Journal of Oceanography, Vol. 58, pp. 109 to 120, 2002
Review
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 Sverdrup
and Munk (1947). More than half a century has passed since then and the study of
ocean surface waves has greatly advanced. The current numerical wave models, supported by many fundamental studies, enable us to compute ocean surface waves on a
global scale with sufficient accuracy for practical purposes. However, physical process controlling the energy balance of ocean surface waves is still not completely understood. The present note is a rough sketch of the historical development of the study
of ocean surface waves in the latter half of the twentieth century when the Oceanographic Society of Japan was founded and grew.
Keywords:
⋅ History,
⋅ ocean surface
waves.
much delayed. By contrast, studies of water waves with
regular and permanent forms as a fluid dynamical phenomenon have a long history. Their fundamental studies
were successfully developed in 19th century even for the
advanced mathematical formulations. Modern studies of
ocean surface waves started only in the 1940s with the
outstanding study by Sverdrup and Munk (1947) of the
Scripps Institution of Oceanography (SIO). The most
important points of their study can be summarized as follows;
1) “Significant waves” are characterized by a kind
of mean wave height and mean wave period. These were
first introduced to describe quantitatively ocean surface
waves that show random properties.
2) The concept of energy balance in a wave system was introduced to understand the wave evolution.
3) Empirical relations for the evolution of ocean
surface waves in dimensionless forms were obtained by
using accumulated wave data. The important quantities
controlling the phenomenon were included in the relations.
Although these are common knowledge today, it is
really surprising that such ideas were proposed when the
similar ideas or studies were almost non-existent, except
for primitive and purely empirical formulas. Since their
study, modern studies of ocean surface waves were developed, and many fundamental properties and dynamic
processes of ocean surface waves have been clarified.
This paper is devoted to a brief history of modern
developments in the study of ocean surface waves. This
is not a detailed history, however, but one that describes
1. Introduction
The wind blowing over the sea surface generates
wind waves. They develop with time and space under the
action of the wind and become huge waves called ocean
surface waves. According to our present knowledge this
process can be described as follows: the wind blowing
over the water surface generates tiny wavelets which have
a two-dimensional spectral structure. The spectral components develop with time and through space by absorbing the energy transferred from the wind. Nonlinear energy transfer among spectral components is also important in the development of the spectrum. The high frequency components then gradually saturate, losing the
absorbed energy as the waves break, while the low frequency components are still growing. In this way, the
spectral energy increases and the spectral peak shifts to
the low frequency side. It took a very long time to arrive
at such a dynamical model of ocean surface waves. The
present note on the development of investigation focuses
mainly on how we reached our present understanding of
the ocean surface waves.
In early days, the major difficulties in the study of
ocean surface waves were their random properties and
the complex mechanisms of their evolution. These properties of ocean surface waves are quite different from
those of regular water waves and due to this difference
the fundamental studies of ocean surface waves were
* E-mail address: [email protected]
Copyright © The Oceanographic Society of Japan.
109
a general picture of modern developments. Therefore only
a limited number of papers are referred to, which are
needed to advance the story. Furthermore, emphasis in
the discussion is put rather on early periods in the study,
because a detailed discussion on the modern development
of the study would become far too large for adequate treatment in this short note.
2.
Modern Development in the Study of Ocean Surface Waves
The study of ocean surface waves extends to a great
many areas. Table 1 has been prepared to give a general
view of the study and its historical development. The problem areas related to the study of ocean surface waves have
been divided into six topics: 1) generation mechanism
(of wind waves) including the generation of initial wavelets and energy transfer from the wind to waves; 2) statistical properties (of wind waves) including the wave
spectrum; 3) nonlinear properties (of wind waves) including the nonlinear interactions among spectral components,
wave instability and wave breaking; 4) laboratory and
ocean experiments; 5) air-sea and wave project and
6) wave forecasting (methods). The decadal change of
each topic together with epoch-making international symposia, and relevant scientific and technological progress
in each decade, are summarized in the Table. Earth observing satellites and international symposia are listed in
the appendix, which also includes typical monographs and
extended reviews of ocean surface waves. The historical
developments in the study of ocean surface waves can be
described referring to Table 1.
2.1 Generation mechanism of wind waves
The wind over the sea surface generates wind waves
(ocean surface waves). Therefore, the mechanisms of wind
wave generation and energy transfer from the wind to the
waves are essential problems in the study of ocean surface waves.
Although it does not appear in Table 1, Jeffreys
(1924, 1925) presented an outstanding theory (sheltering
theory) before the start of the advanced study in the 1940s.
He considered that if the wind velocity is faster than the
wave velocity, the air flow over the wave separates at the
wave crest and transfers the momentum to surface waves
through the form drag associated with flow separation.
Furthermore, based on a consideration of simple energy
balance in the process of wave generation, he estimated
the sheltering coefficient that can be used to calculate the
growth of waves due to the wind.
In order to verify the Jeffreys’s sheltering mechanism, fluid dynamicists carried out laboratory experiments; Stanton et al. (1932) and Motzfeld (1937) did similar laboratory experiments independently on the air flow
over a solid wavy surface. Unfortunately, the measured
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sheltering coefficients were much smaller than expected
from Jeffreys’s investigation. However, the experiment
for waves with sharp crest by Motzfeld (1937) clearly
demonstrated the separation of the air flow at the crest
and an increase of the sheltering coefficient, although the
value was still smaller than expected from Jeffreys’s investigation. As a result of these experiments, the contribution of the sheltering mechanism to wind wave generation came to be questioned. However, further studies
were needed to clarify the contribution of the separation
of air flow to the growth of wind waves. Because many
assumptions were made in Jeffreys’s theory, and the experiments mentioned above were implemented by using
a solid wavy surface. Moreover, recent observations of
air flow over steep water waves have revealed the separation of air flow (Banner and Melville, 1976; Kawai,
1982).
In the 1940s there were not many studies on the wave
generation mechanism, except for a theoretical study by
Wuest (1949) who did a stability analysis of the air-sea
interface, and an experimental study by Francis (1949)
who presented a careful observation of wind-wave generation in a wave tank.
In the 1950s Ursell (1956), who was engaged in the
wartime study of ocean waves in the UK in the 1940s,
presented an extensive review of the wind wave generation study. He summarized the available experimental and
theoretical studies and concentrated all his energy on the
discussion of the results of these studies. He concluded
that neither mechanism was likely to play a dominant role
in wave generation. Stimulated by the review of Ursell
(1956), two epoch-making theories were presented simultaneously by Phillips (1957) and Miles (1957). Phillips
(1957) proposed that random pressure fluctuation in the
wind resonantly generates wind waves on the water surface. However, later laboratory experiments indicated that
the pressure fluctuations in the turbulent wind are much
smaller than that estimated by Phillips (1957) and the
theory could not explain the growth rate of wind waves,
though it is still responsible for the generation of initial
wind waves. On the other hand, Miles theory is a kind of
stability theory that inherits the thoughts of Wuest (1949)
and Lock (1954) but applies a more realistic (logarithmic) wind profile. Miles (1957) showed that the coupling
between the surface waves and wind generates a special
pressure distribution along the wave surface and leads to
an exponential growth of the waves.
