109

Journal of Oceanography, Vol. 58, pp. 109 to 120, 2002

Review

Keywords:⋅ History,⋅ ocean surfacewaves.

* E-mail address: mituyasu@hf.rim.or.jp

Copyright © The Oceanographic Society of Japan.

A Historical Note on the Study of Ocean Surface Waves

HISASHI MITSUYASU*

Professor Emeritus of Kyushu University, 4-16-12 Miwadai, Higashi-ku, Fukuoka 811-0212, Japan

(Received 2 April 2001; in revised form 25 July 2001; accepted 27 July 2001)

The modern study of ocean surface waves started with a pioneer study by Sverdrupand Munk (1947). More than half a century has passed since then and the study ofocean surface waves has greatly advanced. The current numerical wave models, sup-ported by many fundamental studies, enable us to compute ocean surface waves on aglobal scale with sufficient accuracy for practical purposes. However, physical proc-ess controlling the energy balance of ocean surface waves is still not completely un-derstood. The present note is a rough sketch of the historical development of the studyof ocean surface waves in the latter half of the twentieth century when the Oceano-graphic Society of Japan was founded and grew.

much delayed. By contrast, studies of water waves withregular and permanent forms as a fluid dynamical phe-nomenon have a long history. Their fundamental studieswere successfully developed in 19th century even for theadvanced mathematical formulations. Modern studies ofocean surface waves started only in the 1940s with theoutstanding study by Sverdrup and Munk (1947) of theScripps Institution of Oceanography (SIO). The mostimportant points of their study can be summarized as fol-lows;

1) “Significant waves” are characterized by a kindof mean wave height and mean wave period. These werefirst introduced to describe quantitatively ocean surfacewaves that show random properties.

2) The concept of energy balance in a wave sys-tem was introduced to understand the wave evolution.

3) Empirical relations for the evolution of oceansurface waves in dimensionless forms were obtained byusing accumulated wave data. The important quantitiescontrolling the phenomenon were included in the rela-tions.

Although these are common knowledge today, it isreally surprising that such ideas were proposed when thesimilar ideas or studies were almost non-existent, exceptfor primitive and purely empirical formulas. Since theirstudy, modern studies of ocean surface waves were de-veloped, and many fundamental properties and dynamicprocesses of ocean surface waves have been clarified.

This paper is devoted to a brief history of moderndevelopments in the study of ocean surface waves. Thisis not a detailed history, however, but one that describes

1. IntroductionThe wind blowing over the sea surface generates

wind waves. They develop with time and space under theaction of the wind and become huge waves called oceansurface waves. According to our present knowledge thisprocess can be described as follows: the wind blowingover the water surface generates tiny wavelets which havea two-dimensional spectral structure. The spectral com-ponents develop with time and through space by absorb-ing the energy transferred from the wind. Nonlinear en-ergy transfer among spectral components is also impor-tant in the development of the spectrum. The high fre-quency components then gradually saturate, losing theabsorbed energy as the waves break, while the low fre-quency components are still growing. In this way, thespectral energy increases and the spectral peak shifts tothe low frequency side. It took a very long time to arriveat such a dynamical model of ocean surface waves. Thepresent note on the development of investigation focusesmainly on how we reached our present understanding ofthe ocean surface waves.

In early days, the major difficulties in the study ofocean surface waves were their random properties andthe complex mechanisms of their evolution. These prop-erties of ocean surface waves are quite different fromthose of regular water waves and due to this differencethe fundamental studies of ocean surface waves were

110 H. Mitsuyasu

a general picture of modern developments. Therefore onlya limited number of papers are referred to, which areneeded to advance the story. Furthermore, emphasis inthe discussion is put rather on early periods in the study,because a detailed discussion on the modern developmentof the study would become far too large for adequate treat-ment in this short note.

2. Modern Development in the Study of Ocean Sur-face WavesThe study of ocean surface waves extends to a great

many areas. Table 1 has been prepared to give a generalview of the study and its historical development. The prob-lem areas related to the study of ocean surface waves havebeen divided into six topics: 1) generation mechanism(of wind waves) including the generation of initial wave-lets and energy transfer from the wind to waves; 2) sta-tistical properties (of wind waves) including the wavespectrum; 3) nonlinear properties (of wind waves) includ-ing the nonlinear interactions among spectral components,wave instability and wave breaking; 4) laboratory andocean experiments; 5) air-sea and wave project and6) wave forecasting (methods). The decadal change ofeach topic together with epoch-making international sym-posia, and relevant scientific and technological progressin each decade, are summarized in the Table. Earth ob-serving satellites and international symposia are listed inthe appendix, which also includes typical monographs andextended reviews of ocean surface waves. The historicaldevelopments in the study of ocean surface waves can bedescribed referring to Table 1.

2.1 Generation mechanism of wind wavesThe wind over the sea surface generates wind waves

(ocean surface waves). Therefore, the mechanisms of windwave generation and energy transfer from the wind to thewaves are essential problems in the study of ocean sur-face waves.

