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Chapter 10 Waves

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Capillary Waves,

Wind Waves,

Tsunamis, Internal waves

Chapter 10

Waves

big waves

huge waves

rogue waves

small waves

Wave direction

Wave

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

Trough

Crest

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

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

Still water level

Crest

Crest

Trough

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

in reality orbits are not exactly closed and waves DO contribute to mass transport

BUT

- 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.

Seismic disruption

Disturbing force

Gravity

Wind

landslides

Surface tension

Gravity

Restoring force

Tide

Tsunami

Seiche

Wind wave

Capillary wave (ripple)

Type of wave

24 hr.

12 hr.

Amount of energy in ocean surface

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

1

10

100

Period (time, in seconds for two successive wave crests to pass a fixed point)

Frequency (waves per second)

Period (& wavelength) and Wave Energy

Deep- to Shallow-Water Waves

Progressive Waves

L

A

H

Wave Speed

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)

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

- 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:
- * 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

5

4

3

2

1

6

5

4

3

2

1

6

5

4

3

2

7

6

5

4

3

7

6

5

4

3

7

6

5

4

8

7

6

5

8

7

6

5

- 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 – mm 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

Wind Speed, Fetch & Duration

Fetch: uninterrupted distance over which the wind blows without significant change in direction.

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)

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

Wave Interaction - Interference

1

2

a

b

Constructive interference (addition)

Destructive interference (subtraction)

Constructive interference (addition)

- Wave interaction
- Constructive interference; (b) crests of waves coincide
- Destructive interference; (c) crest of one coincides with trough of other

ask surfers about the ‘surf beat’, or impress them explaining that it is ‘just wave interference’!

2

1

5

4

3

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.

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

depth contours

crests

Wave Refraction – slowing and bending of waves as they approach shore at an angle

part of wave in shallow water slows down

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)

Wave refraction in a shallow bay – energy is spread

Wave Reflection

Wave Diffraction

narrow opening

diffraction and wave interaction

Wave diffraction behind the breakwater

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.

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

when????

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

Tsunamis become dangerous only near shore