In the 1960s Miles (1960) combined the two theories of Phillips (1957) and Miles (1957) and showed that
the growth of waves is initially linear but ultimately exponential in time. The field measurement by LonguetHiggins et al. (1963), and laboratory measurement by
Shemdin and Hsu (1967) partly supported the results of
Miles (1957), and Lighthill (1962) gave a physical inter-
A Historical Note on the Study of Ocean Surface Waves
111
List of acronyms in Table 1.
OSJ: The Oceanographic Society of Japan (founded in 1941).
SWOP: Stereo Wave Observation Project; see Cote et al. (1960).
SMB: Sverdrup, Munk and Bretschneider; see Sverdrup and Munk (1947) and Bretschneider (1952).
PNJ: Pierson, Neumann and James; see Pierson et al. (1955).
ICCE: International Conference on Coastal Engineering (started from 1950).
WAM: Wave Model; see The WAMDI Group (1988).
JONSWAP: Joint North Sea Wave Project; see Hasselmann et al. (1973).
JWA3G: Japan Weather Association’s Third Generation Wave Model; see Suzuki and Isozaki (1994).
ARSLOE: Atlantic Remote Sensing Land Ocean Experiment; see Vincent and Lichy (1981).
RIAM Project: Wave Observation Project; see Mitsuyasu et al. (1975).
SWADE: The Surface Waves Dynamics Experiment; see Katsaros et al. (1993).
HEXOS: Humidity EXchange Over the Sea; see Smith et al. (1992).
RASEX: Risø Air-Sea Exchange; see Johnson et al. (1998).
SOWEX: Southern Ocean Waves Experiment; see Banner et al. (1999).
Table 1. Advances in the study of ocean surface waves in the latter half of the twentieth century.
pretation of the Miles (1957) theory. By these results, the
problem of wind wave generation was considered to be
solved. However, the field observations by Snyder and
Cox (1966), and by Barnett and Wilkerson (1967) showed
that the measured growth rates of a spectral component
of ocean surface waves were one order of magnitude
greater than those expected by Miles. Many theoretical
studies started again in the 1970s to explain the mechanism of wave generation.
One direction is to improve the Miles (1957) theory
by 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 are
still not in a position to completely understand the mechanism, while some of the numerical calculations (e.g.,
Al’Zanaidi and Hui, 1984; Miles, 1993) gave fairly good
agreement between the theory and experiments.
Another direction was to measure the growth rate of
wind waves as accurately as possible, because the growth
rates measured by Snyder and Cox (1966), and Barnett
and Wilkerson (1967) were considered, according to our
current knowledge, as overestimates due to the effect of
nonlinear energy transfer. Many field and laboratory
measurements were carried out to obtain more reasonable values, unaffected by nonlinear energy transfer
(Snyder et al., 1981; Mitsuyasu and Honda, 1982; Hsiao
and Shemdin, 1983). Plant (1982) proposed an empirical
formula for the growth rate of wind waves by combining
the observed values of various reliable sources. The measured values are used in the current numerical wave models, but the scatter in the measured growth rate is considerable and the problem still remains unsolved.
One of the most difficult problems is that accurate
measurements of the detailed phenomena near the wind
wave surface are extremely difficult. This has hampered
the derivation of more realistic theoretical models. Therefore, well-focused experiments using advanced measuring techniques are strongly needed to clarify the phenomena near the air-sea interface that will provide a breakthrough to clarify the phenomena.
The above discussions are mainly concerned with the
growth mechanism of wind waves under the action of the
wind. In regard to the generation of initial wind waves
over a still water surface there are several interesting subjects to study. When the wind starts to blow over the water’s surface, a drift current is generated and, a little later,
a tiny capillary wave is generated which develops gradually into wind waves. Kunishi (1963) conducted a comprehensive laboratory experiment on this problem to shed
light on the phenomena. About twenty years later Kawai
(1979) performed both experimental and theoretical studies on this subject examining a coupled shear flow model
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in the air and water to clarify the generation of the initial
wind wave. He obtained fairly good agreement between
the theory and his measurements. Okuda et al. (1976)
made detailed observations of the wind-induced surface
flow in the water by using flow visualization techniques,
before and after the generation of wind waves. They found
an interesting relation between a transition of the surface
flow from laminar to turbulent and the generation of wind
waves. The generation of initial wind waves can also be
treated by the resonance theory of Phillips (1957). Kahma
and Donelan (1988) studied experimentally an initial stage
of wind wave generation, but their results were not necessarily conclusive for the contributions of the two mechanisms of Kawai (1979) and Phillips (1957). Further studies are required to clarify the problem.
2.2 Statistical properties of wind waves
Ocean surface waves are water surface waves, as the
name indicates. However, they display random properties that obstructed our clear understanding of the phenomena in the early days. It is said that Lord Rayleigh
remarked, “The basic law of the seaway is the apparent
lack of any law” (Kinsman, 1965). Sverdrup and Munk
(1947) introduced their significant waves, a kind of statistical mean wave, to describe random properties of ocean
surface waves. Statistical theory of wind waves was
greatly advanced since then based on the theory of random process, in particular on the theory of random noise
that was presented by Rice (1944) of Bell Telephone Laboratory. Following the random noise theory, as the first
approximation, random waves are considered as a sum of
an infinite number of sinusoidal waves in a random phase.
In the 1950s, based on the statistical model above
mentioned, Longuet-Higgins (1952) gave the first theoretical derivation of the statistical distribution of waveheights. Cartwright and Longuet-Higgins (1956) in the
National Institute of Oceanography (NIO) of the United
Kingdom derived the statistical distributions of the maximum values of the random function. The statistical theory
of ocean surface waves was greatly extended by the group
in the NIO and effectively applied to the analysis of accumulated wave data in the 1950s.
On the other hand in the United States, Pierson (1953)
of the New York University (NYU) presented a spectral
model of wind waves that was also greatly affected by
the theory of random noise. Neumann (1953), also of
NYU, determined a spectral form of developing ocean
surface waves by using his observed wave data. By combining the results of their studies, the NYU group presented the famous paper entitled: Practical methods for
observing and forecasting ocean waves by means of wave
spectra and statistics (Pierson et al., 1955).
As for the physics of the wave spectrum, Phillips
(1958) proposed the equilibrium range in the spectrum
of wind waves based on a simple consideration of wave
breaking. The spectral model, which was basically supported by the newly developed random process theory
and various observations including the pioneering study
by NIO, contributed remarkably to advance the study of
ocean surface waves.
With the increase of spectral data in the 1960s many
oceanographers tried to determine a similarity form of
the spectrum of ocean surface waves. The most successful result was obtained by Pierson and Moskowitz (1964).
They proposed a famous spectral form (PM spectrum) for
fully developed wind seas by using wave spectral data
obtained in the North Atlantic Ocean. Their study was
based on the similarity theory of wind wave spectrum
presented by Kitaigorodskii (1962) which was quite analogous to the similarity theory of turbulence developed traditionally in the USSR.
