Waves

Wave speed

The speed the disturbance, and wave crests, travel at.

Wavelength [m] Wave speed = [s] [m/s] Period

Wave speed: Deep water wave ✤ When ocean depth is greater than half the wavelength. Direction of wave

Gravity waves Restoring: Surface Wind Long period tension waves waves Tides Tsunami

Disturbance: Seiche and storm surge Wind Sun and moon Energy

10 1 10-1 10-2 10-3 10-4 10-5 Wave frequency (s-1) 0.1s 1s 10s 30s 5min 12h 24h Period 0.017m 1m 10m 1000m Wavelength Wave speed The speed the wave crests travel at. Deep water wave ✤ Speed dependent on wavelength (or period). gravity ✤ Speed (m/s) = P eriod (seconds). 2⇡ ✤ Speed (m/s) = 1.56 * wave period (seconds). ✤ Longer waves travel faster.

Wave speed: Deep water wave The speed the disturbance, and wave crests, travel at. ✤ Speed = 1.56 * wave period ✤ Longer waves travel faster Brooks/Cole

Storms produce waves of many different periods and heights. Wind wave periods can be up to 30 seconds. Wind wave dispersion

Wavelength increases as period increases.

Longest waves travel fastest away from storm.

Swell Longer waves travel faster (C=1.56*Period). They also decay slower.

Brooks/Cole

Wave speed: Shallow water wave ✤ When ocean depth is shallow compared to wavelength (less than 1/20th of wavelength)

Direction of wave Wave speed: Shallow water wave

✤ When ocean depth is shallow compared to wavelength (less than 1/20th of wavelength) ✤ Speed dependent on ocean depth. ✤ gravity Water depth Speed (m/s) = ⇥ ✤ Speed (m/s) = p3.1 * square root(depth in meters) ✤ Waves travel faster in deeper water.

Wave refraction results in waves being more parallel to shore.

Wave refraction Wave refraction A shallow water wave’s speed is dependent on ocean depth.

Wave refraction A shallow water wave’s speed is dependent on ocean depth.

If part of a wave is in shallower water then it will travel slower.

Wave refraction A shallow water wave’s speed is dependent on ocean depth.

If part of a wave is in shallower water then it will travel slower. Wave reflection

Wave reflection

38cd_wavemotion.swf

Wave diffraction When waves pass through a small gap, they reform and radiate outwards. Wave groups

Deep water wave groups travel at half the speed of individual waves.

New waves appear to form behind the wave group.

Wave groups

matlab movie

Wind waves approaching shore

Waves ‘touch’ the bottom. Wave period remains constant, wavelength decreases. Wavelength Wave speed = Period (Wavelength = Wave speed * Period) and eventually become Shallow water waves, so Speed (m/s) = 3.1 * square root(depth in meters) Wind waves approaching shore

Waves ‘touch’ the bottom. Wave period remains constant, wavelength decreases.

Friction slows the bottom of the wave.

Waves approaching shore ✤ Bottom of wave slows even more as the depth shallows, wave crest moves ahead of the base of the wave. ✤ Wave breaks when the ratio of wave height to water depth is ~3:4. ✤ How waves break depends on the beach slope.

Surf prediction

North shore swells come from Northern Hemisphere winter storms.

South shore swells often come from Southern Ocean storms. Surf prediction

Network of ocean buoys measure wave height, period, and direction.

Then account for height attenuation and local shoaling effects.

hawaiibeachsafety.org

Tsunamis

Hilo, April 1946 after Alaskan earthquake (NOAA) Tsunamis ✤Tsunamis can be caused by Earthquakes, Landslide, volcanoes, and asteroid impacts. All of these suddenly displace a large amount of water.

✤Have periods of about 20 minutes, and wavelengths of about 200 km.

✤Average ocean depth is 4 km, so always a shallow water water (depth < wavelength/20).

Earthquake generation

The March 11 2011 earthquake had a displacement of about 20m over an area ~500 km by ~200 km.

Open ocean detection In the deep ocean Tsunami waves have small amplitudes, 10 to 50 cm.

Combined with their long wavelength, they are hard to detect, enter DART. Why are they dangerous? Because of their long wavelength, the volume of the displacement associated with a tsunami wave is huge.

When it shoals that volume piles up.

japan.mov

How to escape? ✤ Get to higher ground. ✤ Or go above the 3rd floor in a concrete building. ✤ If possible don’t get into your car, traffic jams are inevitable. ✤ If the water recedes, don’t follow it. Run the other way. ✤ Know the evacuation zones are your home and work.

Waikiki Evacuation map

T 8 Y AM ST A T S K 1 FW INGH R S G UILE T H B A N I S 7 E E I T MOKIHA H T N K N NA ST L Y S Kaimuki High T O L E E H A Legend C X S V P A I A A A E 1 O N V N H 1 N H U E D A PALIU T A LI ST S H 1 H E U K Tsunami Evacuation Line 0 T A L A R S A T Kapiolani Medical Center N K C T P H V Central Union PrescS hool and Kindergarden A 9 O E E T T I A A P S N V O H E K W V U I INAM AVE Tsunami Evacuation Zone L L S N E A E N I L D T A T B V A S A K E A E A E G L A T T E I H E

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Notes: Map 1: Waikiki Remain at least 100 feet away from inland waterways and marinas connected to the ocean due to wave surges and possible flooding. K ALAK Ala Moana State Rec Area AUA AVE If possible, remove or deploy vessels to deep water (at least 200

fathoms). 0 200 400 800 Structural steel or reinforced concrete buildings of six or more Scale in Feet stories provide increased protection on or above the third floor. Prepared by: DPP (HOLIS) The evacuation zone is a guideline and should be considered the minimum safe evacuation distance. Data Source: City and County of Honolulu GIS

These maps do not consider the destructive effects of a locally Note: Data represented on this map is not generated tsunami. If you feel shaking, move inland immediately, intended to replace site survey. Copyright City & County of Honolulu well away from the evacuation zone. Date Prepared: Aug. 25, 2010 All Rights Reserved 2010

Some key ideas ✤ Deep water wave, D > L/2, speed: c=1.56*T; Longer waves travel faster than shorter waves; Wave groups travel at half the speed of individual waves.

✤ Shallow water wave, D < L/20, speed: c=3.1*sqrt(H); They feel the bottom; They refract.

✤ Period remains constant when wave approach the shore.

✤ Swim across shore to get out of a rip current.

✤ Tsunamis are shallow water waves. They have periods of around 20 minutes. Get out of their path!