waves break and are their undoubtedly others, may be at odds with occur with larger numbers of waves, heights limited by this? If a rogue wave this. Perhaps there is something more to though this is unlikely to be important does break, what are the implications for be learned about rogue wave formation unless the waves are large. In that case, forces on structures?

72 Oceanography Vol. 18, No. 3, Sept. 2005 As discussed earlier, wave interac- caused by the same nonlinear physics. THE ROLE OF WIND tions and wave breaking help to shape Other factors need to be allowed for. We have been assuming that the role of the wave spectrum in any conditions. Wave breaking tends to occur for wave the wind is just to cause the slow growth Some rogue waves seem to be a product steepness ka>0.3, at least for unidirec- of waves, with dynamic rogue wave for- of strong wave interactions within a nar- tional waves, where a is the wave am- mation occurring on a shorter time scale row spectral peak. There may be simi- plitude and k the wave number equal and so being unaffected by the wind. lar physics for wave breaking: there are to 2π/wavelength. However, for short Some tank experiments, albeit for unidi- routine breaking events from random fetch situations the wave spectrum that rectional waves, suggest that this may not superposition of waves of different fre- is found already has a steepness close to be entirely correct. quencies, but also possibly anomalous 0.3, suggesting that growing waves are In particular, the local wind causes breaking that can arise from the same inhibited by breaking before they can a vertical shear in the current; this may physics that causes rogue waves. achieve rogue wave status. This view is stifl e the resonant interactions that oc- The standard, and elegant, view of supported by observations showing that cur without shear. Some wave breaking wave breaking (Donelan et al., 1972) waves near the peak of the spectrum do is also directly associated with the short started with observations from a com- indeed tend to break in developing seas, waves generated by the local wind. This mercial fl ight and is readily confi rmed by whereas in fully developed seas it is the may interfere with other processes. The the reader (though we recommend ob- smaller scale waves that break. role of gustiness in the wind is also far servations from a few thousand, rather Crossing seas, which occur frequently from being fully understood. However, a than 35,000, feet). as the wind direction changes or as the gusty wind can lead to much larger wave Consider a group of waves moving arrives from separate storms, may heights. A 20 m/s wind with 30% gusti- across the sea surface. The group moves deserve special consideration. As sug- ness (rms deviation), as found often in at half the phase speed of individual gested earlier, they may not be prone to hurricanes and highly unstable atmo- crests, so that these crests appear at the the wave-wave interactions that cause spheric conditions, can lead to signifi cant rear of the group and propagate through anomalous statistics and rogue waves. On wave heights larger than 10 m, as com- it. A given wave reaches its maximum the other hand, the development of large pared to the 8 m of a stable wind quoted height at the maximum of the group and waves by superposition may be so rapid above (Abdalla and Cavaleri, 2002). may break there. The next wave reaches for crossing seas that height limitation by One thing that is clear from wave- the same place one period later, but by breaking is avoided or at least reduced. generation models is that the predictions then the group maximum has moved on half a wavelength. The second wave thus does not catch the group maximum and break there until two periods after the t=0 t=τ t=2τ fi rst wave has broken. Thus wave break- Wave breaking No breaking Wave breaking λ λ ing within a group occurs at time inter- 2 1 2 1 2 vals of two periods, not one, but at space ka=0.3 intervals of one wavelength (Figure 9). 2 31 3 Observations do tend to confi rm this, but in long groups there is also a ten- dency for large breaking waves to emerge by a process called “nonlinear self-focus- ing” that is essentially the Benjamin-Feir x=0 x=0 x=0 mechanism again. Rogue wave forma- Figure 9. A group of waves with a wave at the peak of the group assumed steep enough to break (taking a tion and some wave breaking can thus be critical steepness of 0.3 here). Figure courtesy of Burkard Baschek, Woods Hole Oceanographic Institution.

Oceanography Vol. 18, No. 3, Sept. 2005 73 are sensitive to variations of wind speed often limited to predictions of factors heavily on numerical simulations, most on shorter time and space scales than such as the dominant period and sig- likely using simplifi ed nonlinear model the 1 h and 55 km currently in use on nifi cant wave height. An index derived equations that allow for appropriate a global scale. Better resolution of the from the narrowness of the spectral peak wave-wave interactions but also include wind is a high priority, particularly in and its directional spread is fl agged in representations of wave breaking and areas with strong spatial and temporal some forecasts as an indicator of pos- dissipation. gradients, where presently the models sible rogue wave formation (in the sense We also include here the need for underestimate the peak values for both of a greater than expected occurrence more sophisticated statistical analyses wind and waves. of waves more than twice the signifi cant and appraisal. In particular, questions of wave height), but the validity and value stationarity are key to evaluating the fre- WHERE DO WE GO FROM of this index needs further study. quency of extreme waves. HERE? Predictions need to be accompanied, At present, the evidence for dynamical of course, by some allowance for the way Wave Tank Experiments causes of rogue waves is piling up. How- in which small-scale currents may be Controlled experiments in (large) wave ever, from an objective point of view, increasing the basic wave height. tanks have long been used to study the because of inaccurate, rare, and biased effect of waves on vessels and structures observations, it is still not easy to com- Theory and, more recently, to study the dynamics pletely reject the null hypothesis that This last point emphasizes that there is of highly nonlinear waves. Measurements rogue waves are due to nothing more a need for more detailed analysis to in- confi rm many predictions of inviscid than random superposition. Also, one- corporate wave-current interactions into nonlinear wave theory. The application dimensional time series and two-dimen- wave forecast models. The basic physics is and relevance of these one-dimensional sional images of the sea-surface elevation understood, but, as described earlier, we tank results to the two-dimensional open do not allow any direct inferences about do not have a good understanding of the ocean is a major open research problem its dynamical space-time evolution. role of fi ne-scale variations in the cur- that needs to be resolved.