From the end of the 1960s to the 1970s a great many
experimental studies were done to clarify the wind wave
spectrum. As a result of those extensive studies we clarified many important properties of the wind wave spectrum, such as the evolution of the spectrum (Mitsuyasu,
1968b, 1969; Hasselmann et al., 1973), the spectral form
at a finite fetch (Hasselmann et al., 1973), the similarity
form of the directional spectrum (Mitsuyasu et al., 1975;
Hasselmann et al., 1980; Donelan et al., 1985). On the
other hand, Toba (1972, 1973a, 1973b) presented an important concept of the local equilibrium between winds
and wind-generated waves which means the wind waves
retain their internal self-similar structure when they develop. An important “3/2 power law” for wind waves was
included in it. Toba (1973b) also derived a new equilibrium form of the wave spectrum that was supported by
Kawai et al. (1977) and has a form different from that of
Phillips (1958). Owing to the increased data supporting
the Toba’s new spectral form, Phillips (1985) presented a
new theory that supported the new equilibrium form of
Toba (1973b).
The statistical nature of ocean surface waves again
drew attention in the 1970s and 1980s. Longuet-Higgins
(1975, 1983) studied the joint distribution of the period
and amplitude of random waves which is important for
practical purposes.
After the launch of the SESAT satellite in 1978, studies of ocean wave spectra focused on the high-frequency
part of the wave spectrum to analyze the data of microwave sensors such as a scatterometer and an altimeter.
As the results of many experimental studies during a period from the 1970s to the 1990s, we clarified the winddependence of the high frequency wave spectrum (e.g.,
Mitsuyasu and Honda, 1974; Mitsuyasu, 1977) and the
high wave-number spectrum (e.g., Jähne and Riemer,
1990; Zhang, 1995), which contributed to the analysis of
the data of the scatterometer. The high frequency waves
also attracted attention as a roughness element of the sea
surface. Many studies on this subject were carried out,
clarifying the fine structure of high frequency waves (Cox
and Munk, 1954; Cox, 1958; Kondo et al., 1973), though
the contribution of the high frequency waves to the sea
surface roughness was still unclear and controversial.
2.3 Nonlinear properties of wind waves
Ocean surface waves can be described fairly well by
linear theory as described in Subsection 2.2. This is one
of the reasons why the spectral model can be very effectively used to describe the random ocean surface waves.
However, waves gradually show nonlinear properties with
the increase of wave steepness (wave height/wave length),
e.g., distortion of the wave form, nonlinear interaction
among spectral components, wave instability and final
wave breaking.
In the 1940s, studies on nonlinear waves were still
conducted along lines extending back to the study in 19th
century and mainly confined to the study of regular monochromatic nonlinear waves. The nonlinear theory of regular waves (solitary wave theory) was applied even to ocean
surface waves (e.g., Munk, 1949). This is because ocean
surface waves were described, in many cases, by using
significant waves, that is, a kind of mean wave with a
monochromatic wave property. It was only at the end of
the 1950s that Tick (1959) presented a nonlinear random
model of gravity waves.
The nonlinear theory of ocean surface waves was
greatly advanced in the 1960s. Phillips (1960) and
Hasselmann (1960, 1962, 1963) almost simultaneously
found the nonlinear energy transfer among wave spectral
components which is caused by resonant four-wave interactions. These are remarkable results, because the evolution of the wave spectrum is strongly affected by this
mechanism. Longuet-Higgins and Smith (1966), and
McGoldrick et al. (1966) experimentally confirmed the
resonant four-wave interactions and Mitsuyasu (1968a)
also experimentally confirmed the evolution of the continuous wave spectrum due to this effect. Although the
nonlinear energy transfer plays an important role in the
evolution of the wave spectrum, the problem is its computational difficulty. Many studies attempted to solve the
problem. Longuet-Higgins (1976) and Fox (1976) derived
a nonlinear interaction model that was more easily computable. However, their results were found to be unsuitable for the description of actual phenomena, because the
model holds in principle only for an extremely narrow
spectrum, and observed results show considerable disagreement with Fox’s calculations (Masuda, 1980).
Masuda (1980) studied a new computational scheme
of nonlinear energy transfer based on Hasselmann’s model
and much improved the numerical stability and computational accuracy. Hashimoto et al. (1998) extended the
A Historical Note on the Study of Ocean Surface Waves
113
computational scheme of Masuda (1980) for deep-water
waves to one for shallow water waves. Komatsu and
Masuda (1996) developed a more efficient computational
scheme of nonlinear energy transfer, but the computational
time is still not suitable for practical application to operational wave models.
Since the exact computation of the nonlinear energy
transfer takes too much time and is impractical for application to operational wave forecasting, most of the present
operational wave models use greatly simplified computational schemes of nonlinear energy transfer (Hasselmann
and Hasselmann, 1985; Hasselmann et al., 1985; Suzuki,
1995). The problem still remains, however, because the
accuracy of the simplified computational schemes depends on the forms of the wave spectra. In this connection Hashimoto et al. (1999) improved the accuracy of
the discrete interaction approximation of the nonlinear
energy transfer.
In the 1970s, Ramamonjiarisoa (1974) and
Ramamonjiarisoa et al. (1978) found a very curious phenomenon, that some high-frequency components in the
wind wave spectrum did not follow the dispersion relation. This finding cast serious doubt on the spectral model
of wind waves that assumes, as a first approximation, that
spectral components are free waves and follow an ordinary dispersion relation. Many studies were implemented
to clarify this problem. Among others, Masuda et al.
(1979) and Mitsuyasu et al. (1979) published comprehensive studies. They indicated theoretically and experimentally that, in steep wind waves, high frequency components of nearly twice the frequency of the spectral peak
were dominated by the nonlinear bounded waves that
propagate with the same speed as that of the spectral components near the spectral peak.
From the 1980s to 1990s, fundamental studies on the
nonlinear properties of ocean surface waves were concentrated on the most difficult nonlinear phenomena of
wave breaking. Banner and Peregrine (1993) and Melville
(1996) presented successively comprehensive reviews of
wave breaking. Wave breaking is not only important as
an energy dissipation mechanism in the wave’s evolution
but is also important in various exchange processes at
the air-sea boundary. An example of the recently controversial subject is the effect of wave breaking on CO2 exchange through the air-sea interface. The effect of wave
breaking on the momentum transfer from air to water is
still not clear, either. The problem itself is relatively old
but a new approach for future study is urgently needed.
2.4 Laboratory and ocean experiments
In order to clarify oceanographic phenomena such
as ocean surface waves, field observations are very important, while laboratory experiments under well-controlled condition give us a clear understanding of the funda-
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mental processes involved. Many observational studies
on ocean surface waves were carried out with this consideration, which took the form of the wave observation
projects described below in Subsection 2.5.