Although it does not appear in Table 1, Jeffreys(1924, 1925) presented an outstanding theory (shelteringtheory) before the start of the advanced study in the 1940s.He considered that if the wind velocity is faster than thewave velocity, the air flow over the wave separates at thewave crest and transfers the momentum to surface wavesthrough the form drag associated with flow separation.Furthermore, based on a consideration of simple energybalance in the process of wave generation, he estimatedthe sheltering coefficient that can be used to calculate thegrowth of waves due to the wind.

In order to verify the Jeffreys’s sheltering mecha-nism, fluid dynamicists carried out laboratory experi-ments; Stanton et al. (1932) and Motzfeld (1937) did simi-lar laboratory experiments independently on the air flowover a solid wavy surface. Unfortunately, the measured

sheltering coefficients were much smaller than expectedfrom Jeffreys’s investigation. However, the experimentfor waves with sharp crest by Motzfeld (1937) clearlydemonstrated the separation of the air flow at the crestand an increase of the sheltering coefficient, although thevalue was still smaller than expected from Jeffreys’s in-vestigation. As a result of these experiments, the contri-bution of the sheltering mechanism to wind wave gen-eration came to be questioned. However, further studieswere needed to clarify the contribution of the separationof air flow to the growth of wind waves. Because manyassumptions were made in Jeffreys’s theory, and the ex-periments mentioned above were implemented by usinga solid wavy surface. Moreover, recent observations ofair flow over steep water waves have revealed the sepa-ration of air flow (Banner and Melville, 1976; Kawai,1982).

In the 1940s there were not many studies on the wavegeneration mechanism, except for a theoretical study byWuest (1949) who did a stability analysis of the air-seainterface, and an experimental study by Francis (1949)who presented a careful observation of wind-wave gen-eration in a wave tank.

In the 1950s Ursell (1956), who was engaged in thewartime study of ocean waves in the UK in the 1940s,presented an extensive review of the wind wave genera-tion study. He summarized the available experimental andtheoretical studies and concentrated all his energy on thediscussion of the results of these studies. He concludedthat neither mechanism was likely to play a dominant rolein wave generation. Stimulated by the review of Ursell(1956), two epoch-making theories were presented simul-taneously by Phillips (1957) and Miles (1957). Phillips(1957) proposed that random pressure fluctuation in thewind resonantly generates wind waves on the water sur-face. However, later laboratory experiments indicated thatthe pressure fluctuations in the turbulent wind are muchsmaller than that estimated by Phillips (1957) and thetheory could not explain the growth rate of wind waves,though it is still responsible for the generation of initialwind waves. On the other hand, Miles theory is a kind ofstability theory that inherits the thoughts of Wuest (1949)and Lock (1954) but applies a more realistic (logarith-mic) wind profile. Miles (1957) showed that the couplingbetween the surface waves and wind generates a specialpressure distribution along the wave surface and leads toan exponential growth of the waves.

In the 1960s Miles (1960) combined the two theo-ries of Phillips (1957) and Miles (1957) and showed thatthe growth of waves is initially linear but ultimately ex-ponential in time. The field measurement by Longuet-Higgins et al. (1963), and laboratory measurement byShemdin and Hsu (1967) partly supported the results ofMiles (1957), and Lighthill (1962) gave a physical inter-

A Historical Note on the Study of Ocean Surface Waves 111

Tab

le 1

. A

dvan

ces

in t

he s

tudy

of

ocea

n su

rfac

e w

aves

in

the

latt

er h

alf

of t

he t

wen

tiet

h ce

ntur

y.

Lis

t of

ac r

onym

s in

Ta b

le 1

.O

SJ:

The

Oc e

a nog

raph

ic S

ocie

ty o

f Ja

pan

(fou

nded

in

1941

).S

WO

P:

Ste

reo

Wav

e O

bse r

vati

on P

roje

c t;

see

Cot

e e t

al.

(19

60).

SM

B:

Sve

rdru

p, M

unk

a nd

Bre

tsc h

neid

e r;

see

Sve

rdru

p a n

d M

unk

(194

7) a

nd B

rets

c hne

ide r

(19

52).

PN

J: P

iers

on, N

e um

ann

a nd

Jam

e s;

see

Pie

rson

et

al. (

1955

).IC

CE

: In

tern

a tio

nal

Con

fere

nce

on C

oast

a l E

ngin

e eri

ng (

sta r

ted

from

195

0).

WA

M: W

ave

Mod

e l;

see

The

WA

MD

I G

roup

(19

88).

JON

SW

AP

: Jo

int

Nor

th S

e a W

ave

Pro

jec t

; se

e H

a sse

lman

n e t

al.

(19

73).

JWA

3G:

Japa

n W

e ath

e r A

ssoc

iati

on’s

Thi

rd G

e ne r

a tio

n W

ave

Mod

e l;

see

Suz

uki

a nd

Isoz

a ki

(199

4).

AR

SL

OE

: Atl

a nti

c R

emot

e S

e nsi

ng L

and

Oc e

a n E

xpe r

imen

t; s

e e V

inc e

nt a

nd L

ichy

(19

81).

