Journal of Oceanography, Vol. 58, pp. 3 to 9, 2002
Review
Ocean Waves: Half-a-Century of Discovery
PAUL H. LEBLOND*
Professor Emeritus, Department Earth and Ocean Sciences, University of British Columbia,
Vancouver, British Columbia V6T 1Z4, Canada
(Received 23 March 2001; in revised form 20 August 2001; accepted 27 August 2001)
While the nature of most ocean waves has long been known and their basic physics
understood since the nineteenth century, intense study of ocean waves during the
second half of the twentieth century has taken the subject from the realm of mathematical exercises to that of practical engineering. Modern understanding of the generation, propagation and interactions of ocean waves with each other and with oceanic features has advanced to a quantitative level offering predictive capacity. This
paper presents a brief qualitative review of advances in knowledge of sound waves,
wind waves, tsunamis, tides, internal waves and long-period vorticity waves. The review is aimed at non-specialists who may benefit from an overview of the current
state of the subject and access to a bibliography of general-interest references.
Keywords:
⋅ Ocean waves,
⋅ internal waves,
⋅ tsunamis,
⋅ tides.
review of its own (cf. Spinrad, 1988). This particular review deals only with so-called “mechanical radiation”,
fluid motions ruled by the laws of classical physics and
consisting of travelling oscillations about a stable equilibrium state: for example, the sea-surface for surface
gravity and capillary waves, the ambient pressure for
sound waves. Lighthill (1978) has presented a basic account of wave motion in fluids. A broad overview of ocean
waves may be found in LeBlond and Mysak (1978). Other
recent general references are presented in the text.
1. Introduction
One of my friends, an anthropologist, always expresses surprise that I should still be studying waves. He
is even more astounded when I tell him that hundreds of
brilliant physicists, mathematicians and engineers have
been working on understanding ocean waves for at least
a couple of centuries. What more can there be to learn
about such a familiar phenomenon? Why struggle so hard
to refine knowledge when there are so many new fields
inviting fresh discovery?
Oceanography has become such a wide field of endeavour that I suspect that there may be some ocean scientists who, like my friend the paleontologist, wonder why
so many of their colleagues are still interested in waves.
Why, they might think, labour on such a well-worn topic,
when surprising discoveries await research in other, newer
directions? This review is mainly for them. It describes
in simple terms the progress made in the understanding
of ocean waves of all kinds over the past half-century
and why their study is still important enough to attract
interest.
3. Wave Properties
Waves are characterized by their period, which specifies their repetition rate in time, and by their wave-length,
which describes their periodicity in space. It takes one
period for a wave-length to pass by a fixed observer. The
ratio wave-length/period thus defines a speed called the
phase speed which is the rate of progress of a crest (or a
trough, or any other reference point in the wave). Some
kinds of waves (sound waves, for example) travel at the
same speed, no matter what their wave-length: such waves
are said to be non-dispersive. Other waves (e.g. surface
waves), on the other hand, are dispersive: waves of different lengths travel at different speeds, as does light in a
glass prism. The relation between wave-length and phase
speed is called the dispersion relation.
Dispersiveness plays havoc with signal transmission.
When listening to a piece of music, all sounds of different periods (and hence different wave-lengths) stay in
2. Focus of This Review
There are many kinds of waves. Light is of course a
wave. With the advent of satellite remote sensing, ocean
optics has acquired so much importance that it deserves a
* E-mail address: [email protected]
Copyright © The Oceanographic Society of Japan.
3
step: the same music is heard everywhere. Imagine, on
the other hand, a vibrating piston creating water waves
of a range of different periods (and wave-lengths). Since
waves of different lengths travel at different speeds, observers at different distances will experience different
waves. To fully re-create the motion of the source (the
signal), a remote observer must wait until all the waves
produced have arrived. Dispersive waves—as are most
familiar ocean waves—are thus much more complicated
than non-dispersive waves.
4. Ocean Acoustics
One might well argue that sound waves, like light,
play such an important role in the sea that they deserve
an extensive review of their own. Or, on the other hand,
that ocean acoustics is only a special case—sound waves,
after all, propagate in all compressible media—undeserving of special attention. However, in the past few decades, acoustic applications have become a major tool for
probing the oceans, and I have chosen to emphasize some
of the most significant of these applications.
