```Capillary Waves,
Wind Waves,
Chapter 10
Waves
Tsunamis, Internal waves
big waves
huge waves
rogue waves
small waves
Wave
Wave direction
wave energy –
NOT the water
particles –
moves across
the surface of the sea
wave form moves and
with it, energy is
transmitted
Direction of wave motion
A
B
Wavelength
Height
Still water level
Crest
Frequency: Number of wave
crests passing
point A or point B
each second
Period: Time required for
wave crest at point A
to reach point B
Trough
Orbital path of
individual water
molecule at water
surface
Fig. 10-2, p. 266
Anatomy of a Wave
more like a real wave
more like a sine wave
Parts of a Wave
* Wavelength
* height
* Crest
* trough
* amplitude
* Frequency - # of waves passing a fixed point in
a given length of time
* Period - time for successive crests or troughs
(1 wavelength) to pass a fixed point
Direction of wave motion
Wave-length
Crest
1/2
wavelength
depth
Trough
Still water
level
Crest
then there would be
no net mass
transport and no
contribution of waves
to the surface
currents
No mass
transport
Closed orbit
after one period
BUT
in reality orbits are
not exactly closed
and waves DO
contribute to mass
transport
Stokes drift
(mass
transport)
Open orbit
after one period
How do a waves form?
• Wind blowing across calm water – if gentle breeze capillary
waves. Generating force = wind; restoring force = surface tension
(cohesion); grow up to a wavelength of about 2 centimeters
• As wind speed increases - wave becomes larger. Generating force =
wind; restoring force  changes from surface tension to gravity
Types of waves - (1) progressive & (2) standing waves
(1) progressive = have a speed and move in a direction
• surface waves: deep-water & shallow-water waves
• big’ waves: large swells, tsunamis & episodic waves
• internal waves at the pycnocline
(2) standing waves or seiches - do not progress, they are progressive
waves reflected back on themselves and appear as alternating troughs
and crests at a fixed position called antinodes, oscillating about a
fixed point called node. They occur in ocean basins, enclosed bays
and seas, harbors and in estuaries.
Disturbing
force
Restoring force
Gravity
Amount of energy
in ocean surface
Period (& wavelength) and Wave Energy
Tide
Type of wave
Seismic
disruption
landslides
Wind
Surface
tension
Gravity
Tsunami
Seiche
Wind wave
Capillary wave
(ripple)
2412
hr.hr.
100,000 sec 10,000 sec 1,000 sec 100 sec 10 sec
(1 1/4 days)
(3 hr)
(17 min)
1 sec
1/10 sec
1/100 sec
10
100
Period (time, in seconds for 1
two successive wave crests to Frequency (waves
pass a fixed point)
per second)
Waves transmit energy across the ocean’s surface. Wave energy in the ocean as
a function of the wave period. As the graph shows, most wave energy is typically
concentrated in wind waves. However, large tsunami, rare events in the ocean,
can transmit more energy than all wind waves for a brief time. Ides are waves –
their energy is concentrated at periods of 12 and 24 hours.
Deep- to Shallow-Water Waves
Progressive waves. Classification depends on their wavelength
relative to the depth of water through which they are passing.
Note the importance of the relationship between wavelength and
depth in determining wave type.
Extra Credit Assignment - 12/05/2008
Write a 2-page essay on one of the following topics:
1. Rogue Waves
2. Tsunami
Guidelines:
1. Select one of the two topics above.
2. Do some “research” on your topic, take notes, connect
the information you gather to the material of this class,
make sure you can explain your notes, and only then start
An excellent place to begin research about your
3. Essay is due Friday Dec. 12, by the time of class (2:10
pm) - this is an ABSOLUTE deadline. Essay must be
TYPED! Can be sent electronically to the class email
Keep in mind the key ideas in chapter 10:
• Waves transmit energy MOSTLY, not water mass, across the
ocean's surface.
• Most waves affect only the ocean’s surface layer. Movement
ceases at a depth equal to about half the wave’s wavelength.