Laboratory experiment has many purposes, such as
to discover new phenomena, to clarify fundamental processes in the phenomena and to verify the results of new
theories. As shown in the previous sections, experimental studies have made important contributions to clarifying the dynamic processes of wind waves. Toba (1998)
presented a comprehensive review of the experimental
studies on wind waves as an air-sea boundary process.
Recently satellite observations of the wind and waves
in the ocean by using microwave sensors have moved from
experiments to attain the status of routine operations
(Bernstein, 1985; Stewart, 1985; Douglas and Cheney,
1990). They provide an enormous amount of accurate data
on wind and waves in the ocean. Such wind and waves
data on the global scale, in association with advanced
numerical wave models, contribute to accurate wave forecasts (e.g., Romeiser, 1993). However, the theories of
microwave backscattering at the sea surface are unsatisfactory even now (e.g., Apel, 1994; Keller et al., 1995),
and the measurement still largely depends on various
empirical formulas. Further fundamental studies are required to clarify this problem, too.
2.5 Air-sea and wave projects
Accurate and systematic observations of wind and
waves in the ocean, or more generally air-sea interaction
phenomena, tend inevitably to be big projects, because
they require the cooperation of many scientists and engineers. As shown in Table 1, many projects have been conducted, both national and international.
In the 1950s, two remarkable wave-observation
projects (Sun Glitter Project and Stereo Wave Observation Project) were conducted in the United States. Cox
and Munk (1954) of the SIO took aerial photographs of
the sun’s glitter on the sea surface in the Hawaiian area
under various wind conditions. They clarified the statistical distribution of wave slopes and its dependence on
the wind speed. On the other hand, Cote et al. (1960) of
the NYU conducted a large project called the Stereo Wave
Observation Project (SWOP), in which they took aerial
stereo photographs of the sea surface in the North Atlantic. Through the very laborious analysis of the data, they
were the first to determine the directional spectrum of
ocean surface waves.
In the 1960s, Longuet-Higgins et al. (1963) of the
NIO in the United Kingdom presented an important paper. They made pioneering observations of the directional
wave spectrum and atmospheric pressure fluctuations near
the sea surface by using a pitch-and-roll buoy newly developed by the NIO. They used the data extensively to
clarify the properties of the directional wave spectrum
and the wave generation theories by Miles (1957) and
Phillips (1957). In the 1960s, very celebrated project
JONSWAP (Joint North Sea Wave Project) was also conducted in Europe by an international team (Hasselmann
et al., 1973). It provided the following important results
on the evolution of wave spectrum at finite fetches; fetch
relations for the spectral parameters, similarity forms of
the wave spectrum at finite fetches, and the effect of
nonlinear energy transfer in the evolution of the wave
spectrum.
During the period from 1971 to 1974, a group of scientists and engineers at the Research Institute for Applied
Mechanics (RIAM) of Kyushu University conducted a
wave observation project (Mitsuyasu et al., 1975). They
conducted a comprehensive observation of the directional
wave spectrum in the North Pacific Ocean and the East
China Sea by using a cloverleaf buoy that was developed
by RIAM, based on the original NIO design. They first
presented a similarity form of the directional wave spectrum in the generation area. The result was further extended by similar observations in 1980s by Hasselmann
et al. (1980) and by Donelan et al. (1985). Currently we
have a fairly clear understanding on the directional property of the dominant part of the wave spectrum, while the
directional property of the high frequency part is still
controversial (Banner et al., 1989).
In the 1990s, many air-sea and wave observation
projects have been conducted, typical examples of which
are listed in the Table 1. The purposes of these projects
were mainly to clarify the air-sea exchanges of various
quantities such as momentum, heat, humidity, etc. Particular attention was focused on the effects of wind waves
on the air-sea exchange processes. We have accumulated
various new results on the phenomena, though it will take
more time to derive definite conclusions.
2.6 Wave forecasting
Accurate forecasting of ocean surface waves is one
of the important goals in the study of ocean waves. As
has repeatedly been mentioned, modern development in
the study of ocean surface waves started from the study
on wave forecasting done by Sverdrup and Munk (1947)
during World War II. By using newly accumulated ocean
wave data in the 1950s, Bretschneider (1952, 1958) and
Wilson (1961, 1965) greatly improved the wave forecasting method of Sverdrup and Munk (1947), and presented
a revised forecasting method, usually called the SMB
method. Furthermore, in the 1950s, a statistical theory of
random ocean waves was presented and the spectral structure of ocean surface waves was clarified to some extent.
The accumulated knowledge in such fundamental study
was effectively used to construct a spectral wave forecasting method by Pierson et al. (1955).
Inoue (1967) and Barnett (1968) presented numerical wave models in the 1960s with further progress in
fundamental 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 numerical wave model in an earlier period, the 1950s (Gelci et
al., 1957).
In Japan the MRI wave model was developed by
Isozaki and Uji (1973) and used for routine wave forecasting at the Japan Meteorological Agency. About ten
years later it was replaced by the MRI- II wave model
(Uji, 1984). Various wave models were developed in many
countries. And they were improved successively as summarized in the monograph “Ocean Wave Modeling (The
SWAMP Group, 1985)”, in which typical wave models
developed in various countries were described. The
TOHOKU Wave Model (Toba et al., 1985) and the MRI
Wave Model (Uji, 1985), developed in Japan, were included.
At present, third generation wave models such as the
WAM model (The WAMDI Group, 1988), JWA3G model
(Suzuki and Isozaki, 1994; Suzuki, 1995) and MRI-III
model (Ueno and Ishizaka, 1997) have been developed
with the support of recent studies on the fundamental processes that control the energy source terms, i.e., the energy input from the wind, the nonlinear energy transfer
among spectral components and the energy dissipation
due to wave breaking. In particular, the explicit computation of the nonlinear energy transfer characterizes the
third generation wave models, which are used to predict
the ocean surface waves at global scale with practically
sufficient accuracy. However, even in the most advanced
third generation wave models, some of the energy source
terms depend largely on empirical knowledge. Further
studies are needed to develop a more improved wave
model, constructed on a sound physical basis.
2.7 International symposia
In 1961 Sir George Deacon organized the first international symposium on “Ocean Wave Spectra”, held at
Eaton, Maryland, in the USA. World leading scientists
and engineers presented in this meeting a summary of
the present state-of-the-art in the several fields of ocean
wave studies. They also discussed the current research
trends, future needs and the most recent techniques for
ocean wave measurement and analysis. The meeting contributed greatly to the rapid progress in the study of ocean
surface waves in the succeeding periods.
Since then, similar symposia have been held until
now, as shown in Table 1. However, the role of the symposium is slightly changing, because now we can exchange information quickly by other various ways and
means. Main topics in the symposia are also gradually
A Historical Note on the Study of Ocean Surface Waves
115
changing, from the dynamics of ocean surface waves to
their contributions to the air-sea exchange process, and
to contributions on recent problems in the changing global environment. Such a change of the aims or scope of
the symposia is reflected on the very long titles of the
symposia as shown in the appendix.
3. Concluding Remarks
The historical development of the study of ocean
surface waves can be roughly divided into four periods;
initial period (before and in 1940s), growing period (1950s
and 1960s), expanding period (1970s and 1980s), and the
present period (post-1980s).