RIA

M P

roje

c t:

Wav

e O

bse r

vati

on P

roje

c t;

see

Mit

suya

su e

t al

. (19

75).

SW

AD

E: T

he S

urfa

c e W

ave s

Dyn

amic

s E

xpe r

imen

t; s

e e K

a tsa

ros

e t a

l. (

1993

).H

EX

OS

: H

umi d

i ty

EX

chan

ge O

ver

t he

Sea

; se

e S

mi t

h et

al.

(19

92).

RA

SE

X:

Ri s

ø A

i r-S

ea E

xcha

nge;

see

Joh

nson

et

al. (

1998

).S

OW

EX

: S

out h

ern

Oce

an W

aves

Exp

eri m

ent ;

see

Ban

ner

et a

l. (

1999

).

112 H. Mitsuyasu

pretation of the Miles (1957) theory. By these results, theproblem of wind wave generation was considered to besolved. However, the field observations by Snyder andCox (1966), and by Barnett and Wilkerson (1967) showedthat the measured growth rates of a spectral componentof ocean surface waves were one order of magnitudegreater than those expected by Miles. Many theoreticalstudies started again in the 1970s to explain the mecha-nism of wave generation.

One direction is to improve the Miles (1957) theoryby introducing the effects of turbulence in the wind (e.g.,Townsend, 1972; Davis, 1972; Gent and Taylor, 1976).The studies along this line were continued until the 1980s(e.g., Al’Zanaidi and Hui, 1984) and also 1990s (e.g.,Belcher and Hunt, 1993; Miles, 1993). However, we arestill not in a position to completely understand the mecha-nism, while some of the numerical calculations (e.g.,Al’Zanaidi and Hui, 1984; Miles, 1993) gave fairly goodagreement between the theory and experiments.

Another direction was to measure the growth rate ofwind waves as accurately as possible, because the growthrates measured by Snyder and Cox (1966), and Barnettand Wilkerson (1967) were considered, according to ourcurrent knowledge, as overestimates due to the effect ofnonlinear energy transfer. Many field and laboratorymeasurements were carried out to obtain more reason-able values, unaffected by nonlinear energy transfer(Snyder et al., 1981; Mitsuyasu and Honda, 1982; Hsiaoand Shemdin, 1983). Plant (1982) proposed an empiricalformula for the growth rate of wind waves by combiningthe observed values of various reliable sources. The mea-sured values are used in the current numerical wave mod-els, but the scatter in the measured growth rate is consid-erable and the problem still remains unsolved.

One of the most difficult problems is that accuratemeasurements of the detailed phenomena near the windwave surface are extremely difficult. This has hamperedthe derivation of more realistic theoretical models. There-fore, well-focused experiments using advanced measur-ing techniques are strongly needed to clarify the phenom-ena near the air-sea interface that will provide a break-through to clarify the phenomena.

The above discussions are mainly concerned with thegrowth mechanism of wind waves under the action of thewind. In regard to the generation of initial wind wavesover a still water surface there are several interesting sub-jects to study. When the wind starts to blow over the wa-ter’s surface, a drift current is generated and, a little later,a tiny capillary wave is generated which develops gradu-ally into wind waves. Kunishi (1963) conducted a com-prehensive laboratory experiment on this problem to shedlight on the phenomena. About twenty years later Kawai(1979) performed both experimental and theoretical stud-ies on this subject examining a coupled shear flow model

in the air and water to clarify the generation of the initialwind wave. He obtained fairly good agreement betweenthe theory and his measurements. Okuda et al. (1976)made detailed observations of the wind-induced surfaceflow in the water by using flow visualization techniques,before and after the generation of wind waves. They foundan interesting relation between a transition of the surfaceflow from laminar to turbulent and the generation of windwaves. The generation of initial wind waves can also betreated by the resonance theory of Phillips (1957). Kahmaand Donelan (1988) studied experimentally an initial stageof wind wave generation, but their results were not nec-essarily conclusive for the contributions of the two mecha-nisms of Kawai (1979) and Phillips (1957). Further stud-ies are required to clarify the problem.

2.2 Statistical properties of wind wavesOcean surface waves are water surface waves, as the

name indicates. However, they display random proper-ties that obstructed our clear understanding of the phe-nomena in the early days. It is said that Lord Rayleighremarked, “The basic law of the seaway is the apparentlack of any law” (Kinsman, 1965). Sverdrup and Munk(1947) introduced their significant waves, a kind of sta-tistical mean wave, to describe random properties of oceansurface waves. Statistical theory of wind waves wasgreatly advanced since then based on the theory of ran-dom process, in particular on the theory of random noisethat was presented by Rice (1944) of Bell Telephone Labo-ratory. Following the random noise theory, as the firstapproximation, random waves are considered as a sum ofan infinite number of sinusoidal waves in a random phase.

In the 1950s, based on the statistical model abovementioned, Longuet-Higgins (1952) gave the first theo-retical derivation of the statistical distribution of wave-heights. Cartwright and Longuet-Higgins (1956) in theNational Institute of Oceanography (NIO) of the UnitedKingdom derived the statistical distributions of the maxi-mum values of the random function. The statistical theoryof ocean surface waves was greatly extended by the groupin the NIO and effectively applied to the analysis of ac-cumulated wave data in the 1950s.

