Ocean Studies
Introduction to Oceanography
American Meteorological Society
Chapter 7
Ocean Waves and Tides
© AMS
Case in Point
– Unusually high waves, known as rogue waves, occur
in the open ocean as well as some coastal areas.
– Many ships, including modern supertankers struck by
rogue waves have been extensively damaged or sunk
with loss of life.
– By one convention, a wave is considered rogue if its
height is 2.2 or more times the significant wave height
(average height of the tallest one-third of waves observed in a patch of ocean).
– Exceptionally high waves have been attributed to an
amplifying interaction between waves, called
constructive interference.
– Rogue waves occur in all ocean basins, in stormy
weather or under tranquil conditions, with a probability
of >3% in any hour, and with little or no warning.
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Ocean Waves and Tides
• Driving Question:
– What are sea waves and tides and what
causes them?
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Ocean Waves and Tides
• In this chapter, we discuss
– the formation and life cycle of waves,
– their generation as wind-waves or “sea,” plus
– their existence at sea as free waves and swell
before expending their energy as breakers on
a distant reef or shoreline.
• We also describe internal waves and
tsunamis.
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Wind-Driven Waves
– A sea wave is an oscillation on the ocean surface that
propagates along the interface between the
atmosphere and ocean.
– The highest point reached by the oscillating water surface is
called the wave crest and the lowest point is the wave trough.
– The wave height is the vertical distance between trough and
crest.
– The horizontal distance between successive wave crests (or
equivalently between any other two corresponding points of two
consecutive waves) is the wavelength.
– The time needed for two successive wave crests (one
wavelength) to pass a fixed point is the wave period.
– The number of waves passing a fixed point over an interval of
time is the wave frequency, the inverse of the wave period.
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Wind-Driven Waves
Vertical cross-section of an idealized sea wave.
© AMS
Wind-Driven Waves
• WIND-WAVE GENERATION
– If the air over the ocean were always calm, the sea
surface would be smooth and motion-less, a condition
sailors refer to as flat calm.
– Wind disturbs this equilibrium state as some of its
kinetic energy is transferred to surface ocean waters
as the wave-generating force.
– Waves begin as small ripples, called capillary
waves, with wavelengths of less than 1.7 cm (0.7 in.).
At these short wavelengths, water’s surface tension is
the restoring force that smoothes out and flattens
these relatively small waves.
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Wind-Driven Waves
• WIND-WAVE GENERATION
– Strengthening winds increasingly disturb the water
surface, producing larger waves having longer
wavelengths and greater wave heights.
– For these larger waves, gravity is the restoring force
working to level the wave crests and fill in the wave
troughs.
• Gravity pulls the crested water downward, but momentum
causes the water to continue downward and a trough is
formed. The lowered water is buoyed upward and the next
crest rises.
– Wind and gravity are responsible for most waves
observed on the ocean surface.
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Wind-Driven Waves
As a wave propagates along the air/ocean interface, water particles
oscillate in approximately circular orbits. In relatively deep water, the
orbital diameter of a water particle at the ocean surface equals the wave
height. As a complete wave passes a fixed point, a water particle
completes one orbit and returns to approximately its original location.
Orbits decrease in diameter with depth below the water surface and
eventually dissipate completely. This depth of no wave motion, called
wave-base, approximately corresponds to one-half the wavelength.
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Wind-Driven Waves
• WIND-WAVE GENERATION
– No net horizontal transport of water mass
occurs with each wave cycle. Instead, the
wave’s energy is propagated in packets in the
direction of travel.
– A wave crest travels twice as fast as the wave
energy
• a wave arises in the back of the packet, grows in
height, moves through the packet twice as fast as
the packet, and disappears at the front of the
packet.
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Wind-Driven Waves
• WIND-WAVE GENERATION
– Water wave formation and evolution depend primarily
on the wind’s
•
•
•
•
speed,
turbulence,
duration (the length of time the wind blows from the same direction) and
fetch (the distance the wind blows over a continuous water surface).
– In general, waves continue to build in height and
length as long as the energy supplied to the waves by
winds exceeds the amount of energy dissipated in
breaking waves.