The initial period is characterized by the wartime
studies during World War II. The most fruitful result was
obtained by Sverdrup and Munk (1947) who proposed
not only an advanced forecasting method but also a framework for the study of ocean surface waves in the succeeding period when the measured wave data increased
rapidly. Studies at the NIO in the UK also greatly contributed by developing measurement and analysis techniques for the wave data.
The most outstanding contributions in the 1950s were
the presentations of the two wave generation theories by
Phillips (1957) and by Miles (1957). These theories were
not necessarily in good agreement with observations but
gave a fundamental framework for succeeding studies.
The formulation of the statistical theory of random waves
in this period was a great contribution too. Particularly
spectral model, which was fundamentally supported by
the random process theory, greatly advanced the study of
ocean surface waves. It was a surprising event that such
large projects as SWOP and the Sun Glitter Project were
successfully accomplished in the early 1950s.
One of the most important studies in the 1960s was
the theoretical study of the nonlinear energy transfer
among spectral components, which is a very important
energy source term in the wave evolution in association
with the energy transfer from wind to waves, though another important term of the energy dissipation due to wave
breaking remains. The formulation of the numerical wave
model based on the energy balance equation was also an
important contribution in this period, opening the way to
the development of more advanced models in succeeding
periods. These two important studies contributed later to
the development of a more advanced model, the third
generation wave model.
Roughly speaking, the dominant framework for the
study on ocean surface waves was constructed until 1960s;
we derived the statistical model to describe the random
ocean surface waves, the dynamic model to describe the
evolution of ocean surface waves, and the numerical wave
116
H. Mitsuyasu
model to predict ocean surface waves at global scale. Studies in the 1970s and 1980s were devoted to adding more
accurate information or to improving the results obtained
previously. Typical examples of the important results are
accurate descriptions of the evolution of the wave spectra, determination of the similarity forms of wave spectra, the derivation of the concept of local equilibrium in
the wave evolution, and accurate computations of the
nonlinear energy transfer. These fundamental studies supported the development of the advanced numerical wave
models of the third generation.
In the present period, starting from the 1990s, the
study of the mechanism by which wind waves are generated is continuing, because the mechanism is still not
completely understood, even now. However, more attention is being paid to the most difficult problem of wave
breaking. Studies of wave breaking as a fluid dynamic
phenomenon were greatly advanced by Longuet-Higgins
and many other fluid dynamicists. However, many problems have still remained unsolved related to the contribution of wave breaking to the following phenomena:
wave energy dissipation, which is an important element
in the source term of energy balance equation, and various exchange processes at the air-sea boundary, which is
greatly affected by wave breaking. Recent studies are
focused on these problems, as described by Melville
(1996).
About half a century ago, Ursell (1956) stated in his
famous review, “Wind blowing over water surface generates waves in the water by a physical process which can
not be regarded as known.” A great many studies conducted after that time have given us a tremendous amount
of information on the statistical and dynamic properties
of ocean surface waves and made it possible to compute
the waves at global scale with sufficient accuracy for practical purposes. However it will be difficult, even now, to
answer the question, “Have we really clarified the physical process of wind wave generation and decay?”
Acknowledgements
I wish to express my sincere thanks to Professor A.
Masuda of Kyushu University for many stimulating discussions and for his critical reading of the manuscript,
which contributed greatly to improving this paper. I also
wish to thank Professor H. Honji of Kyushu University
for his invaluable advice and constant encouragement.
Without his encouragement it would have been difficult
to complete this article. My sincere thanks are extended
to Professor Emeritus Y. Toba of Tohoku University for
his valuable comments and to anonymous reviewers for
their careful reviews and constructive comments.
Appendix 1: Earth Observing Satellites
SEASAT: (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 Proceedings
1948: Ocean Surface Wave; New York, USA
Ocean Surface Wave. p. 343–572. In Annals of New
York Academy of Sciences, Vol. 5, Art 3, ed. by B.
Haurwitz, Published by the Academy (1949), New
York.
1950: International Conference on Coastal Engineering;
Berkeley, California, USA
Proceeding of First Conference on Coastal Engineering. Council of Wave Research, Engineering Foundation (1951).
1961: Ocean Wave Spectra; Eaton, Maryland, USA
Ocean Wave Spectra. Prentice-Hall, INC.,
Englewood Cliffs, New Jersey (1963), 357 pp.
1977: Turbulent Fluxes through Sea Surface, Wave Dynamics and Prediction; Marseille, France
Turbulent Fluxes through Sea Surface, Wave Dynamics and Prediction, ed. by A. Favre and K.
Hasselmann, NATO Conference Series V, Air-Sea
Interactions. Plenum Press, New York (1978), 677
pp.
1981: Wave Dynamics and Radio Probing of Ocean Surface; Miami, USA
Wave Dynamics and Radio Probing of Ocean Surface, ed. by O. M. Phillips and K. Hasselmann, Plenum Press (1986), 694 pp.
1984: The Ocean Surface, Wave Breaking, Turbulent
Mixing and Radio Probing; Sendai, Japan
The Ocean Surface, Wave Breaking, Turbulent Mixing and Radio Probing, ed. by Y. Toba and H.
Mitsuyasu, D. Reidel Publishing Company (1985),
586 pp.
1991: Breaking Waves: IUTAM Symposium; Sydney,
Australia
Breaking Waves, ed. by M. L. Banner and R. H. J.
Grimshow, Springer-Verlag (1992), 387 pp.
1993: The Air-Sea Interface, Radio and Acoustic Sensing, Turbulence and Dynamics; Marseille, France
The Air-Sea Interface, Radio and Acoustic Sensing,
Turbulence and Dynamics, ed. by M. A. Donelan,
W. H. Hui and W. J. Plant, Published by University
of Miami (1996), 789 pp.
1997: Wind-over-Wave Coupling; Salford, the United
Kingdom
Wind-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, Electromagnetic and Acoustic Sensing, Wave Dynamics and Turbulent Fluxes; Sydney, Australia
The Wind-driven Air-Sea Interface, Electromagnetic
and Acoustic Sensing, Wave Dynamics and Turbulent Fluxes, ed. by M. L. Banner, The Univ. New
South Wales (1999), 448 pp.
[The year in ( ) means the year of the publication of
the proceeding. ]
Appendix 3: Typical Monographs and Comprehensive 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 ocean
surface waves. p. 117–182. In Basic Developments
in 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, 256
pp.
Stewart, R. H. (1985): Method of Satellite Oceanography. 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): Dynamics and Modelling of Ocean Waves. Cambridge
University Press, 532 pp.
Mitsuyasu, H. (1995): Physics of Ocean Waves. Iwanami
Shoten, 210 pp. (in Japanese).
Ochi, M. K. (1998): Ocean Waves. Cambridge Ocean
Technology Series 6. Cambridge University Press,
319 pp.
Perrie, W. (1998): Nonlinear Ocean Waves (Advances in
Fluid Mechanics, Vol. 17, Series editor: M. Rahman).