On the other hand in the United States, Pierson (1953)of the New York University (NYU) presented a spectralmodel of wind waves that was also greatly affected bythe theory of random noise. Neumann (1953), also ofNYU, determined a spectral form of developing oceansurface waves by using his observed wave data. By com-bining the results of their studies, the NYU group pre-sented the famous paper entitled: Practical methods forobserving and forecasting ocean waves by means of wavespectra and statistics (Pierson et al., 1955).

As for the physics of the wave spectrum, Phillips(1958) proposed the equilibrium range in the spectrum

A Historical Note on the Study of Ocean Surface Waves 113

of wind waves based on a simple consideration of wavebreaking. The spectral model, which was basically sup-ported by the newly developed random process theoryand various observations including the pioneering studyby NIO, contributed remarkably to advance the study ofocean surface waves.

With the increase of spectral data in the 1960s manyoceanographers tried to determine a similarity form ofthe spectrum of ocean surface waves. The most success-ful result was obtained by Pierson and Moskowitz (1964).They proposed a famous spectral form (PM spectrum) forfully developed wind seas by using wave spectral dataobtained in the North Atlantic Ocean. Their study wasbased on the similarity theory of wind wave spectrumpresented by Kitaigorodskii (1962) which was quite analo-gous to the similarity theory of turbulence developed tra-ditionally in the USSR.

From the end of the 1960s to the 1970s a great manyexperimental studies were done to clarify the wind wavespectrum. As a result of those extensive studies we clari-fied many important properties of the wind wave spec-trum, such as the evolution of the spectrum (Mitsuyasu,1968b, 1969; Hasselmann et al., 1973), the spectral format a finite fetch (Hasselmann et al., 1973), the similarityform of the directional spectrum (Mitsuyasu et al., 1975;Hasselmann et al., 1980; Donelan et al., 1985). On theother hand, Toba (1972, 1973a, 1973b) presented an im-portant concept of the local equilibrium between windsand wind-generated waves which means the wind wavesretain their internal self-similar structure when they de-velop. An important “3/2 power law” for wind waves wasincluded in it. Toba (1973b) also derived a new equilib-rium form of the wave spectrum that was supported byKawai et al. (1977) and has a form different from that ofPhillips (1958). Owing to the increased data supportingthe Toba’s new spectral form, Phillips (1985) presented anew theory that supported the new equilibrium form ofToba (1973b).

The statistical nature of ocean surface waves againdrew attention in the 1970s and 1980s. Longuet-Higgins(1975, 1983) studied the joint distribution of the periodand amplitude of random waves which is important forpractical purposes.

After the launch of the SESAT satellite in 1978, stud-ies of ocean wave spectra focused on the high-frequencypart of the wave spectrum to analyze the data of micro-wave sensors such as a scatterometer and an altimeter.As the results of many experimental studies during a pe-riod from the 1970s to the 1990s, we clarified the wind-dependence of the high frequency wave spectrum (e.g.,Mitsuyasu and Honda, 1974; Mitsuyasu, 1977) and thehigh wave-number spectrum (e.g., Jähne and Riemer,1990; Zhang, 1995), which contributed to the analysis ofthe data of the scatterometer. The high frequency waves

also attracted attention as a roughness element of the seasurface. Many studies on this subject were carried out,clarifying the fine structure of high frequency waves (Coxand Munk, 1954; Cox, 1958; Kondo et al., 1973), thoughthe contribution of the high frequency waves to the seasurface roughness was still unclear and controversial.

2.3 Nonlinear properties of wind wavesOcean surface waves can be described fairly well by

linear theory as described in Subsection 2.2. This is oneof the reasons why the spectral model can be very effec-tively used to describe the random ocean surface waves.However, waves gradually show nonlinear properties withthe increase of wave steepness (wave height/wave length),e.g., distortion of the wave form, nonlinear interactionamong spectral components, wave instability and finalwave breaking.

In the 1940s, studies on nonlinear waves were stillconducted along lines extending back to the study in 19thcentury and mainly confined to the study of regular mono-chromatic nonlinear waves. The nonlinear theory of regu-lar waves (solitary wave theory) was applied even to oceansurface waves (e.g., Munk, 1949). This is because oceansurface waves were described, in many cases, by usingsignificant waves, that is, a kind of mean wave with amonochromatic wave property. It was only at the end ofthe 1950s that Tick (1959) presented a nonlinear randommodel of gravity waves.