© AMS
• When the amount of dissipated energy equals the amount of
energy supplied by the wind, no further wave build up occurs.
Wind-Driven Waves
• WIND-WAVE GENERATION
– Wave interference also influences the growth and
decay of sea waves.
© AMS
• In constructive wave interference, two or more wave crests
coincide to form composite waves having heights greater
than any of the original wave components (e.g. rogue
waves).
• On the other hand, sets of waves can also interact such that
the crests in one set of waves coincide with the troughs in
another set, partially canceling both sets. The product is a
composite wave whose height is smaller than that of the
original wave components. This interaction is known as
destructive wave interference.
• Both types of wave interference are almost always
happening at sea and contribute to the continually changing
pattern of waves on the open ocean.
Wind-Driven Waves
• DEEP-WATER AND SHALLOW-WATER
WAVES
– An ocean surface disturbed by winds becomes a
mass of waves of various heights and lengths,
moving in many different directions. This condition is
known as sea.
– Waves continue to propagate well beyond the area of
strong storm winds. Such waves, called swell, are
lower and more rounded than waves forming directly
under the storm winds.
– Celerity is the speed of the wave relative to the
water.
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Wind-Driven Waves
• DEEP-WATER AND SHALLOW-WATER
WAVES
– Waves in water that is deeper than their
wave-base are known as deep-water waves.
– The celerity of deep-water waves depends on
wavelength and gravity and can be computed
using the formula:
C =√(1.56 × wavelength),
where C is the celerity in m per sec and the
wavelength is given in meters.
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Wind-Driven Waves
• DEEP-WATER AND SHALLOW-WATER
WAVES
– In relatively deep water, waves with longer
wavelengths travel faster than waves with
shorter wavelengths.
– With deep-water waves, there is no
interaction between the orbital motions of the
wave and sea bottom.
– With little dissipation due to friction, swell can
travel thousands of kilometers from its source.
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Wind-Driven Waves
• DEEP-WATER AND SHALLOW-WATER
WAVES
– When waves enter waters shallower than
wave-base, they are restricted by water
depth.
– These are now shallow-water waves where
the orbits of water particles gradually flatten
with increasing depth, changing to a backand-forth motion near the bottom.
– Wave period is unchanged so its wavelength
shortens, and its wave height increases.
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Wind-Driven Waves
• DEEP-WATER AND SHALLOW-WATER
WAVES
– When waves enter waters having a depth of
less than one-half the wavelength, the wave
celerity depends on water depth and gravity
but not wavelength and is computed as:
C = √(g × depth)
where C is the celerity in m per sec, g is
gravity, and depth is given in meters.
– Shallow-water waves slow as they enter
© AMS shoaling water
Wind-Driven Waves
In shallow-water waves, the orbits of water particles gradually
flatten with increasing depth, changing from circular to elliptical
and ultimately to a back-and-forth motion near the ocean bottom.
© AMS
Wind-Driven Waves
• DEEP-WATER AND SHALLOW-WATER
WAVES
– Waves break when the ratio of wave height to
wavelength approaches 1 to 7; at this point
the wave-crest angle is close to 120 degrees.
– Wave energy is dissipated when breakers
form.
– A nearly continuous train of waves breaking
along a shore is called surf.
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Wind-Driven Waves
As the water shoals, particles of water in the building wave crest move
forward faster than the wave propagates toward shore. The wave
becomes steeper and eventually unstable. When the ratio of wave height
to wavelength approaches 1 to 7, the crest plunges forward as a breaker.
© AMS
Wind-Driven Waves
• SEICHE
– A seiche is a rhythmic oscillation of water in an
enclosed basin.
– Unlike wind-driven progressive waves, a seiche is a
standing wave; crests alternate vertically with
troughs but at fixed locations.
– During a seiche, the water level in a basin commonly
rises at one end while simultaneously falling at the
other end.
– Water level near the center (node) does not change at
all.
– This is analogous to the motion of a seesaw.
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Wind-Driven Waves
A seiche in an enclosed basin with a single node. The maximum vertical
© AMS motion of the water takes place at the antinodes and the maximum
horizontal motion occurs at the node.