Computational Mechanics Publications, Southampton and Boston, 258 pp.
Isozaki, I. and Y. Suzuki (1999): Analysis and Forecasting of Ocean Waves. Tokai University Press, 274 pp.
(in Japanese).
A Historical Note on the Study of Ocean Surface Waves
117
References
Al’Zanaidi, M. A. and H. W. Hui (1984): Turbulent air flow
over water waves—A numerical study. J. Fluid Mech., 48,
225–246.
Apel, J. R. (1994): An improved model of the ocean surface
wave vector spectrum and its effects on radar backscatter.
J. Geophys. Res., 99, C8, 16269–16291.
Banner, M. L. and W. K. Melville (1976): On the separation of
air flow over water waves. J. Fluid Mech., 77, 825–842.
Banner, M. L. and D. H. Peregrine (1993): Wave breaking in
deep water. Annu. Rev. Fluid Mech., 25, 373–397.
Banner, M. L., Ian S. F. Jones and J. C. Trinder (1989): Wave
number spectra of short gravity waves. J. Fluid Mech., 198,
321–344.
Banner, M. L., W. Chen, E. J. Walsh, J. B. Jensen, S. Lee and
C. Fandry (1999): The Southern Ocean Waves Experiment.
Part 1: Overview and mean results. J. Phys. Oceanogr., 29,
2130–2145.
Barnett, T. P. (1968): On the generation, dissipation and prediction of ocean wind waves. J. Geophys. Res., 73, 513–
529.
Barnett, T. P. and J. C. Wilkerson (1967): On the generation of
ocean wind waves as inferred from airborne radar measurements of fetch-limited spectra. J. Mar. Res., 25, 292–
321.
Belcher, S. E. and J. C. R. Hunt (1993): Turbulent shear flow
over slowly moving waves. J. Fluid Mech., 251, 109–148.
Bernstein, R. L. (1985): Seasat Special Issue 1: Geophysical
Evaluation (reprinted from J. Geophys. Res., 87, C5, 1982).
Bretschneider, C. L. (1952): The generation and decay of wind
waves in deep water. Trans. A.G.U., 33(3), 381–389.
Bretschneider, C. L. (1958): Revision; in wave forecasting deep
and shallow water. Proc. 6th Conf. on Coastal Eng., 30–67.
Cartwright, D. E. and M. S. Longuet-Higgins (1956): Statistical distribution of the maxima of a random function. Proc.
Roy. Soc. A, 237, 212–232.
Cote, L. J. and 8 authors (1960): The Directional Spectrum of
Wind Generated Sea as Determined from Data Obtained by
the Stereo Wave Observation Project, ed. by W. J. Pierson,
Jr., Coll. Engrg., N.Y.U., Met. Paper, Vol. 2, No. 6, 88 pp.
Cox, C. S. (1958): Measurements of slopes of high-frequency
wind waves. J. Mar. Res., 16, 199–225.
Cox, C. S. and W. H. Munk (1954): Statistics of sea surface
derived from sun glitter. J. Mar. Res., 13, 198–227.
Davis, R. E. (1972): On the prediction of the turbulent flow
over a wavy boundary. J. Fluid Mech., 52, 287–306.
Donelan, M. A., J. Hamilton and W. H. Hui (1985): Directional
spectra of wind-generated waves. Phil. Trans. Roy. Soc.
London, A, 315, 509–562.
Douglas, B. C. and R. E. Cheney (1990): Geosat: Beginning a
new era in satellite oceanography. J. Geophys. Res., 95, C3,
2833–2836.
Fox, M. J. H. (1976): On the nonlinear transfer of energy in the
peak of a gravity-wave spectrum—II. Proc. Roy. Soc. A,
348, 467–483.
Francis, J. R. D. (1949): Laboratory experiments on wind-generated waves. J. Mar. Res., VIII, 2, 120–131.
Gelci, R., H. Cazale and J. Vassale (1957): Prévision de la houle.
La méthode des densités spectroangulaires. Bull. Inform.
118
H. Mitsuyasu
Comité Central Océanogr. d’Etude Côtes, 9, 416–435.
Gent, P. R. and P. A. Taylor (1976): A numerical model of the
air flow above water waves. J. Fluid Mech., 77, 105–128.
Hashimoto, N., H. Tsuruya and Y. Nkagawa (1998): Numerical
computation of the nonlinear energy transfer of gravitywave spectra in finite water depths. Coast. Eng. J., 40, No.
1, 23–40.
Hashimoto, N., K. Kawaguchi and M. Suzuki (1999): An extension of the discrete interaction approximation of the
nonlinear energy transfer in ocean waves. Proc. Coastal
Engineering, JSCE, Vol. 46, 231–235 (in Japanese).
Hasselmann, D. E., M. Dunkel and J. A. Ewing (1980): Directional wave spectra observed during JONSWAP 1973. J.
Phys. Oceanogr., 10, 1264–1280.
Hasselmann, K. (1960): Grundgleichungen der
Seegangsvoraussage. Schiffstechnik, 1, 191–195.
Hasselmann, K. (1962): On the non-linear energy transfer in a
gravity wave spectrum. Part 1. J. Fluid Mech., 12, 481–
500.
Hasselmann, K. (1963): On the non-linear energy transfer in a
gravity wave spectrum. Part 2. J. Fluid Mech., 15, 273–
281; Part 3. 15, 385–398.
Hasselmann, K. and 15 authors (1973): Measurements of wind
wave growth and swell decay during the Joint North Sea
Wave Project (JONSWAP). Dt. Hydrogr. Z., A8(12), 95 pp.
Hasselmann, S. and K. Hasselmann (1985): Computations and
parameterizations of the nonlinear energy transfer in a gravity wave spectrum. Part 1: A new method for efficient computations of the exact nonlinear transfer integral. J. Phys.
Oceanogr., 15, 1369–1377.
Hasselmann, S., K. Hasselmann, J. H. Allender and T. P. Barnett
(1985): Computations and parameterizations of the
nonlinear energy transfer in a gravity-wave spectrum. Part
II. Parameterizations of the nonlinear energy transfer for
application in wave models. J. Phys. Oceanogr., 15, 1378–
1391.
Hsiao, S. V. and O. H. Shemdin (1983): Measurements of wind
velocity and pressure with a wave follower during
MARSEN. J. Geophys. Res., 88, C14, 9841–9849.
Inoue, T. (1967): On the growth of the spectrum of a windgenerated sea according to a modified Miles-Phillips mechanism and its application to wave forecasting. N.Y.U.,
Geophys. Sci. Lab. Rep. No. TR 67-5, 74 pp.
Isozaki, I. and T. Uji (1973): Numerical prediction of ocean
wind waves. Paper Meteorol. Geophys., 24, 207–231.
Jähne, B. and K. S. Riemer (1990): Two-dimensional wave
number spectra of small-scale water surface waves. J.
Geophys. Res., 95, C7, 11531–11546.
Jeffreys, H. (1924): On the formation of waves by wind. Proc.