Echo sounders are not new. They were introduced
soon after the Titanic disaster as a by-product of efforts
to echo-locate icebergs. The crude analog echo-sounder
of yesteryears has by now been followed by multi-beam
digital equipment capable of high resolution mapping and
bottom characterization. Sounders capable of detecting
Doppler shifts in the return signal allow measurement of
current profiles while under way, revealing details of the
flow structure unaccessible to other means of measurement. Acoustic fish locators enhance fishing effectiveness; improvements in sensitivity and signal processing
hold promise for acoustic stock assessment.
Because they are non-dispersive and attenuate only
slowly with distance, sound waves are also an effective
means of long-distance communication within the oceans
and of probing its large-scale properties. The speed of
sound is about five times greater in water than in air; it
increases with increasing temperature, salinity and pressure. One would thus expect the speed of sound to increase with depth, as the pressure increases. It does, but
in most oceanic areas, polar regions excepted, there is a
sharp decrease in temperature downwards across the main
thermocline. Around that level, the temperature dependence dominates and the sound speed decreases to a minimum, increasing again with depth as the pressure continues to increase. The layer of mimimum sound speed acts
as a wave-guide within which sound rays bounce back
and forth and can travel across the oceans with little attenuation. It is thus possible to detect sound sources (e.g.
submarines, volcanic eruptions) at great distances, even
across entire ocean basins.
Measuring travel time from a controlled source to a
distant receiver provides an estimate of the average sound
4
P. H. LeBlond
speed along the path, and in turn a measure of the average temperature along the same path. This is a simple
way to take the temperature of the ocean without having
to make a great number of spot observations. Seasonal
changes can be detected; so can gradual changes, as in
global warming. This is what the ATOC (Acoustic Thermometry of Ocean Climate) program proposes to do, using a source at Heard Is., in the southern Indian Ocean,
and detectors on both Atlantic and Pacific coasts of the
U.S.A. (Munk, 1989).
Using sound travel-time in the ocean to infer seawater properties between source and receiver is of course
exactly analogous to the methods used by seismologists
to deduce the properties of the Earth’s interior from earthquake waves (a combination of compression/sound waves
and shear waves in rocks). Acoustic tomography uses this
idea to infer acoustic properties in a slice of material: it
has already received wide-spread medical application. In
the ocean, the slice probed lies between two vertical moorings a thousand kilometres apart, say, one containing
sources, the other receivers. Changes in travel times between different pairs of sources and receivers provides
information on the large scale properties of the intervening water masses and their changes with time (Munk and
Worcester, 1988; Spiesberger and Metzger, 1992). Combined with satellite remote sensing of ocean temperature
and altimetry, such techniques may come to play an important role in global ocean monitoring.
Progress in ocean acoustics in the past decades has
been comparable to that of wireless communication in
the atmosphere in the development of digital technology,
increases in sensitivity, and the proliferation of high-precision devices. One should expect further developments
and the appearance of mixed optical-acoustic techniques
for communication (e.g. with marine mammals, cf. Clark,
1995), for remote species identification (Parrish, 1999),
and for measurement of ocean properties and their variability (see for example Catipovic et al., 1993; Frye et
al., 2000; Orcutt et al., 2000). There is a high demand
and a bright future for ocean acousticians.
5. Wind Waves
What most people have in mind when they think of
ocean waves are the wind-driven oscillations of the airsea interface: wind waves. Because gravity is the main
force which restores the displaced interface towards its
equilibrium position, these waves are called gravity
waves. Although for very small-scale displacements (less
than a cm or so) surface tension plays an important role,
small capillary waves are of limited interest. They are
however important when considering the reflectivity of
the ocean to short-wave radar (scatterometry—from which
wind-speed may be deduced—cf. Donelan and Pierson,
1987).
Gravity waves come in a range of periods (and wavelengths). Wind waves have periods between 0.5 seconds
(short 0.5 m long waves) and 25 seconds (very long swell,
with 1 km between crests in deep water). Tsunamis, generated by large scale seismic motions, range in periods
between 5 min and 2 hours; tides are mainly semi-diurnal and diurnal, with both longer period astronomical
components and higher frequency shallow-water harmonics.
Surface gravity waves have fascinated mathematicians for over two centuries. Although many of their basic properties were known by the middle of the last century, wind-wave generation remained an empirical subject until relatively recently. The wind produces a whole
spectrum of wave periods, characterized by a sharp peak
at the dominant frequency and a long high-frequency tail.
