Chapter 10 Waves

Direction of wave motion 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 level Crest Trough 1/2 wave-length depth

Stokes drift (mass transport) 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 Stokes drift (mass transport) No mass transport Wave Closed orbit after one period Open orbit

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.

Frequency (waves per second) Period (& wavelength) and Wave Energy Seismic disruption Disturbing force landslides Gravity Wind Restoring force Surface tension Type of wave Tide Tsunami Seiche Wind wave Capillary wave (ripple) 24 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 Period (time, in seconds for two successive wave crests to pass a fixed point) 1 10 100 Frequency (waves per second) 12 hr.

Deep- to Shallow-Water Waves Progressive Waves

Wave Speed is C - Group Speed is V 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 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

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 5 4 3 2 1 7 6 8

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)

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

Constructive interference (addition) 1 2 a b Constructive interference (addition) Destructive interference (subtraction)

Deep-water waves change to shallow-water waves as they approach the shore and they break 1 2 4 5 3 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 part of wave in shallow water slows down depth contours crests 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 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.