• Arranged from short to long wavelengths (and therefore from
slowest to fastest), ocean waves are generated by very small
disturbances (capillary waves), wind (wind waves), rocking of
water in enclosed spaces (seiches), seismic and volcanic activity
or other sudden displacements (tsunami), and gravitational
attraction (tides).
Next:
• The speed of ocean waves usually depends on their wavelength,
with long waves moving fastest.
• The behavior of a wave depends largely on the relation between
the wave’s size and the depth of water through which it is
moving.
• Wind strength and duration determine the wavelength and speed
of wind waves.
Wave Speed – C
Speed is equal to wavelength, L,
divided by period, T. Example:
the speed of a wave with a
wavelength of 233 meters and a
period of 12 seconds is 19.4
meters per second.
The easiest wave characteristic
to measure exactly is period
Wave propagates with C – Energy moves with V
Wave Speed is C - Group Speed is V
wave speed = wavelength / period
or
C=L/T
T is determined by generating force so it remain the same
after the wave formed, but C changes. In general, the longer
the wavelength the faster the wave energy will move through
the water.
Deep Water Waves
* surface waves progressing in waters of D larger than 1/2 L
* as the wave moves through, water particles move in circular orbit
* diameter of orbits decrease with depth, orbits do not reach bottom,
particles do not move below a depth D = L/2
Period of up to about 20 seconds
Wavelength of up to at most 600
meters (extreme)
Speed can be up to 100 km/hr (70
mi/hr) (extreme)
* The wave speed can be calculated from knowing either the
wavelength or the wave period:
C = 1.56 m/s2 T or C2 = 1.56 m/s2 L
Example: a 300 meters wave with a 14 sec
period, propagates at 22 meters per second
* Group Speed (which really transport the energy) is half of the
wave speed for deep-water waves: V = C/2
Shallow-Water Waves
• surface waves generated by wind and progressing in waters of D
less than (1/20) L
• wave motion: as the wave moves through, water particles move in
elliptical orbits
• diameter of orbits remains the same with depth, orbits do reach the
bottom where they ‘flatten’ to just an oscillating motion back and
forth along the bottom
Period up to about 20 minutes
kilometers and more
km/hr (close to 500 mi/hr!!)
* The wave speed and the wavelength are controlled by the depth D of
the waters only:
C  gD  3.1 D
Example: a 300 meters wave propagating in a 10 meterdeep channel has a speed of 9 meters per second
* Group Speed (which transport the energy) is the same as the wave
speed for shallow-water waves: V = C
Wind Blowing over the Ocean Generates Waves
Waves development and growth are affected by:
Wind Speed: velocity at which the wind is blowing
Fetch:
distance over which the wind is blowing
Duration:
length of time wind blows over a given area
Larger Swell
Move Faster 
waves separate
into groups
wave separation
is called
dispersion
Fetch:
uninterrupted
distance over
which the wind
blows without
significant
change in
direction.
Factors affecting wind wave
development: Wind Speed, Fetch &
Duration
Wave size increases with increased wind speed, duration, and
fetch. A strong wind must blow continuously in one direction for
nearly three days for the largest waves to develop fully.
Pacific Ocean: wind speed of 50 mi/hr, blowing steadily for about 42 hours
over a region of size 800 miles will results in 8 meters waves – can get to 17
meter waves! (see Table 10.2)
Interference Produces Irregular Wave Motions
When waves meet up, they interfere with one another.
Wave interference can be:
Destructive interference – two waves that cancel each other out,
resulting in reduced or no wave
Constructive interference – additive interference that results in
waves larger than the original waves
Rogue waves - these freak waves occur due to interference and
result in a wave crest higher than the theoretical maximum
1
2
a
b
Constructive
interference
Destructive
interference
(subtraction)
Constructive
interference
Constructive and destructive interference.
Two waves of different wavelength (different storms) overlapping, one in blue and
one in green. The ‘blue wave’ has a slightly longer wavelength. (b) The waves will
interfere with each other to form a composite wave with (1) a very large crests and
troughs if the interfere CONSTRUCTIVELY, or (2) the two waves will
destructively interfere, and the crests and troughs will be very small.