Roy. Soc. A, 107, 189–206.
Jeffreys, H. (1925): On the formation of waves by wind, II.
Proc. Roy. Soc. A, 110, 341–347.
Johnson, H. K., J. Højstrup, H. J. Vested and S. E. Larsen (1998):
On the dependence of sea surface roughness on wind waves.
J. Phys. Oceanogr., 28, 1702–1716.
Kahma, K. K. and M. A. Donelan (1988): A laboratory study of
the minimum wind speed for wind wave generation. J. Fluid
Mech., 192, 339–364.
Katsaros, K. B., M. A. Donelan and W. M. Drennan (1993):
Flux measurements from a SWATH ship in SWADE. J. Mar.
Sys., 4, 117–132.
Kawai, S. (1979): Generation of initial wavelets by instability
of a coupled shear flow and their evolution to wind waves.
J. Fluid Mech., 93, 661–703.
Kawai, S. (1982): Structure of air flow separation over wind
wave crests. Boundary Layer Meteorology, 23, 503–521.
Kawai, S., K. Okada and Y. Toba (1977): Field data support of
three-seconds power law and gu*σ–4 spectral form for growing wind waves. J. Oceanogr. Soc. Japan, 33, 137–150.
Keller, M. R., B. L. Gotwols, W. J. Plant and W. A. Keller
(1995): Comparison of optically-derived spectral densities
and microwave cross sections in a wind-wave tank. J.
Geophys. Res., 100, C8, 16163–16178.
Kinsman, B. (1965): Wind Waves; Their Generation and Propagation on the Ocean Surface. Prentice Hall, Inc., 676 pp.
Kitaigorodskii, S. A. (1962): Applications of the theory of similarity to the analysis of wind-generated wave motion as a
stochastic process. Izv., Geophys. Ser. Acad. Sci., USSR, 1,
105–117.
Komatsu, K. and A. Masuda (1996): A new scheme of nonlinear
energy transfer among wind waves: RIAM method—Algorithm and performance. J. Oceanogr., 52, 509–537.
Kondo, J., Y. Fujinawa, and G. Naito (1973): High frequency
components of ocean waves and their relation to the aerodynamic roughness. J. Phys. Oceanogr., 3, 197–202.
Kunishi, H. (1963): An experimental study on the generation
and growth of wind waves. Bulletin of Disaster Prevention
Research Institute, Kyoto Univ., No. 61, 1–41.
Lighthill, M. J. (1962): Physical interpretation of mathematical theory of wave generation by wind. J. Fluid Mech., 14,
385–398.
Lock, R. C. (1954): Hydrodynamic stability of the flow in the
laminar boundary layer between parallel streams. Proc.
Camb. Phil. Soc., 50, 105–124.
Longuet-Higgins, M. S. (1952): On the statistical distribution
of the height of sea waves. J. Mar. Res., 11, 245–266.
Longuet-Higgins, M. S. (1975): On the joint distribution of the
periods and amplitudes of sea waves. J. Geophys. Res., 80,
2688–2694.
Longuet-Higgins, M. S. (1976): On the nonlinear transfer of
energy in the peak of a gravity-wave spectrum: a simplified model. Proc. Roy. Soc. A, 347, 311–328.
Longuet-Higgins, M. S. (1983): On the joint distribution of the
periods and amplitudes in a random wave field. Proc. Roy.
Soc. London A, 389, 241–258.
Longuet-Higgins, M. S. and N. D. Smith (1966): An experiment on third order resonant wave interactions. J. Fluid
Mech., 25, 417–435.
Longuet-Higgins, M. S., D. E. Cartwright and N. D. Smith
(1963): Observations of the directional spectrum of sea
waves using the motion of a floating buoy. p. 111–136. In
Ocean Wave Spectra, Englewood Cliffs, N.J., Prentice-Hall.
Masuda, A. (1980): Nonlinear energy transfer between wind
waves. J. Phys. Oceanogr., 10, 2082–2092.
Masuda, A., Yi-Yu Kuo and H. Mitsuyasu (1979): On the dispersion relation of random gravity waves, Part 1, Theoretical framework. J. Fluid Mech., 92, 717–730.
McGoldrick, M. F., O. M. Phillips, N. Huang and T. Hodgson
(1966): Measurement of resonant wave interactions. J. Fluid
Mech., 25, 437–456.
Melville, W. K. (1996): The roll of surface-wave breaking in
air-sea interaction. Annu. Rev. Fluid Mech., 28, 279–321.
Miles, J. W. (1957): On the generation of surface waves by shear
flow. J. Fluid Mech., 3, 185–204.
Miles, J. W. (1960): On the generation of surface waves by turbulent shear flow. J. Fluid Mech., 7, 469–478.
Miles, J. W. (1993): Surface wave generation revisited. J. Fluid
Mech., 256, 427–441.
Mitsuyasu, H. (1968a): A note on the nonlinear energy transfer
in the spectrum of wind-generated waves. Rept. Res. Inst.
Appl. Mech., Kyushu Univ., 16, 251–264.
Mitsuyasu, H. (1968b): On the growth of the spectrum of windgenerated waves, I. Rept. Res. Inst. Appl. Mech., Kyushu
Univ., 16, 459–465.
Mitsuyasu, H. (1969): On the growth of the spectrum of windgenerated waves, II. Rept. Res. Inst. Appl. Mech., Kyushu
Univ., 17, 235–243.
Mitsuyasu, H. (1977): Measurement of high frequency spectrum of ocean surface waves. J. Phys. Oceanogr., 7, 882–
891.
Mitsuyasu, H. and T. Honda (1974): The high frequency spectrum of wind-generated waves. J. Oceanogr. Soc. Japan,
30, 185–198.
Mitsuyasu, H. and T. Honda (1982): Wind-induced growth of
water waves. J. Fluid Mech., 123, 425–442.
Mitsuyasu, H., F. Tasai, T. Suhara, S. Mizuno, M. Ohkusu, T.
Honda and K. Rikiishi (1975): Observation of the directional spectrum of ocean waves using a cloverleaf buoy. J.
Phys. Oceanogr., 5, 750–760.
Mitsuyasu, H., Yi-Yu, Kuo and A. Masuda (1979): On the dispersion relation of random gravity waves, Part 2, An experiment. J. Fluid Mech., 92, 731–749.
Motzfeld, H. (1937): Die turbulente Strömung an welligen
Wänden. Z. angew. Math. Mech., 17, 193–212.
Munk, W. H. (1949): The solitary wave theory and its application to surf problems. N.Y. Acad. Sci., 52(3), 376–424.
Neumann, G. (1953): On ocean wave spectra and a new method
of forecasting wind-generated sea. Beach Erosion Board,
Tech. Mem., No. 43. 42 pp.
Okuda, K., S. Kawai, M. Tokuda and Y. Toba (1976): Detailed
observation of the wind-exerted surface flow by use of flow
visualization methods. J. Oceanogr. Soc. Japan, 32, 53–64.
Phillips, O. M. (1957): On the generation of waves by turbulent wind. J. Fluid Mech., 2, 417–445.