The nonlinear theory of ocean surface waves wasgreatly advanced in the 1960s. Phillips (1960) andHasselmann (1960, 1962, 1963) almost simultaneouslyfound the nonlinear energy transfer among wave spectralcomponents which is caused by resonant four-wave in-teractions. These are remarkable results, because the evo-lution of the wave spectrum is strongly affected by thismechanism. Longuet-Higgins and Smith (1966), andMcGoldrick et al. (1966) experimentally confirmed theresonant four-wave interactions and Mitsuyasu (1968a)also experimentally confirmed the evolution of the con-tinuous wave spectrum due to this effect. Although thenonlinear energy transfer plays an important role in theevolution of the wave spectrum, the problem is its com-putational difficulty. Many studies attempted to solve theproblem. Longuet-Higgins (1976) and Fox (1976) deriveda nonlinear interaction model that was more easily com-putable. However, their results were found to be unsuit-able for the description of actual phenomena, because themodel holds in principle only for an extremely narrowspectrum, and observed results show considerable disa-greement with Fox’s calculations (Masuda, 1980).

Masuda (1980) studied a new computational schemeof nonlinear energy transfer based on Hasselmann’s modeland much improved the numerical stability and computa-tional accuracy. Hashimoto et al. (1998) extended the

114 H. Mitsuyasu

computational scheme of Masuda (1980) for deep-waterwaves to one for shallow water waves. Komatsu andMasuda (1996) developed a more efficient computationalscheme of nonlinear energy transfer, but the computationaltime is still not suitable for practical application to op-erational wave models.

Since the exact computation of the nonlinear energytransfer takes too much time and is impractical for appli-cation to operational wave forecasting, most of the presentoperational wave models use greatly simplified compu-tational schemes of nonlinear energy transfer (Hasselmannand Hasselmann, 1985; Hasselmann et al., 1985; Suzuki,1995). The problem still remains, however, because theaccuracy of the simplified computational schemes de-pends on the forms of the wave spectra. In this connec-tion Hashimoto et al. (1999) improved the accuracy ofthe discrete interaction approximation of the nonlinearenergy transfer.

In the 1970s, Ramamonjiarisoa (1974) andRamamonjiarisoa et al. (1978) found a very curious phe-nomenon, that some high-frequency components in thewind wave spectrum did not follow the dispersion rela-tion. This finding cast serious doubt on the spectral modelof wind waves that assumes, as a first approximation, thatspectral components are free waves and follow an ordi-nary dispersion relation. Many studies were implementedto clarify this problem. Among others, Masuda et al.(1979) and Mitsuyasu et al. (1979) published compre-hensive studies. They indicated theoretically and experi-mentally that, in steep wind waves, high frequency com-ponents of nearly twice the frequency of the spectral peakwere dominated by the nonlinear bounded waves thatpropagate with the same speed as that of the spectral com-ponents near the spectral peak.

From the 1980s to 1990s, fundamental studies on thenonlinear properties of ocean surface waves were con-centrated on the most difficult nonlinear phenomena ofwave breaking. Banner and Peregrine (1993) and Melville(1996) presented successively comprehensive reviews ofwave breaking. Wave breaking is not only important asan energy dissipation mechanism in the wave’s evolutionbut is also important in various exchange processes atthe air-sea boundary. An example of the recently contro-versial subject is the effect of wave breaking on CO2 ex-change through the air-sea interface. The effect of wavebreaking on the momentum transfer from air to water isstill not clear, either. The problem itself is relatively oldbut a new approach for future study is urgently needed.

2.4 Laboratory and ocean experimentsIn order to clarify oceanographic phenomena such

as ocean surface waves, field observations are very im-portant, while laboratory experiments under well-control-led condition give us a clear understanding of the funda-

mental processes involved. Many observational studieson ocean surface waves were carried out with this con-sideration, which took the form of the wave observationprojects described below in Subsection 2.5.

Laboratory experiment has many purposes, such asto discover new phenomena, to clarify fundamental proc-esses in the phenomena and to verify the results of newtheories. As shown in the previous sections, experimen-tal studies have made important contributions to clarify-ing the dynamic processes of wind waves. Toba (1998)presented a comprehensive review of the experimentalstudies on wind waves as an air-sea boundary process.

Recently satellite observations of the wind and wavesin the ocean by using microwave sensors have moved fromexperiments to attain the status of routine operations(Bernstein, 1985; Stewart, 1985; Douglas and Cheney,1990). They provide an enormous amount of accurate dataon wind and waves in the ocean. Such wind and wavesdata on the global scale, in association with advancednumerical wave models, contribute to accurate wave fore-casts (e.g., Romeiser, 1993). However, the theories ofmicrowave backscattering at the sea surface are unsatis-factory even now (e.g., Apel, 1994; Keller et al., 1995),and the measurement still largely depends on variousempirical formulas. Further fundamental studies are re-quired to clarify this problem, too.

2.5 Air-sea and wave projectsAccurate and systematic observations of wind and

waves in the ocean, or more generally air-sea interactionphenomena, tend inevitably to be big projects, becausethey require the cooperation of many scientists and engi-neers. As shown in Table 1, many projects have been con-ducted, both national and international.