Wave Height, Wavelength & Wave Steepness
Typical ratio wave height to wavelength in open ocean = 1:7 =
wave steepness – angle of the crest = 120°
Exceed these conditions and wave will break at sea 
whitecaps
7 across
1 high
120°
Wave Height is controlled by (1) wind speed, (2) wind duration and (3)
fetch (= the distance over water that the wind blows in the same direction
and waves are generated)
Significant Wave Height - average wave height of the highest one-third
of the waves measured over a long time
Deep-water waves change to shallow-water waves as they approach
the shore and they break
1
2
3
4 5
Depth = 1/2 wavelength
Surf zone
(1) The swell “feels” bottom when the water is shallower than half the
wavelength. (2) The wave crests become peaked because the wave’s energy is
packed into less water depth. (3) Water’s circular motion due to wave is
constrained by interaction with the ocean floor and slows the wave, while waves
behind it maintain their original rate. (4) The wave approaches the critical 1:7
ratio of a wave height to wavelength. (5) The wave breaks when the ratio of wave
height to water depth is about 3:4. The movement of water particles is shown in
red. Note the transition from a deep-water wave to a shallow-water wave.
The Surf Zone - Breakers
Wave Breaking: wave becomes
unstable as water particles at
the crest travel much
faster/farther than water
particles in the trough
spiller
plunger
Breaker type is
determined by slope,
composition and
contours of the
bottom
Breaker Types
Tsunami
• Vertical sea floor displacement
• Shallow water waves
 Long wavelength
 Relatively long period (compared to wind
waves)
• Wave height changes (quite dramatically!)
 At point of origin
 Close to shore where depth decreases
Landslides, Icebergs falling from glaciers, Volcanic
eruptions, Asteroid impacts, Other direct displacements
of the water surface CAN also generate tsunami
Read sections 10.24 through 10.29 and review questions 24
through 30 (page 291 of current textbook)
The great Indian Ocean tsunami of
26 December 2004 began when a
rupture along a plate junction lifted
the sea surface above. The wave
moved outward at speeds of 212
meters per second (472 miles per
hour).
At this speed, it took only about 15
minutes to reach the nearest
Sumatran coast and 28 minutes to
travel to the city of Banda Ache.
Tsunami Move at High Speed
The speed of a tsunami can be calculated using the same
formula used for other shallow-water waves:
__
C = gd
g = 9.8 meters per second (the acceleration due to gravity)
d = depth (a typical Pacific abyssal depth is 4,600 meters)
Eleven destructive tsunami have claimed more than 180,000
lives since 1990.
Cartoon Illustration
Tsunamis become dangerous
only near shore
More Key ideas to keep in mind:
• Waves can interfere with one another, resulting in larger or smaller
waves.
• Most waves change shape and speed as they approach shore. They
may plunge of spill at the surf zone and bend to break nearly parallel
to shore.
• A storm surge is a short-lived, abrupt bulge of water driven on shore
by a tropical cyclone or a frontal storm (from Ch. 8). Although storm
surges are sometimes called storm tides or storm waves, storm
surges consist of only a crest, so they cannot be assigned a period or
wavelength, and cannot be called a wave.
• Tsunami are always shallow-water waves. No ocean basin is deeper
than one-half their wavelength. Tsunami have been responsible for
large losses of life and property.
• Tsunami are caused when water is displaced by the forces that
cause earthquakes or by landslides, eruptions, or asteroid impacts.
Typically tsunami resemble a fast-onrushing tide, not a breaking
wave. They are not dangerous in the open sea.
And there is more:
Even greater waves exist: the tides. Yes, two
“tidal waves” move along most coasts each day; the
crests are the day’s high tides; and the troughs,
the day’s low tides. Tides are shallow-water
waves no matter how deep the ocean they’re
moving through. Tides can be destructive, but
among all waves their ability to cause damage is
fortunately not proportional to their wavelengths.