The energy as well as the period of the spectral peak are
observed, not surprisingly, to increase with wind speed,
duration and fetch. The wind makes waves basically
through the combination of a resonance mechanism between atmospheric pressure fluctuations and waves
(Phillips, 1957) followed by interfacial shear instability
of the sea surface (Miles, 1957). Neither mechanism, singly or jointly, can fully describe the observed shape and
evolution of the wave spectrum. It is only by taking into
account the continuous exchange of energy between
waves of different periods over the whole spectrum that
a satisfactory model emerges. In a series of papers starting in the 60’s, an international collaboration led by Klaus
Hasselmann managed to unravel the complexity of wavewave interaction processes and develop practical methods for calculating wind-wave spectra (see Komen et al.,
1994, for more details). While enormous progress has
been made, operational wind-wave prediction requires
accurate winds, correct physics and good numerics.
Progress is still required on all three fronts.
As human activities encroach further upon the ocean
domain, exposure to marine hazards increases. The likelihood of extreme events, capable of causing catastrophic
damage, dictates engineering design of offshore platforms
and onshore installations. Waves are clearly the main
safety concern at sea. Their interactions with currents and
the bathymetry influence the magnitude of the expected
extremes. Improved understanding of these interactions
as well as site-specific studies are required to ensure safe
design of marine platforms.
Overall, the extensive advances in understanding
wind waves over the past decades have moved the field
from the realm of basic science to that of practical engineering.
6. Tsunamis
Tsunamis are the most spectacular and dreaded gravity waves, evoking images of mountainous breakers and
large scale destruction. Tsunamis are produced by earthquakes or landslides, and travel thousands of kilometers
across the ocean. Because their wavelengths are very long
(tens to hundreds of kilometers) they travel at a speed
determined only by the ocean’s depth and are nearly nondispersive. Given a large-scale map of ocean bathymetry,
it is thus relatively simple to calculate the time they take
to travel from their source to a distant point, and to estimate the amount of focusing brought about by refraction
along the path. A Tsunami Warning System, based in
Honolulu, issues warnings based on the intensity of seismic sources and nearby sea-level disturbances. The system is useful however only for distant sources, when there
is adequate warning time. Tsunami waves take many hours
to cross the Pacific and there is ample time for evacuation of coastal communities in Japan, say, in advance of
the arrival of a wave generated in Chile.
Many of the most devastating recent tsunamis, as
described by Gonzalez (1999), have been caused by
nearby seismic events. The tsunami which claimed over
2,000 victims in Papua New Guinea in July 1998 resulted
from a local earthquake too weak to trigger a Pacific-wide
warning. The quake which caused the 1992 Nicaragua
tsunami which killed 170 people and left 13,000 homeless was anomalous in that much of its energy was in low
frequency motions which were neither detected by narrow-band seismographs nor felt by people on the shore.
These events have focused attention on two elements necessary for any effective tsunami warning system. They
are the need to identify the scope of the local tsunami
hazard, and the need for local, or at least regional, tsunami warning systems. (ITIC, 2000).
Tsunami generation by landslides, both sub-aerial and
underwater, can cause serious damage on a local scale.
The gigantic wave caused by a rockslide in Lituya Bay,
Alaska, washed trees from a mountainside 500 m above
sea-level (Miller, 1960). Submarine landslides on the
Hawaiian Ridge have been suspected of causing giant
local waves (Moore et al., 1989; Johnson and Mader,
1994), although there is some debate about the effectiveness of submarine slides in causing large surface waves
(LeBlond and Jones, 1995).
Determination of local tsunami hazards involves
characterization of the likely nature of nearby seismic
events and the response of the coastal area to the waves
they are likely to produce. The extent of the inundation
caused by a tsunami is highly dependent on offshore
bathymetric features, which may focus the waves, as well
as on the shape of land features: narrow valleys, for example, are highly susceptible to extensive inundation.
Avalanches, both above and below water, are also likely
sources of local tsunamis. Thus, although the physics of
tsunami generation and propagation are, on the whole,
rather well known, there are still gaps in understanding
Ocean Waves: Half-a-Century of Discovery
5
the coupling between seismic events, sea-floor motions,
and the waves which they produce. From the point of view
of ensuring public safety, much remains to be done to
ensure that tsunamis, rather than being seen passively as
“an act of God”, become an accountable hazard, circumscribed within probability limits, that can be managed
through reliable emergency responses. Systematic efforts
at reducing tsunami impacts have been described by
Bernard (1998).
7. Tides
The study of tides has a history even longer than that
of wind waves. Many natural philosophers toyed with a
variety of theoretical explanations before Newton recognized the cause of the tides as unbalanced residual forces
between orbiting bodies. Through the next two centuries,
fluid mechanicists gradually developed a theory of tides
as forced gravity waves within complex ocean basins.