In the 1950s, two remarkable wave-observationprojects (Sun Glitter Project and Stereo Wave Observa-tion Project) were conducted in the United States. Coxand Munk (1954) of the SIO took aerial photographs ofthe sun’s glitter on the sea surface in the Hawaiian areaunder various wind conditions. They clarified the statis-tical distribution of wave slopes and its dependence onthe wind speed. On the other hand, Cote et al. (1960) ofthe NYU conducted a large project called the Stereo WaveObservation Project (SWOP), in which they took aerialstereo photographs of the sea surface in the North Atlan-tic. Through the very laborious analysis of the data, theywere the first to determine the directional spectrum ofocean surface waves.

In the 1960s, Longuet-Higgins et al. (1963) of theNIO in the United Kingdom presented an important pa-per. They made pioneering observations of the directionalwave spectrum and atmospheric pressure fluctuations nearthe sea surface by using a pitch-and-roll buoy newly de-veloped by the NIO. They used the data extensively to

A Historical Note on the Study of Ocean Surface Waves 115

clarify the properties of the directional wave spectrumand the wave generation theories by Miles (1957) andPhillips (1957). In the 1960s, very celebrated projectJONSWAP (Joint North Sea Wave Project) was also con-ducted in Europe by an international team (Hasselmannet al., 1973). It provided the following important resultson the evolution of wave spectrum at finite fetches; fetchrelations for the spectral parameters, similarity forms ofthe wave spectrum at finite fetches, and the effect ofnonlinear energy transfer in the evolution of the wavespectrum.

During the period from 1971 to 1974, a group of sci-entists and engineers at the Research Institute for AppliedMechanics (RIAM) of Kyushu University conducted awave observation project (Mitsuyasu et al., 1975). Theyconducted a comprehensive observation of the directionalwave spectrum in the North Pacific Ocean and the EastChina Sea by using a cloverleaf buoy that was developedby RIAM, based on the original NIO design. They firstpresented a similarity form of the directional wave spec-trum in the generation area. The result was further ex-tended by similar observations in 1980s by Hasselmannet al. (1980) and by Donelan et al. (1985). Currently wehave a fairly clear understanding on the directional prop-erty of the dominant part of the wave spectrum, while thedirectional property of the high frequency part is stillcontroversial (Banner et al., 1989).

In the 1990s, many air-sea and wave observationprojects have been conducted, typical examples of whichare listed in the Table 1. The purposes of these projectswere mainly to clarify the air-sea exchanges of variousquantities such as momentum, heat, humidity, etc. Par-ticular attention was focused on the effects of wind waveson the air-sea exchange processes. We have accumulatedvarious new results on the phenomena, though it will takemore time to derive definite conclusions.

2.6 Wave forecastingAccurate forecasting of ocean surface waves is one

of the important goals in the study of ocean waves. Ashas repeatedly been mentioned, modern development inthe study of ocean surface waves started from the studyon wave forecasting done by Sverdrup and Munk (1947)during World War II. By using newly accumulated oceanwave data in the 1950s, Bretschneider (1952, 1958) andWilson (1961, 1965) greatly improved the wave forecast-ing method of Sverdrup and Munk (1947), and presenteda revised forecasting method, usually called the SMBmethod. Furthermore, in the 1950s, a statistical theory ofrandom ocean waves was presented and the spectral struc-ture of ocean surface waves was clarified to some extent.The accumulated knowledge in such fundamental studywas effectively used to construct a spectral wave fore-casting method by Pierson et al. (1955).

Inoue (1967) and Barnett (1968) presented numeri-cal wave models in the 1960s with further progress infundamental studies, such as wave generation mechanism,nonlinear energy transfer and energy balance equation(Hasselmann, 1960). It should be mentioned, however,that a French group independently developed the numeri-cal wave model in an earlier period, the 1950s (Gelci etal., 1957).

In Japan the MRI wave model was developed byIsozaki and Uji (1973) and used for routine wave fore-casting at the Japan Meteorological Agency. About tenyears later it was replaced by the MRI- II wave model(Uji, 1984). Various wave models were developed in manycountries. And they were improved successively as sum-marized in the monograph “Ocean Wave Modeling (TheSWAMP Group, 1985)”, in which typical wave modelsdeveloped in various countries were described. TheTOHOKU Wave Model (Toba et al., 1985) and the MRIWave Model (Uji, 1985), developed in Japan, were in-cluded.

At present, third generation wave models such as theWAM model (The WAMDI Group, 1988), JWA3G model(Suzuki and Isozaki, 1994; Suzuki, 1995) and MRI-IIImodel (Ueno and Ishizaka, 1997) have been developedwith the support of recent studies on the fundamental proc-esses that control the energy source terms, i.e., the en-ergy input from the wind, the nonlinear energy transferamong spectral components and the energy dissipationdue to wave breaking. In particular, the explicit compu-tation of the nonlinear energy transfer characterizes thethird generation wave models, which are used to predictthe ocean surface waves at global scale with practicallysufficient accuracy. However, even in the most advancedthird generation wave models, some of the energy sourceterms depend largely on empirical knowledge. Furtherstudies are needed to develop a more improved wavemodel, constructed on a sound physical basis.