Phillips, O. M. (1958): The equilibrium range in the spectrum
of wind-generated ocean waves. J. Fluid Mech., 4, 426–
434.
Phillips, O. M. (1960): On the dynamics of unsteady gravity
waves of finite amplitude, Part 1. J. Fluid Mech., 9, 193–
217.
Phillips, O. M. (1985): Spectral and statistical properties of the
equilibrium range of wind-generated gravity waves. J. Fluid
Mech., 156, 505–531.
Pierson, W. J. (1953): A unified mathematical theory for the
analysis, propagation and refraction of storm generated
ocean surface waves, Parts I and II, N.Y.U., Coll. of Eng.,
Res. Div., Dept. Meteorol. and Oceanogr., 461 pp.
A Historical Note on the Study of Ocean Surface Waves
119
Pierson, W. J. and L. Moskowitz (1964): A proposed spectral
form for fully developed wind seas based on the similarity
theory of S. A. Kitaigorodskii. J. Geophys. Res., 69, 5181–
5190.
Pierson, W. J., G. Neumann and R. W. James (1955): Practical
Methods for Observing and Forecasting Ocean Waves by
means of Wave Spectra and Statistics. U.S. Navy
Hydrographic Office, Pub. No. 603, 284 pp.
Plant, W. J. (1982): A relationship between wind stress and wave
slope. J. Geophys. Res., 87, 1961–1967.
Ramamonjiarisoa, A. (1974): Cotribution a l’etude de la structure statistique et des mechanismes de generation des vagues
de vent. These de Doctrat d’Etat, Universite de Provence
(Inst. Mech. Stat. De la Turbunce, no. A.O. 10, 023).
Ramamonjiarisoa, A., S. Baldy and I. Choi (1978): Laboratory
studies on wind-wave generation, amplification and evolution. p. 403–420. In Turbulent Fluxes through the Sea Surface, Wave Dynamics, and Prediction, ed. by A. Favre and
K. Hasselmann, Plenum Press, New York and London.
Rice, S. O. (1944): Mathematical Analysis of Random Noise.
Reprint in Selected Papers on Noise and Stochastic Proceses,
Dover Pub. Inc., p. 133–294.
Romeiser, R. (1993): Global validation of the wave model WAM
over a one-year period using GEOSAT wave height data. J.
Geophys. Res., 98, C3, 4713–4726.
Shemdin, O. H. and E. Y. Hsu (1967): The dynamics of wind in
the vicinity of progressive water waves. J. Fluid Mech., 30,
403–416.
Smith, S. D. and Co-authors (1992): Sea surface wind stress
and drag coefficients: The HEXOS results. Boundary Layer
Meteor., 60, 109–142.
Snyder, R. L. and C. S. Cox (1966): A field study of the wind
generation of ocean waves. J. Mar. Res., 24, 141–178.
Snyder, R. L., F. W. Dobson, J. A. Elliott and R. B. Long (1981):
Array measurements of atmospheric pressure fluctuations
above surface gravity waves. J. Fluid Mech., 102, 1–59.
Stanton, T. E., D. Marshal and R. Houghton (1932): The growth
of waves on water due to the action of the wind. Proc. Roy.
Soc. A, 137, 283–293.
Stewart, R. H. (1985): Method of Satellite Oceanography. University of California Press, 360 pp.
Suzuki, Y. (1995): Development and application of a global
ocean wave prediction model including nonlinear interactions and dissipation. Dr. Thesis, University of Tokyo, 182
pp.
Suzuki, Y. and I. Isozaki (1994): On the development of a global ocean wave model JWA3G. Proc. Pacific Ocean Remote Sensing Conf. in Melbourne, Australia, 195–201.
Sverdrup, H. U. and W. H. Munk (1947): Wind, sea and swell.
Theory of relations for forecasting. U.S. Navy Hydrographic
Office, Washington, Pub. No. 601, 44 pp.
The SWAMP Group (24 authors) (1985): Ocean Wave Modeling.
120
H. Mitsuyasu
Plenum Press, New York, 256 pp.
The WAMDI Group (13 authors) (1988): The WAM model—A
third genereation ocean wave prediction model. J. Phys.
Oceanogr., 18, 1775–1810.
Tick, L. J. (1959): A non-linear random model of gravity waves
1. J. Math. Mech., VIII, No. 5, 643–651.
Toba, Y. (1972): Local balance in the air-sea boundary processes I. On the growth process of wind waves. J. Oceanogr.
Soc. Japan, 28, 109–120.
Toba, Y. (1973a): Local balance in the air-sea boundary processes II. Partition of wind stress to waves and current. J.
Oceanogr. Soc. Japan, 29, 70–75.
Toba, Y. (1973b): Local balance in the air-sea boundary processes III. On the spectrum of wind waves. J. Oceanogr. Soc.
Japan, 29, 209–220.
Toba, Y. (1998): Wind-forced strong wave interactions and
quasi-local equilibrium between wind and windsea with the
friction velocity proportionality. p. 1–59. In Nonlinear
Ocean Waves, ed. by W. Perrie (Advances in Fluid Mechanics, Vol. 17, Series editor: M. Rahman), Computational
Mechanics Publications, Southampton and Boston.
Toba, Y., S. Kawai and P. S. Joseph (1985): The TOHOKU wave
model. p. 201–210. In Ocean Wave Modeling, ed. by The
SWAMP group, Plenum Press, New York and London.
Townsend, A. A. (1972): Flow in a deep turbulent boundary
layer over a surface distorted by water waves. J. Fluid
Mech., 55, 719–735.
Ueno, K. and M. Ishizaka (1997): Efficient computational
scheme of nonlinear energy transfer of wind waves. Sokko
Jihou, 64, 75–80 (in Japanese).
Uji, T. (1984): A coupled discrete wave model MRI-II. J.
Oceanogr. Soc. Japan, 40, 303–313.
Uji, T. (1985): The MRI wave model. p. 157–166. In Ocean
Wave Modeling, ed. by The SWAMP group, Plenum Press,
New York and London.
Ursell, F. (1956): Wave generation by wind. p. 216–249. In
Surveys in Mechanics, ed. by G. K. Batchelor, Cambridge
University Press.
Vincent, C. L. and D. E. Lichy (1981): Wave measurements in
ARSLOE. p.71–85. In Proc. Conf. on Directional Wave
Spectra Applications, ed. by R. L. Wiegel, ASCE, Berkeley,
Calif., U.S.A.
Wilson, B. W. (1961): Deep water wave generation by moving
wind system. Proc. ASCE, 87(WW2), 113–141.
Wilson, B. W. (1965): Numerical prediction of ocean waves in
the North Atlantic for December, 1959. Dt. Hydrogr. Z., 18,
114–130.
Wuest, W. (1949): Beitrag zur Entstehung von Wasserwellen
durch Wind. Z. angew. Math. Mech., 29, 239–252.
Zhang, X. (1995): Capillary-gravity and capillary waves generated in a wind wave tank. J. Fluid Mech., 289, 51–82.