Capillary Waves,
Wind Waves,
Anatomy of a Wave
Chapter 10
Waves
more like a real wave
big waves
Tsunamis, Internal waves
huge waves
rogue waves
small waves
more like a sine wave
Wave direction
Wave
Parts of a Wave
wave energy –
NOT the water
particles –
moves across
the surface of the sea
* Wavelength
* height
* Crest
* trough
* amplitude
wave form moves and
with it, energy is
transmitted
* 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
Direction of wave motion
Wave-length
A
B
Wavelength
Crest
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
Still water
level
Crest
Trough
Orbital path of
individual water
molecule at water
surface
1/2
wavelength
depth
Fig. 10-2, p. 266
1
BUT
Period (& wavelength) and Wave Energy
in reality orbits are
not exactly closed
and waves DO
contribute to mass
transport
Disturbing
force
Restoring force
Type of wave
Stokes drift
(mass
transport)
No mass
transport
W
W
av
e
av
e
Amount of energy
in ocean surface
If we had this below,
then there would be
no net mass
transport and no
contribution of waves
to the surface
currents
Gravity
Seismic
disruption
landslides
Wind
Surface
tension
Gravity
Tide
Tsunami
Seiche
Wind wave
2412
hr.hr.
100,000 sec 10,000 sec 1,000 sec 100 sec 10 sec
(1 1/4 days)
(3 hr)
(17 min)
Closed orbit
after one period
Capillary wave
(ripple)
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)
Open orbit
after one period
Deep- to Shallow-Water Waves
How do a waves form?
• Wind blowing across calm water – if gentle breeze Æcapillary
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 Æ 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.
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.
2
Deep Water Waves
Shallow-Water Waves
• Period to about 20 seconds
• Wavelength to at most 600
meters (extreme)
• Speed to about 100
kilometers/hour (70 mi/hr)
(extreme)
C=
gL
gT
= 1.25 L =
= 1.56T
2π
2π
For example, for a 300 meters wave and 14 sec
period, the speed is about 22 meters per second
• 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
Deep Water Waves
* surface waves progressing in waters of D larger than 1/2 L
Waves development and growth are affected by:
* as the wave moves through, water particles move in circular orbit
Wind Speed: velocity at which the wind is blowing
* diameter of orbits decrease with depth, orbits do not reach bottom,
Fetch:
distance over which the wind is blowing
Duration:
length of time wind blows over a given area
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!!)
Larger Swell
Move Faster Æ
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 Æ 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
3
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
Fetch:
uninterrupted
distance over
which the wind
blows without
significant
change in
direction.
5
6
Wave Height, Wavelength & Wave Steepness
4
3
2
1
5
4
3
2
1
4
3
2
6
7
5
6
5
7
6
4
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 Æ
whitecaps
3
7 across
7
8
5
4
3
6
5
4
7
6
5
8
7
6
1 high
120°
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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
Wave Interaction - Interference
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)
1
2
a
b
Constructive
interference
(addition)
Destructive
interference
(subtraction)
Constructive
interference
(addition)
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Wave interaction
™ Constructive interference; (b) crests of waves coincide
™ Destructive interference; (c) crest of one coincides with
trough of other
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
ask surfers about the ‘surf beat’, or impress them explaining that
it is ‘just wave interference’!
Deep-water waves change to shallow-water waves as they approach
the shore and they break
2
1
3
oblique angle between
direction of motion of
waves and depth contours
part of same wave still in deep
water hence faster
Wave refraction- propagation of waves around obstacles, for
example over a shallow ridge – energy is focused (waves get
‘interrupted’, waves generate other waves)
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 in a shallow bay – energy is spread
5
Wave Reflection
when????
Tsunamis
• Vertical sea floor displacement
• Shallow water waves
™ Long wavelength
™ Low period
• Wave height changes (quite dramatically!)
™ At point of origin
™ Close to shore where depth decreases
Wave Diffraction
narrow opening
diffraction and wave interaction
Review:
Refraction: waves approaching shore are refracted (bent)
as they move from deep to shallow water - change in
wavelength and wave speed
Diffraction: spread of wave energy sideways to the
direction of wave travel.
Reflection: Waves that encounter a solid vertical surface
(such as a seawall) will abruptly change direction without
much loss of energy. Though not as simple as a ball
bouncing off a wall, the reflection of a wave obeys the
same principles, where the angle of incidence is equal to
the angle of reflection. When the angle is zero (as
measured from a line perpendicular to the reflecting
surface), reflection may generate standing waves.
This numerical simulation by the US Geological Survey shows the
spreading for the tsunami triggered by the quake.
http://walrus.wr.usgs.gov/tsunami/sumatraEQ/tectonics.html
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Satellite images of a
coastal village in Banda
Aceh, Indonesia,
before and after the
December 26, 2004
tsunami.
http://www.seed.slb.com/en/scictr/watch/living_planet/tsunami.htm
Site of potential collapse
“Cumbre Vieja Volcano-Potential
Collapse and Tsunami at
La Palma, Canary Islands”
(Ward and Day, GRL, 2001)
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