Wind-Driven Waves
• SEICHE
– Wind, air pressure gradients, earthquakes, or
astronomical tides can induce a seiche.
– The natural period of a seiche is directly
proportional to basin length and inversely
proportional to water depth.
– A seiche grows as a consequence of
resonance meaning that the period of the
disturbance (e.g., earthquake, wind) matches
the natural period of oscillation of the basin.
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Wind-Driven Waves
• WAVE MEDIATED ATMOSPHERE-OCEAN
TRANSFER
– Sea waves help bring about transfer of energy and
matter between the atmosphere and ocean, a major
interaction among subsystems of the Earth system.
• The largest wind-generated waves on the ocean surface are
important in driving ocean currents by transferring
momentum from the wind to ocean surface waters.
• Waves with shorter wavelengths play a major role in heat
transfer from the ocean surface to the atmosphere through
latent heating and sensible heating.
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Wind-Driven Waves
• WAVE MEDIATED ATMOSPHERE-OCEAN
TRANSFER
– Waves with shorter wavelengths (especially breaking
waves) deliver tiny salt particles to the atmosphere
where they function as cloud condensation nuclei
spurring development of clouds.
• Droplets of ocean spray transfer microscopic marine algae
and viruses into the atmosphere where winds can transport
them long distances.
• Breaking waves capture myriads of air bubbles that are
dissolved and carried tens of meters below the ocean
surface.
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– This process, known as bubble injection, is an important
source of dissolved oxygen and carbon dioxide for surface
waters.
Internal Waves
– Internal waves form within the ocean along
interfaces where the change in density with
depth is relatively abrupt.
– Favorable sites for development of internal
waves include the base of the mixed layer
and interfaces (pycnoclines) between water
masses having different densities.
– Internal waves also form in estuaries along
the pycnocline between fresh river water and
salty ocean water.
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Ocean Tides
– Astronomical tides are the regular rise and
fall of the sea surface caused by the
gravitational attraction between the rotating
Earth and the moon and sun.
– Tides are shallow-water waves so that wave
celerity depends on water depth.
• For an average ocean depth of 4000 m (13,000 ft),
tidal celerity is about 200 m per sec (400 mph).
– Tides are measured mostly at coastal
locations as local changes in water level
© AMS through time.
Ocean Tides
Note the watermark on the dock
indicating the level of the water at
high tide.
The average vertical difference in
height between water levels at
high and low tides is called the
tidal range and generally varies
between less than a meter to
several meters.
The time between successive high
tides is the tidal period.
© AMS
Ocean Tides
• TIDE-GENERATING FORCES
– Produced by the combination of
• the gravitational attraction between Earth and the moon and
sun;
• the rotations of the Earth-moon and Earth-sun systems.
– According to the law of universal gravitation, the
gravitational attraction between two bodies is directly
proportional to the product of the masses of the two
bodies and inversely proportional to the square of the
distance between them.
© AMS
• For this reason, the moon exerts a greater gravitational pull
on Earth.
Ocean Tides
Two ocean tidal bulges produced by the gravitational attraction of the
moon combined with the rotation of the Earth-moon system on an
idealized water-covered Earth.
© AMS
Ocean Tides
• TIDE-GENERATING FORCES
– The gravitational pull of the moon on Earth is primarily
responsible for the bulge in the ocean surface that is oriented
toward the moon.
– Newton’s first law of motion predicts that a net force must
operate in any rotating system.
• This net force in the rotating Earth-moon system gives rise to the
tidal bulge on the planet opposite the moon.
– In the equilibrium model of tides, which assumes a frictionless
Earth entirely covered by water, ocean bulges would always
align with the celestial body that caused them and any location
moving through these bulges would experience tides.
• If only one celestial body was present, each day a low-latitude
location would experience two high tides and two low tides.
© AMS
• If the positions of the Earth and moon remained fixed in space, the
period of these tidal waves would be 12 hrs.
Ocean Tides
• TIDE-GENERATING FORCES
– While the Earth is rotating, the moon is rotating
around Earth.