Until relatively recently, all tidal measurements were
made at or near the shore line—all offshore estimates were
extrapolated. Over the past few decades, direct deep-water measurements of tides through benthic pressure gauges
and satellite altimetry have greatly improved knowledge
of deep-sea tides and provided data to tune global tidal
models and test theoretical refinements. While there is
perhaps little new of a fundamental nature to be learned
about tides, the presence of density stratification, the influence of friction and the complexity of coastal geometry still present practical challenges and interesting effects.
On a regional scale, tidal currents mix coastal waters, and do so most effectively in shallow areas, giving
rise to frontal zones of biogeographical significance.
Tidally induced residual currents are important contributors to coastal circulation (cf. Parker, 1991; Garrett and
Maas, 1993). There are even occasional surprises: for
example, the tide no longer behaves as a wave when frictional forces dominate, as in shallow rivers (LeBlond,
1978).
On a global scale, lunar and solar tides dissipate the
energy of the Earth-Moon and the Earth-Sun orbital systems, slowly increasing the length of the day, while the
moon gradually recedes from the Earth. These effects have
long been of interest to geophysicists and astronomers
(Munk and MacDonald, 1968). The details of the energy
cascade from tides, to internal tides, to internal waves
and finally to turbulence and their contribution to ocean
mixing, as sketched in Fig. 1, remain of great interest
(Munk and Wunsch, 1998).
The theory as well as the practice of tidal power generation are, by now, well understood (Godin, 1969). It is
the water-level differences, not the tidal currents, which
can yield practical power generation. Although a plethora
of plans and projects have been put forward, only one
6
P. H. LeBlond
Fig. 1. The flux of tidal energy, as per Munk and Wunsch
(1997). Rates of energy flux are given in terawatts (TW =
1012 watts). Contributions of the principal semi-diurnal tidal
component M 2, the single most important tidal component,
are identified. Thick lines represent processes for which
measurements provide some quantitative estimates; thin
lines are speculative.
tidal power plant, in the estuary of La Rance river, in
Brittany, has been functioning in a practical way, contributing to a national power grid. Economic considerations, and in particular the magnitude of installation costs,
have prevented further investment in tidal power plants.
Environmental problems such as siltation and changes in
salinity regimes may also arise. The emplacement of restraining barrages may also alter tidal regimes, especially
in basins where the tides are near resonance. For example, some power generation schemes in the Bay of Fundy
could cause flooding in Boston (Garrett and Maas, 1993).
8. Internal Waves
Ocean waters are stratified: density usually increases
gradually with depth, but sometimes changes rapidly
across sharp pycnoclines. Oscillations of density inter-
Fig. 2. The extended dynamic balance of the oceanic internal wave field, after Müller and Briscoe (2000). The shaded box
represents the internal wave field, consisting of near-inertial waves (“f”), the continuum, and the tides (“M2”). There is
clearly some overlap between this representation and that of Fig. 1.
faces within the ocean are entirely analogous to those of
the sharper air-sea interface. Interfacial waves were first
recognized in estuarine areas, at the sharp interface below a fresh upper layer. Interaction of such internal waves
with slow vessels leads to the phenomenon of “dead water”, known since antiquity, but first explained by Ekman
(1904). These waves create alternating zones of convergence and divergence of the sea surface, with corresponding bands of rough and smooth water clearly visible from
above. Satellite imagery has revealed the ubiquity of such
waves on continental shelves, in areas where tidal currents interact with bottom topography.
In continuously stratified waters, internal waves
travel at an angle to the vertical and carry the energy of
disturbances created at ocean boundaries, mainly by the
wind and tides, into the ocean’s interior. While such waves
are just as variable in time and space as the phenomena
that generate them, wave-wave interactions spread out
their energy in a nearly universal spectral distribution,
first synthesized by Garrett and Munk (1972), through
processes analyzed in more detail by Hibiya et al. (1998).
Müller and Briscoe (2000) have reviewed the current state
of understanding of internal waves in the oceans, confirming the observation of spectral peaks at the inertial
frequency and at that of the semi-diurnal tide, arising from
wind and tidal forcing respectively, and of a continuum
in the intermediary frequencies (Fig. 2). The primary focus of current internal wave research is the understanding of the pathways which distribute energy through the
spectrum.
9. Vorticity Waves
There also exist, in the ocean as well and in the atmosphere, oscillations of such large scale and long periods that they are not directly perceptible as waves to human senses. Their wavy nature is only revealed by obser-
vations over sufficiently long times and large areas. Such
large-scale waves, dubbed planetary waves, were discovered in the atmospheric circulation by C. G. Rossby and
found to be the key to a better understanding of weather
variability and prediction. Meanders of the Gulf Stream
and of other western boundary currents were soon recognized to partake of similar dynamics (cf. LeBlond and
Mysak, 1978; or Gill, 1982).