Analysis of Existing Data As discussed earlier, the tendency for dy- ...there is a need for more extensive routine namical rogue wave formation is likely measurements with useful precision; at present, to be very dependent on the directional spread of waves. It would be very use- too many records of alleged rogue waves ful to have highly resolved directional are anecdotal rather than instrumental. spectra. These may emerge from real and synthetic aperture data as we learn how to interpret these more accurately.

Nonetheless, a number of operational rents, or of the loss of energy from steep- New Observations and research requirements have been ened waves by breaking and wave-wave Our understanding of rogue waves is hinted at already in this article. We may interactions. Many of the existing ap- greatly hampered by the lack of compre- be more explicit in a number of areas. proaches for deep-water waves also need hensive observations in space and time. to be extended to allow for application in Data at a point cannot provide infor- Operational Forecasting shallow water where the seafl oor infl u- mation on the persistence of individual Forecasts of wave conditions used for ences wave propagation and interactions. extreme waves or the environment in safety precautions and ship routing are These theoretical extensions will rely which they occur.

74 Oceanography Vol. 18, No. 3, Sept. 2005 Observational programs in simple instrumental. We need to devise instru- The fourteenth ‘Aha Huliko’a Hawaiian situations may be particularly reveal- ment packages that can be installed on Winter Workshop was supported by the ing of the basic physics. One possibil- merchant ships of opportunity, or at Department of the Navy grant number ity is a fetch-limited situation where least on Navy ships. Data would be par- N00014-00-1-0168, issued by the Offi ce strong winds blow offshore, though as ticularly valuable from extreme wave of Naval Research.

REFERENCES Abdalla, S., and L. Cavaleri. 2002. Effect of wind variability and variable air den- Th e Marine Observer was a fascinating repository of sity in wave modelling. Journal of Geo- physical Research 107(C7/7):1-17, doi strange observations at sea. Its replacement by a more 10.1029/2000JC000639. formal reporting mechanism deserves consideration. Donelan, M., M.S. Longuet-Higgins, and J.S. Turner. 1972. Whitecaps. Nature 239:449- 451. Gemmrich, J.R., T.D. Mudge, and V.D. Polonich- ko. 1994. On the energy input from wind to suggested earlier, in this situation, wave hotspots such as the Agulhas Current. surface waves. Journal of Physical Oceanogra- phy 24:2413-2417. breaking makes the emergence of rogue This is not to discount the value of Janssen, P. 2003. Nonlinear four-wave interac- waves unlikely. Another natural labora- simple observations by mariners. In tions and freak waves. Journal of Physical tory worth considering is a tidal front, a particular, the persistence of individual Oceanography 33:863-884. situation where there are large gradients crests is something that might come most Komen, G.J., L. Cavaleri, M. Donelan, K. Has- selmann, S. Hasselmann, and P.A.E.M. Jans- in currents caused by tidal interaction convincingly from visual observations; sen. 1994. Dynamics and Modelling of Ocean with topography. In particular, there are would that Ernest Shackleton had had a Waves. Cambridge University Press, London, estuarine situations where dense water stopwatch! The Marine Observer was a UK, 532 pp. is advected over a sill by a fl ood and fascinating repository of strange obser- Longuet-Higgins, M.S. 1952. On the statistical distribution of the heights of sea waves. Jour- sinks below light water, providing a well- vations at sea. Its replacement by a more nal of Marine Research 11:245-262. defi ned convergence with dramatic ef- formal reporting mechanism deserves Sand, S.E., N.E. Ottesen Hansen, P. Klinting, fects on wave height. consideration. O.T. Gudmestad, and M.J. Sterndorff. 1990. In any observational program, tech- Freak wave kinematics. Pp. 535-549 in Water Wave Kinematics, A. Tørum and O.T. Gud- niques can include airborne observations ACKNOWLEDGMENTS mestad, eds. Kluwer Academic Publishers, as well as instruments in the ocean. In- We thank the participants of the work- Dordrecht, NL. struments that can be deployed by air in shop for their input to this report and Shackleton, E. 1919. South: The Story of Shack- the path of a hurricane can be a source for their permission to quote unpub- leton’s Last Expedition 1914-1917. William Heinemann, London, UK, 376 pp. of unique data. With regards to near- lished material, and Marshall Tulin for Tayfun, M.A. 1980. Narrow-band nonlinear shore programs, for example tidal fronts, a critical reading of an earlier draft. We sea waves. Journal of Geophysical Research radars of different frequency bands will also thank Diane Henderson for techni- 85:1,548-1,552. be a particularly valuable tool as they can cal assistance. Copies of the proceedings Welch, S., C. Levi, E. Fontaine, and M.P. Tulin. 1999. Experimental study of the ringing of provide information on currents as well are available from Peter Müller, Universi- a vertical cylinder in breaking wave groups. as waves. ty of Hawaii, School of Ocean and Earth International Journal of Offshore Polar Engi- Quite apart from focused programs, Science and Technology, Department of neering 9:276-282. there is a need for more extensive rou- Oceanography, 1000 Pope Road, Hono- tine measurements with useful precision; lulu, Hawaii, 96822. The proceedings at present, too many records of alleged are available online at http://www.soest. rogue waves are anecdotal rather than hawaii.edu/PubServices/AhaHulikoa.html.

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