2.7 International symposiaIn 1961 Sir George Deacon organized the first inter-

national symposium on “Ocean Wave Spectra”, held atEaton, Maryland, in the USA. World leading scientistsand engineers presented in this meeting a summary ofthe present state-of-the-art in the several fields of oceanwave studies. They also discussed the current researchtrends, future needs and the most recent techniques forocean wave measurement and analysis. The meeting con-tributed greatly to the rapid progress in the study of oceansurface waves in the succeeding periods.

Since then, similar symposia have been held untilnow, as shown in Table 1. However, the role of the sym-posium is slightly changing, because now we can ex-change information quickly by other various ways andmeans. Main topics in the symposia are also gradually

116 H. Mitsuyasu

changing, from the dynamics of ocean surface waves totheir contributions to the air-sea exchange process, andto contributions on recent problems in the changing glo-bal environment. Such a change of the aims or scope ofthe symposia is reflected on the very long titles of thesymposia as shown in the appendix.

3. Concluding RemarksThe historical development of the study of ocean

surface waves can be roughly divided into four periods;initial period (before and in 1940s), growing period (1950sand 1960s), expanding period (1970s and 1980s), and thepresent period (post-1980s).

The initial period is characterized by the wartimestudies during World War II. The most fruitful result wasobtained by Sverdrup and Munk (1947) who proposednot only an advanced forecasting method but also a frame-work for the study of ocean surface waves in the suc-ceeding period when the measured wave data increasedrapidly. Studies at the NIO in the UK also greatly con-tributed by developing measurement and analysis tech-niques for the wave data.

The most outstanding contributions in the 1950s werethe presentations of the two wave generation theories byPhillips (1957) and by Miles (1957). These theories werenot necessarily in good agreement with observations butgave a fundamental framework for succeeding studies.The formulation of the statistical theory of random wavesin this period was a great contribution too. Particularlyspectral model, which was fundamentally supported bythe random process theory, greatly advanced the study ofocean surface waves. It was a surprising event that suchlarge projects as SWOP and the Sun Glitter Project weresuccessfully accomplished in the early 1950s.

One of the most important studies in the 1960s wasthe theoretical study of the nonlinear energy transferamong spectral components, which is a very importantenergy source term in the wave evolution in associationwith the energy transfer from wind to waves, though an-other important term of the energy dissipation due to wavebreaking remains. The formulation of the numerical wavemodel based on the energy balance equation was also animportant contribution in this period, opening the way tothe development of more advanced models in succeedingperiods. These two important studies contributed later tothe development of a more advanced model, the thirdgeneration wave model.

Roughly speaking, the dominant framework for thestudy on ocean surface waves was constructed until 1960s;we derived the statistical model to describe the randomocean surface waves, the dynamic model to describe theevolution of ocean surface waves, and the numerical wave

model to predict ocean surface waves at global scale. Stud-ies in the 1970s and 1980s were devoted to adding moreaccurate information or to improving the results obtainedpreviously. Typical examples of the important results areaccurate descriptions of the evolution of the wave spec-tra, determination of the similarity forms of wave spec-tra, the derivation of the concept of local equilibrium inthe wave evolution, and accurate computations of thenonlinear energy transfer. These fundamental studies sup-ported the development of the advanced numerical wavemodels of the third generation.

In the present period, starting from the 1990s, thestudy of the mechanism by which wind waves are gener-ated is continuing, because the mechanism is still notcompletely understood, even now. However, more atten-tion is being paid to the most difficult problem of wavebreaking. Studies of wave breaking as a fluid dynamicphenomenon were greatly advanced by Longuet-Higginsand many other fluid dynamicists. However, many prob-lems have still remained unsolved related to the contri-bution of wave breaking to the following phenomena:wave energy dissipation, which is an important elementin the source term of energy balance equation, and vari-ous exchange processes at the air-sea boundary, which isgreatly affected by wave breaking. Recent studies arefocused on these problems, as described by Melville(1996).

About half a century ago, Ursell (1956) stated in hisfamous review, “Wind blowing over water surface gener-ates waves in the water by a physical process which cannot be regarded as known.” A great many studies con-ducted after that time have given us a tremendous amountof information on the statistical and dynamic propertiesof ocean surface waves and made it possible to computethe waves at global scale with sufficient accuracy for prac-tical purposes. However it will be difficult, even now, toanswer the question, “Have we really clarified the physi-cal process of wind wave generation and decay?”

AcknowledgementsI wish to express my sincere thanks to Professor A.

Masuda of Kyushu University for many stimulating dis-cussions and for his critical reading of the manuscript,which contributed greatly to improving this paper. I alsowish to thank Professor H. Honji of Kyushu Universityfor his invaluable advice and constant encouragement.Without his encouragement it would have been difficultto complete this article. My sincere thanks are extendedto Professor Emeritus Y. Toba of Tohoku University forhis valuable comments and to anonymous reviewers fortheir careful reviews and constructive comments.

A Historical Note on the Study of Ocean Surface Waves 117

Appendix 1: Earth Observing SatellitesSEASAT: (1978)GEOSAT: Geodetic Satellite (1985–1989)ERS 1: Earth Research Satellite 1 (1991–1996)ERS 2: Earth Research Satellite 2 (1995–2001)ADEOS: Advanced Earth Observation Satellite

(1996–1997)[The years in ( ) show the year of launch and life.]