Oceanic Rossby waves are waves of vorticity: oscillations of rotating fluid columns across lines of constant
latitude, or of constant depth. They manifest themselves
as varying currents, accompanied by minor variations of
sea-level, with periods of days to years and horizontal
scales of tens to hundreds of kilometers. Such meso-scale
motions, sometimes represented as eddies, have been
found to be a common feature of the ocean and to account for much of its long-term variability. These eddies
are analogous to synoptic pressure systems in the atmosphere, being however much smaller in horizontal extent
(typically, one hundred compared to one thousand kilometres), with the consequence that the ocean, while occupying a fraction of the Earth’s surface, has room for
more of them than does the atmosphere. This disparity of
scales requires denser sampling for a description of oceanic variability comparable to that of the atmosphere, as
well as higher resolution modeling of the oceanic circulation. Hurlburt et al. (1996), found that a resolution of
1/8° (approx. 12 km) was necessary for realistic modeling
of the Kuroshio. The need for high spatial resolution at
long time scales in ocean modeling presents a significant
challenge to the study of climate variations; because
Rossby waves are slow, it also takes a very long time for
the oceanic part of coupled ocean-atmosphere models to
respond to changes and to reach equilibrium.
Continental slopes, mid-ocean ridges and trenches
act as wave-guides for vorticity waves. Measurements
Ocean Waves: Half-a-Century of Discovery
7
(e.g. Hickey et al., 1991) show that a large fraction of the
variability of near-shore currents can be attributed to continental shelf waves, trapped along the coast, travelling
with shallow water to their right (in the North Hemisphere). Prediction of ocean properties on continental
shelves on time scales of days to months must rely on a
correct understanding of the behaviour of both forced (by
local atmospheric effects) and free (produced elsewhere)
continental shelf waves.
The equator also acts as a wave-guide for gravity as
well as vorticity waves, which both play an important role
in the oceanic phase of the ENSO phenomenon.
Philander (1990) has described the interactions between
the ocean and the atmosphere and the wave motions responsible for El Niño and La Niña. Equatorial waves that
reach the eastern shore of the ocean continue to travel
poleward along the coasts of North and South America as
trapped waves, carrying the El Niño signal to mid-latitudes (Melsom et al., 1999). In the Gulf of Alaska, these
waves are scattered westward across the Pacific, reaching, and influencing, the Kuroshio region a decade after
the equatorial event that generated them (Jacobs et al.,
1994).
Vorticity waves and advection of air and water
masses are the mechanisms whereby long-term fluctuations in ocean and atmospheric properties are communicated around the Earth. The role of such slow waves in
inter-decadal variability and regime shifts remains a topic
of great interest and relevance. In the North Pacific, for
example, Zhang and Levitus (1997) find a decadal-scale
cycle of upper ocean temperature anomalies circulating
clockwise around the subtropical gyre, a phenomenon
which they attribute to Rossby wave propagation. The
recently discovered Antarctic Circumpolar Wave, which
takes about eight years to go around Antarctica from west
to east, is another example of a long period oscillation
involving, like the ENSO, both the atmosphere and the
ocean (Baines and Cai, 2000).
10. Conclusions
Over the past fifty years, there has been enormous
progress in the understanding of ocean waves of all kinds.
Advances in mathematical methods and in computing
power have expanded the realm of description beyond
linear plane waves to fully nonlinear oscillations and to
the evolution of broad spectra of interacting wave ensembles. Progress has come about as much from open and
vigorous international collaboration as from advances in
technology. In some areas, particularly with surface gravity waves (wind waves, tsunamis, tides) enough confidence has been gained for robust engineering applications
and reliable prediction. The properties of long-period
vorticity waves have been described and their role in some
large-scale oceanic phenomena (such as El Niño) clari-
8
P. H. LeBlond
fied. Nevertheless, much remains to be explained about
the interactions of these long-period waves with each
other, with current systems, and with atmospheric forcing, in processes resulting in decadal-scale variability,
regime shifts and climate change.
Wave motions at all scales in time and space are fundamental physical processes of ocean dynamics,
transfering energy and momentum over large distances
without commensurate transport of mass. Regardless of
the degree of sophistication with which they are known,
waves will always remain a major part of the tool-kit of
the ocean physicists and engineers.
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