• This gives rise to the tidal day (24 hrs, 50 minutes).
• The times of high and low tide change by about 50 minutes
from one solar day to the next.
• The ocean’s tidal bulges produced by the moon remain in the
same alignment relative to the moon, but change their
latitudinal positions on Earth as they follow the moon during
its monthly revolution about Earth.
– Sun-related tidal bulges are produced in the same
way as those caused by Earth-moon interactions.
• The sun’s tidal pull is about 46% of the moon’s pull.
– The tide-generating force is inversely proportional to
the cube of the distance between Earth and another
© AMS celestial body.
• Diurnal Tide
– Period of 24 hrs and 50 min
• Semi-diurnal Tide
– Two equal high tides and
two equal low tides per day
– Period of 12 hrs and 25 min
• Mixed Tide
– Two unequal high tides and
two unequal low tides per
day
– Difference in height
between successive high
(or low) tides is the diurnal
inequality
• Maximum – tropic tides
• Minimum – equatorial tides
© AMS
(A) Spring tides occur twice each month at or near the times of new moon and
full moon when the gravitational pull of the sun reinforces that of the moon;
this causes an unusually large or increased tidal range.
(B) Neap tides have the least monthly tidal range occurring at the first and third
quarter phases of the moon, when the sun’s pull on Earth is at right angles to
the pull of the moon.
© AMS
Ocean Tides
• TIDES IN OCEAN BASINS
– Many non-astronomical forces modify tides, including
ocean-bottom topography, the presence of continents,
coastline configuration, the Coriolis Effect, winds, and
water depth.
– The dynamic model of tides applies reasonably well to
seas and large embayments as well as the open ocean.
© AMS
• As Earth rotates from west to east, the tidal bulge shifts toward
the western boundary of the ocean basin and the water surface
slopes gently downward toward the east.
• The tidal crest rotates around the basin in a counterclockwise
direction (Northern Hemisphere) due to the Coriolis Effect.
• When the tide is high on one side of the basin, it is low on the
opposite side.
In this idealized Northern
Hemisphere ocean basin bordered
on all sides by land (top), a tide
wave rotates in a counterclockwise
direction (viewed from above).
Lines radiating outward from the
central node are cotidal lines that
join points where high tide occurs
at the same tide of day. This is a
semi-diurnal tide. Also shown
(bottom) is a vertical cross-section
from point A to point B. Note that
the tidal range varies from zero at
the node to a maximum at the
antinodes.
© AMS
Ocean Tides
• TIDES IN OCEAN BASINS
– The natural period of oscillation of a shallow basin
may match the period of the tide-generating force
causing resonance.
• Example: Bay of Fundy has tidal range up to 16 m (53 ft)
during spring tide
– Non-astronomical factors explain why locations on the
U.S. Atlantic coast have predominately semi-diurnal
tides whereas many places on the Gulf Coast have
mostly diurnal tides, and localities on the Pacific
Coast and portions of Canada’s Atlantic coast have
mostly mixed tides.
© AMS
ASTER satellite image of the Bay
of Fundy, Nova Scotia, Canada, at
high tide (top) on 20 April 2001, and
low tide (bottom) on 30 September
2002. The world’s highest
astronomical tides (tidal range of 16
m) occur in Minas Basin at the
eastern extremity of the Bay of
Fundy due to resonance of the Bay
of Fundy-Gulf of Maine system; that
is, the natural period of oscillation
of about 13 hrs is close to the 12
hrs 25 min period of the lunar tide
of the Atlantic Ocean.
© AMS
Ocean Tides
• TIDAL CURRENTS
– Alternating horizontal movements of water
accompanying the rise and fall of astronomical tides
in coastal areas are known as tidal currents.
– When tidal currents are directed toward the land,
water levels rise in harbors and rivers; these are
called flood tides
– Tidal currents flowing seaward with falling sea levels
are called ebb tides.
– In some coastal areas where the tidal range is
relatively large and the flood tide enters a narrow bay
or channel, a tidal bore forms and moves upstream
in a river or shallow estuary. A tidal bore is a wall of
turbulent water, usually less than a meter in height.
