The Physics of Tsunamis

Wayne M. Lawton

Department of Mathematics

National University of Singapore

2 Science Drive 2

Singapore 117543

Email matwml@nus.edu.sgTel (65) 874-2749

Tsunamis in the Media

movie Impact – U.S. President claims tsunami speed = 2*sound

is his claim realor exaggerated ?

what about thistsunami photofrom Phuket ?

Hollywood Hypetsunami speedPhysical Facts:

Pacific Ocean: 1-7 kmhttp://www.es.flinders.edu.au/~mattom/regoc/text/8topo.html

Atlantic Ocean: 1-7 kmhttp://www.es.flinders.edu.au/~mattom/regoc/text/14topo.html

Indian Ocean: 1-7 kmhttp://www.es.flinders.edu.au/~mattom/regoc/text/11topo.html

dg 2ondmeters/sec 9.8 g depth ocean d

356 < speed (4 km) = 713km/hour < 943

speed of sound in air (0 C) = 1192 km / hour

ocean depth needs to be 7 km * 6.4 = 44.8 km

Internet AssertionBe sure and open the picture for a shock of your life to see what the tsunami looked like just before hitting Puket, Thailand.

This picture is not a fake. It appears to have been taken from a hi-rise building window in downtown Phuket Thailand.

The power of nature is hard to comprehend, especially the destructiveness of water.

We have all seen the pictures on TV but I don't think any of us really understand how big or how bad this wave was. This may be the most impressive picture I've seen. It gives me a better understanding of how 150,000 people perished in this disaster. If you look at this picture that was taken right before the wave hit, it will send a chill down your spine. Just look at the top of the wave compared to the top of the building it is about to hit.

Urban LegendsOrigins:   This is another photograph being circulated as a picture of the tsunami that struck Indian Ocean shorelines in Asia on 26 December 2004, this one purportedly taken from atop a high-rise building in Phuket, Thailand. This looks to be another case of any image depicting large waves being grabbed and passed around as a "real photograph" of the December 2004 tsunami. The image clearly doesn't fit its accompanying description because: It looks like something other than a photograph, such as a still frame from a movie or a composite image. The waves that struck the coast of Thailand after the December 2004 Indian Ocean earthquake were about 4 meters in height, but the ones pictured here look several stories tall. The skyline depicted doesn't appear resemble the city of Phuket. The traffic flow shown isn't right for Thailand, where motorists drive on the left-hand side of the road. As the operator of the World City Photo Archive helpfully informed us, this image is actually a manipulated depiction of the skyline of Antofagasta, Chile:

Scientific Approach to Tsunamiswhile lacking the entertainment appeal, provides understanding that has proven both necessary and useful for the prediction and control of natural events

Why are earthquakes the major source of tsunamis ?Why do many earthquakes not cause tsunamis ?What is the surface geometry of tsunamis ?What is the water movement in tsunamis ?How is energy transported in tsunamis ?How, after a powerful earthquake, can a tsunami bedetected and how can its propagation be predicted ?

Tsunamis

which of the following energy sources can physicallygenerate tsunamis ? sun heating, whales, impactsfrom extraterrestrial objects (meteorites, comets, asteroids), thermonuclear explosions, storms,landslides, earthquakes, tidal forces, evil spirits,volcanoes

are physically generated by events that result in the rapid and coherent (in the same direction) motion of a massive amount of sea water

Energy of an Earthquake

One Ton (2000 lbs) TNT = 4.148x10^9 J1 J (joule) = kg * meter^2 / second^2 = watt * second

http://www.seismo.unr.edu/ftp/pub/louie/class/100/magnitude.html

log E(joules) = 4.8 + 1.5*Richter-Scale-Magnitude

Richter TNT for Seismic Example Magnitude Energy Yield (approximate) -1.5 6 ounces Breaking a rock on a lab table 1.0 30 pounds Large Blast at a Construction Site 2.0 1 ton Large Quarry or Mine Blast 4.0 1,000 tons Small Nuclear Weapon 4.5 5,100 tons Average Tornado (total energy) 5.0 32,000 tons 6.0 1 million tons Double Spring Flat, NV Quake, 1994 7.0 32 million tons Hyogo-Ken Nanbu, Japan Quake, 1995; Largest Therm. Weapon 7.5 160 million tons Landers, CA Quake, 1992 8.0 1 billion tons San Francisco, CA Quake, 1906 8.5 5 billion tons Anchorage, AK Quake, 1964 (THIS IS 2 X 10^19 j)9.0 32 billion tons Chilean Quake, 1960 12.0 160 trillion tons (Fault Earth in half through center, OR Earth's daily solar energy)