Review
1. Wavelength Is the Most Useful Measure of Wave
Size
2. The Behavior of Waves Is Influenced by the Depth
of Water through Which They Are Moving
3. Wind Blowing over the Ocean Generates Waves – we
call these ‘wind waves’
4. Storm Surges are NOT waves
5. Tsunami are long-wavelength, shallow-water,
progressive waves Caused by Water Displacement
6. Tsunami Are Always Shallow-Water Waves
Chapter 11 – Tides
A tidal bore is formed
when a tide arrives to
an enclosed river
mouth. This is a
forced wave that
breaks.
Tidal range can be very large
Tide - rhythmic oscillation of the ocean surface due to gravitational &
centrifugal forces (‘inertia’) between the Earth, Moon and Sun.
Tide Patterns - regular, cyclic patterns of low water-high water
Tidal cycle – one low tide and one high tide consecutively
diurnal tide - one low tide, one high tide a day;
semidiurnal tide - high water-low water sequence twice a day;
2 high, 2 low, about the same level
semidiurnal mixed tide - same as semidiurnal but 2 highs and 2 lows
do not reach/drop to the same level; may be
the result of a combination of tide types
Tide Patterns - regular, cyclic patterns of low water-high water
diurnal tide
semidiurnal tide
semidiurnal mixed tide
Semidiurnal tides
Diurnal tides
Mixed tides
Most of
the world’s
ocean
coasts
have
semidiurnal
tides.
d
(ft)
14
10
6
4
0
–4
Mixed tide, Los Angeles
Diurnal tide, Mobile, Alabama Semidiurnal tide, Cape
Cod
Higher high tide
High tide
Lower high tide
High tide
Lower
low tide
Higher low
tide
(m)
4
3
2
1
0
–1
Low tide
Low tide
0 612 18 24 30 36 42 48
0 6 12 18 24 30 36 42 48 0 6 12 18 24 30 36 42 48
a
Time (hr)
b
Time (hr)
c
Time (hr)
Flood Tide: tide wave is propagating (onto shore) onshore –
water level is rising
High Tide: water level reaches highest point
Ebb Tide: tide is moving out to sea – water level is dropping
Low Tide: water level reaches lowest point
Slack tide: period when tide wave is reversing –
low current velocity
Water currents are generated by the tides, the speed of the incoming
tide is about the same but in the opposite direction of the outgoing
tide. Moving waters have to slow down and reverse, from flood to
ebb and vice versa (slack tide). This is a good time for navigation
through narrow places, particularly those characterized by strong
tides (East River, for example).
Tides Are the Longest of All Ocean Waves
Characteristics and Causes of tides:
Tides are caused by the gravitational force of the moon and sun
and the motion of earth.
The wavelength of tides can be half the circumference of earth.
Tides are the longest of all waves.
Tides are forced waves because they are never free of the forces
that cause them.
Study of Tides:
Equilibrium Tidal Theory - ideal approach to understand basic
principles, assumes an earth covered with water and an infinitely deep
basin.
Dynamical Tidal Analysis - realistic approach, studying the tides as
they occur on earth, accounts for modification due to landmasses,
geometry of ocean basins, earth’s rotation.
Chapter 11 – Summary
Tides are huge shallow-water waves-the largest waves in the ocean.
Tides are caused by a combination of the gravitational force of the
moon and sun and the motion of Earth.
The moon's influence on tides is about twice that of the sun's.
The equilibrium theory of tides deals primarily with the position and
attraction of the Earth, moon, and sun. It assumes that the ocean
conforms instantly to the forces that affect the position of its
surface, and only approximately predicts the behavior of the tides.
The dynamic theory of tides takes into account the speed of the longwavelength tide wave in water of varying depth, the presence of
interfering continents, and the circular movement or rhythmic backand-forth rocking of water in ocean basins. It predicts the behavior
of the tides more accurately than the equilibrium theory.
These huge shallow-water waves are forced waves: never free of the
forces that cause them and so act in unusual but generally predictable
ways.
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