© AMS
Ebb tide and flood tide in a harbor viewed from above.
© AMS
Ocean Tides
• OBSERVING AND
PREDICTING TIDES
– Prediction is relatively simple
and is very important for major
ports.
– Tides are waves so that local
tides can be resolved
mathematically into the various
components, called partial
tides.
© AMS
• Some 60 components are
commonly used.
• More than 100 components
may be used to predict tides
along a complex coastline.
Ocean Tides
• OPEN-OCEAN TIDES
– These are important in mixing deep-ocean water.
– Tidal currents flowing over topographic irregularities
on the ocean floor generate internal tide waves that
propagate away from their source.
• Can travel thousands of kilometers from their source and can
have very large wavelengths
• Can break like surf on a beach, but under water, locally
mixing waters
• Are important in mixing cold bottom waters with warmer
surface waters
• Can influence the gradient of the continental slope
© AMS
Tsunami
– A rapidly propagating shallow-water wave that
develops when a submarine earthquake, landslide, or
volcanic eruption disrupts deep ocean water
– Wave is unnoticed moving under a ship at ship, but
can build to tremendous height in shoaling coastal
waters
– Can have a long reach, transporting potentially
destructive energy from its source to coastlines many
thousands of kilometers away
– Threat is generally much greater in the Indian and
Pacific Oceans than in the Atlantic Ocean
– A tsunami on 26 December 2004 devastated portions
of the coastal area rimming the Indian Ocean and
claimed an estimated 230,000 lives, the highest death
toll ever recorded by a tsunami.
© AMS
Tsunami
The Scotch Cap Lighthouse on Unimak Island, Alaska before and after the
earthquake and tsunami of April 1946. A magnitude 8.0 (Mw) earthquake with
the source to the south of Unimak Island generated a tsunami that destroyed
the five-story lighthouse, located 9.8 m above sea level.
© AMS
Tsunami
– The Hawaiian tsunami of 1946 led to the
establishment of the Pacific Tsunami Warning Center
in 1948.
– Warnings are based on earthquakes occurrences
detected by seismic networks around the Pacific Rim
plus tide gauge readings in coastal areas.
– Issues include:
• a high false alarm ratio;
• undersea earthquakes do not always generate a tsunami;
• warnings provided by coastal tide gauges generally arrive too
late for adequate warning of the public.
– Prior to the December 2004 tsunami, there was no
warning system in the Indian Ocean
© AMS
• An international effort lead by UNESCO has been rectifying
the situation.
Saving lives through improved early warning of an approaching tsunami is the goal of the
NOAA Deep-ocean Assessment and Reporting of Tsunamis (DART) system. Each DART
station has a tsunameter, consisting of a pressure sensor anchored to the ocean floor at
depths to 500 m (1640 ft) that measures slight variations in pressure exerted by the
overlying water column in response to a passing tsunami wave. This map shows the
location of completed and planned DART and Tsunameter Stations as of November
2007 for real-time detection of tsunamis.
© AMS
Data from DART sensors are
essential components of the U.S.
National Tsunami Hazard
Mitigation Program, a partnership
that includes representatives of
various federal agencies (i.e.,
NOAA, FEMA, and the U.S.
Geological Survey) and the
Pacific Coast states. In recent
years, this program has also
installed new shore-based tide
gauges and upgraded
seismometers operated by the
USGS. An essential outcome of
the program is public awareness
of the tsunami hazard and the
construction of maps that identify
coastal areas most susceptible to
inundation by a tsunami.
© AMS
Conclusions
– Winds supply the kinetic energy that forms waves on
the ocean surface, which then propagate horizontally
until they expend their energy by breaking on a
distant shore.
– Wave behavior depends on wind speed, fetch, and
duration as well as water depth.
– In terms of interaction with the ocean bottom, a
distinction is made between deep-water waves and
shallow-water waves.
– The gravitational attraction of the moon and sun
combined with the rotations of the Earth-moon and
Earth-sun coupled systems generate planetary-scale
shallow-water tide waves in the ocean basins.
© AMS