Physical Properties of Water

Water is incompressible, viscous, massive

which of these properties explains the following ?

1. when the container is turned the water does not immediately turn with it, but eventually will start to turn as long as the container is turning

2. the water will fall when the bottom is not held

3. when the container is raised the water is raised raises the same distance

Energy Transmission

Earthquakes generate tsunamis when they cause large water displacements, this requires that theycause large movements of earth in direction normal(perpendicular) to the earth-ocean interface

which of the motions can generate tsunamis?

ocean ocean ocean

earth earth earth

earth

Slow Rising of Ocean FloorWe consider a large area of ocean floor that raises up

if it moves very slowly it transmits energy from theearthquake (seismic energy) into potential energy ofthe water, equivalent to lifting a certain volume of,water up to the sea level.

ocean

air

earth

the potential energy remains as potential energy

Fast Rising of Ocean Floor

if it moves fast it transmits more energy from theearthquake (seismic energy) into more potentialenergy of the water, equivalent to lifting a certainvolume of water up to a height above sea level

ocean

air

earth

why does the earth do more work when it rises fast ?

does the lifted water stay above the sea level ?

Falling of Lifted Water

As gravity works to restore equilibrium to theincompressible water the falling water lifts water n its sides and that water falls in a cascade

Real Picture

of course water near the edge is rounded, after severalfall-rise cycles the picture (from far right side looksmore like) at the bottom

direction of

propagation

wavelength

Surface Geometry

direction of propagation

x

y

wave height )( tvxH

graph of )(xHy

Wave Velocity

depends on both wavelength and water depth

)/2(tanh2

dg

v

deep water - surface (wind generated) waves

2/gvd shallow water - tsunami waves

dgvd

http://hyperphysics.phy-astr.gsu.edu/hbase/waves/watwav2.html

Surface Wave Parameters on the Deep Ocean

v/Period = time one cycle of wave to go by =

Amplitude = maximum H(x), y = 0 sea level

Wind Waves A = 10ft

Tsunamis A = 1.6ft

http://observe.arc.nasa.gov/nasa/exhibits/tsunami/tsun_physics.html

= 300 ft

= 316800 ft

v

v

= 10-20mph

= 450-650mph

what is ratio of periods of tsunamis to wind waves ?

why are tsunamis hard to detect ON the deep ocean ?

convert these parameter values into civilised units !

Water Movement in Tsunamis

Wind Waves: water particles move in near circles, whose diameters decrease rapidly with depth

Tsunamis: water particles move in elongated ellipseswhose lengths decrease linearly to zero at the bottom

http://electron4.phys.utk.edu/141/dec8/December%208.htm

http://mmu.jcu.edu.au/coastal/wavemaker.html

would tsunamis be easy to detect by scuba divers ?

http://www.coastal.udel.edu/faculty/rad/linearplot.html

Energy Transport in Tsunamis

is through kinetic energy of horizontal water motion

in deep ocean, and in contrast to wind waves

little viscosity loss since velocity changes slowly

no dispersion since v does not depend on wavelength

as wave approaches land amplitude increases toA > 100 ft, lambda = 5000-10000ft, v = 30-200mph

Tsunami Detection and Prediction

how can tsunamis be detected in deep oceans ?

once detected how can their future propagation be predicted rapidly to issue effective warnings ?

http://serc.carleton.edu/NAGTWorkshops/visualization/collections/tsunami.html

http://wcatwc.arh.noaa.gov/