chapter 10 waves
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Chapter 10 Waves
Fig. 10-2, p. 266
Direction of wave motion
A B
Wavelength
Height
Still water level Crest Trough
Frequency: Number of wave crests passing point A or point B each second
Orbital path of individual water molecule at water surface
Period: Time required for wave crest at point A to reach point B
Direction of wave motion
Wave-length
Still water levelCrest Trough Crest
1/2 wave-length depth
Stokes drift (mass
transport)
No mass transport
Wave
Wave
Closed orbit after one period
Open orbit after one period
If we had this below, then there would be no net mass transport and no contribution of waves to the surface currents
BUT
in reality orbits are not exactly closed and waves DO contribute to mass transport
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 baysand seas, harbors and in estuaries.
Seismic disruptionDisturbing forcelandslides
Gravity Wind
Restoring force GravitySurface tension
Type of wave Tide Tsunami Seiche Wind wave Capillary wave (ripple)
24 hr.
Am
ou
nt
of
ener
gy
in o
cean
su
rfac
e
100,000 sec (1 1/4 days)
10,000 sec (3 hr)
1,000 sec (17 min)
100 sec 10 sec 1 sec 1/10 sec 1/100 sec
Period (time, in seconds for two successive wave crests to
pass a fixed point)
1 10 100
Frequency (waves per second)
12 hr.
Period (& wavelength) and Wave Energy
Progressive Waves
Deep- to Shallow-Water Waves
H
L
A
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 Vwave 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.
Wave Speed
Deep Water Waves
TgT
LgL
C 56.12
25.12
For example, for a 300 meters wave and 14 sec period, the speed is about 22 meters per second
• Period to about 20 seconds
• Wavelength to at most 600 meters (extreme)
• Speed to about 100 kilometers/hour (70 mi/hr) (extreme)
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
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!!)
DgDC 1.3
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:
* Group Speed (which transport the energy) is the same as the wave speed for shallow-water waves: V = C
DgDC 1.3
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
Wind Blowing over the Ocean Generates Waves
Waves development and growth are affected by:
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
5 4 3 2 1
7 6 5 4 3
6 5 4 3 2
8 7 6 5
8 7 6 5
7 6 5 4 3
7 6 5 4
6 5 4 3 2 1
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 deep-water waves, as depth decreases waves become shallow-water waves, they slow down until C=V
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.
Fetch: uninterrupted distance over which the wind blows without significant change in direction.
Wind Speed, Fetch & Duration
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.
7 across
1 high
120°
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
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)
1 2 4 53
Depth = 1/2 wavelength
Surf zone
Deep-water waves change to shallow-water waves as they approach the shore and they break
(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
crests
oblique angle between direction of motion of waves and depth contours
part of wave in shallow water slows down
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)
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
• Displacement of a large volume of water
• Shallow water waves Long wavelength Long period (few minutes to over an hr)
Tsunami (Harbor Wave)
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
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