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