Chapter 10 Waves
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
Direction of wave motion
Wave-length
Crest
1/2
wavelength
depth
Trough
Still water
level
Crest
If we had this below,
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 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.
Period (& wavelength) and Wave Energy
Disturbing
force
Restoring force
Amount of energy
in ocean surface
Type of wave
Gravity
Seismic
disruption
landslides
Wind
Surface
tension
Gravity
Tide
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)
Deep- to Shallow-Water Waves
Progressive Waves
Wave Speed
L
A
H
Keep in mind: wave energy, NOT the water particles move
across the surface of the sea. 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
• Period to about 20 seconds
• Wavelength to at most 600 meters
(extreme)
• Speed to about 100
kilometers/hour (70 mi/hr)
(extreme)
gL
gT
C
 1.25 L 
 1.56T
2
2
For example, for a 300 meters wave and 14 sec
period, the speed is about 22 meters per second
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
* The wave speed can be calculated from knowledge of either the
wavelength or the wave period:
C = 1.56 m/s2 T or C2 = 1.56 m/s2 L
* Group Speed (which really transport the energy) is half of the
wave speed for deep-water waves:
V = C/2
Shallow-Water Waves
C  gD  3.1 D
Seismic Sea Waves – Shallow-Water Waves
• Period to about 20 minutes
• Wavelength of about 200 kilometers
• Speed of about 750-800 km/hr (close to 500 mi/hr!!)
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
* The wave speed and the wavelength are controlled by the depth D
of the waters only:
C  gD  3.1 D
* 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
• Storm centers and dispersion
• Winds flow around low pressure
• Variety of periods and heights are generated  grouped
into wave trains
Waves with longer period (T) and larger length move faster
- these get ahead of the ‘pack’.
Wave sorting of these free waves is dispersion
Wave Train (‘pack’, group)
• wave 1 transfers ½ of its
energy to water (gets orbital
motion going) and ½ to wave 2 (to
keep that going)
• wave 1 disappear – later 2 and
3 and so on will disappear also as
wave 6, 7, etc. form
• waves 1, 2, 3, etc. move at
their deep-water wave speed C
but the wave train moves at ½ of
C = V, the group velocity, speed
at which energy moves forward
Dispersion only affects deepwater waves, as depth decreases
waves become shallow-water
waves, they slow down until C=V
5
6
4
3
2
1
5
4
3
2
1
6
5
4
3
2
7
6
5
7
6
7
8
4
5
3
4
3
6
5
4
7
6
5
8
7
6
5
Fetch:
uninterrupted
distance over
which the wind
blows without
significant
change in
direction.
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)
Cortes Bank is a dangerously shallow chain of
underwater mountains in the Pacific Ocean,
about 115 miles (188 kilometers) west of Point
Loma San Diego, USA, and about 50 miles (82
kilometers) south-west of San Clemente Island.
The chain of peaks is about 18 miles (30
kilometers) long and they rise from the ocean
floor from about 1/2 mile (about 1 km) down.
Some of the peaks come to just 3 to 6 feet (1–2
m) below the surface at Bishop Rock,
depending on the tides.
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
1
2
a
b
Constructive
interference
(addition)
Destructive
interference
(subtraction)
Constructive
interference
(addition)
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.
Breaker Types
Wave Refraction – slowing and bending of waves as they
approach shore at an angle
depth contours
part of wave in shallow water
slows down
crests
part of same wave still in deep
water hence faster
oblique angle between
direction of motion of
waves and depth contours
Wave refraction- propagation of waves around obstacles, for
example over a shallow ridge – energy is focused (waves get
‘interrupted’, waves generate other waves)
Wave refraction in a shallow bay – energy is spread
Wave Diffraction
narrow opening
Internal & Planetary Waves
Internal & Planetary Waves
Rossby Waves: only move westward along
lines of latitude through conservation of
vorticity
Kelvin Waves
Travel eastward along the equator as a
double wave ‘equatorial wave guide’
Travel along coasts (coast on right in the
NH and on the left in the SH)
Balance between pressure gradient force
and coriolis force.
Kelvin waves in the thermocline can have dramatic effects,
particularly in low latitudes where the mixed surface layer is thin.
Northward migration of ITCZ in western Atlantic generates
disturbance that propagates eastward
Splits into two coastal Kelvin waves when hits the eastern boundary
The region of the disturbance where the thermocline bulges upward
cold nutrient rich sub-thermocline water can reach the surface
4-6 week travel time
ENSO: El Nino – Southern Oscillation
Internal & Planetary Waves
Tsunami (Harbor Wave)
•
•
Displacement of a large volume of water
Shallow water waves
 Long wavelength
 Long period (few minutes to over an hr)
http://www.seed.slb.com/en/scictr/watch/living_planet/tsunami.htm
Satellite images of a coastal village in Banda Aceh,
Indonesia, before and after the December 26, 2004
tsunami.