Appendix 2: Symposia and Their Proceedings1948: Ocean Surface Wave; New York, USA

Ocean Surface Wave. p. 343–572. In Annals of NewYork Academy of Sciences, Vol. 5, Art 3, ed. by B.Haurwitz, Published by the Academy (1949), NewYork.

1950: International Conference on Coastal Engineering;Berkeley, California, USAProceeding of First Conference on Coastal Engineer-ing. Council of Wave Research, Engineering Foun-dation (1951).

1961: Ocean Wave Spectra; Eaton, Maryland, USAOcean Wave Spectra. Prentice-Hall , INC.,Englewood Cliffs, New Jersey (1963), 357 pp.

1977: Turbulent Fluxes through Sea Surface, Wave Dy-namics and Prediction; Marseille, FranceTurbulent Fluxes through Sea Surface, Wave Dynam-ics and Prediction, ed. by A. Favre and K.Hasselmann, NATO Conference Series V, Air-SeaInteractions. Plenum Press, New York (1978), 677pp.

1981: Wave Dynamics and Radio Probing of Ocean Sur-face; Miami, USAWave Dynamics and Radio Probing of Ocean Sur-face, ed. by O. M. Phillips and K. Hasselmann, Ple-num Press (1986), 694 pp.

1984: The Ocean Surface, Wave Breaking, TurbulentMixing and Radio Probing; Sendai, JapanThe Ocean Surface, Wave Breaking, Turbulent Mix-ing and Radio Probing, ed. by Y. Toba and H.Mitsuyasu, D. Reidel Publishing Company (1985),586 pp.

1991: Breaking Waves: IUTAM Symposium; Sydney,AustraliaBreaking Waves, ed. by M. L. Banner and R. H. J.Grimshow, Springer-Verlag (1992), 387 pp.

1993: The Air-Sea Interface, Radio and Acoustic Sens-ing, Turbulence and Dynamics; Marseille, FranceThe Air-Sea Interface, Radio and Acoustic Sensing,Turbulence and Dynamics, ed. by M. A. Donelan,W. H. Hui and W. J. Plant, Published by Universityof Miami (1996), 789 pp.

1997: Wind-over-Wave Coupling; Salford, the UnitedKingdomWind-over-Wave Coupling—Perspectives and Pros-

pects—, ed. by S. G. Sajiadi, N. H. Thomas and J.G. R. Hunt, Clarendon Press Oxford (1999), 356 pp.

1999: The Wind-driven Air-Sea Interface, Electromag-netic and Acoustic Sensing, Wave Dynamics and Tur-bulent Fluxes; Sydney, AustraliaThe Wind-driven Air-Sea Interface, Electromagneticand Acoustic Sensing, Wave Dynamics and Turbu-lent Fluxes, ed. by M. L. Banner, The Univ. NewSouth Wales (1999), 448 pp.[The year in ( ) means the year of the publication of

the proceeding. ]

Appendix 3: Typical Monographs and Comprehen-sive Reviews

[1950s]Ursell, F. (1956): Wave generation by wind. p. 216–249.

In Surveys in Mechanics, ed. by G. K. Batchelor,Cambridge University Press.

[1960s]Kinsman, B. (1965): Wind Waves; their Generation and

Propagation on the Ocean Surface, Prentice Hall,Inc., 676 pp.

Hasselmann, K. (1968): Weak interaction theory of oceansurface waves. p. 117–182. In Basic Developmentsin Fluid Mechanics, Vol. 2, ed. by M. Holt, Academic.

[1970s]Phillips, O. M. (1977): The Dynamics of the Upper Ocean.

Cambridge University Press, 336 pp.Barnett, T. P. and K. E. Kenyon (1975): Recent advances

in the study of wind waves. Rep. Prog. Phys., 38,667–729.

[1980s]The SWAMP Group (24 Authors) (1985): Ocean Wave

Modeling. Plenum Press, New York and London, 256pp.

Stewart, R. H. (1985): Method of Satellite Oceanogra-phy. University of California Press, 360 pp.

[1990s]Komen, G. J., L. Cavaleiri, M. Donelan, K. Hasselmann,

S. Hsselmann and P. A. E. M. Janssen (1994): Dy-namics and Modelling of Ocean Waves. CambridgeUniversity Press, 532 pp.

Mitsuyasu, H. (1995): Physics of Ocean Waves. IwanamiShoten, 210 pp. (in Japanese).

Ochi, M. K. (1998): Ocean Waves. Cambridge OceanTechnology Series 6. Cambridge University Press,319 pp.

Perrie, W. (1998): Nonlinear Ocean Waves (Advances inFluid Mechanics, Vol. 17, Series editor: M. Rahman).Computational Mechanics Publications, Southamp-ton and Boston, 258 pp.

Isozaki, I. and Y. Suzuki (1999): Analysis and Forecast-ing of Ocean Waves. Tokai University Press, 274 pp.(in Japanese).

118 H. Mitsuyasu

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