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(Math) Waves: The Math Of Deadly Waves

 
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adedios
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PostPosted: Tue Feb 21, 2006 8:04 am    Post subject: (Math) Waves: The Math Of Deadly Waves Reply with quote






Source: Natural Sciences and Engineering Research Council

Posted: February 20, 2006

The Math Of Deadly Waves

When Walter Craig saw the images of the devastating 2004 Boxing Day Indian Ocean tsunami he felt compelled to act. So he grabbed a pencil and envelope and started calculating.

A little more than a year later, the mathematical analyst says that mathematics has a role to play in washing away misconceptions and myths about these deadly waves -- and potentially saving lives.

"Predicting earthquakes is a grand challenge problem that's presently beyond us. But predicting a tsunami's potential based on these earthquakes is a doable problem and I think mathematicians can play an important role in this," says Dr. Craig, the Canada Research Chair for Mathematical Analysis and its Applications, at McMaster University in Hamilton, Canada.

"Mathematics is particularly well suited to defining the possibilities and limitations for a tsunami early warning system," says Dr. Craig. It's a conviction that's prompted him to co-organize the symposium on Tsunamis: Their Hydrodynamics and Impact on People at the annual meeting of the American Association for the Advancement of Science (AAAS) in St. Louis, on Sunday, February, 19.

Dr. Craig studies the mathematical theory of wave equations that are derived from physics. In collaboration with colleagues he has applied these theories to scientific problems large and small, from the quantum mechanical oscillations of electrons to the cosmic waves that rippled through the newborn universe. But rarely, he says, does the mathematics of wave propagation meet a subject so full of immediate human importance as with understanding rogue waves.

Mathematics, he says, has a key role to play in dispelling mistaken assumptions about these waves. One such popular belief is that a tsunami's first wave surge is always the biggest.

"It's not necessarily the biggest crest in front," he cautions. "For example, in Sri Lanka the biggest crest was the third or fourth." In one case, he says, a vacationing British geologist at one Sri Lankan resort noted the initial modest, non-destructive surge and warned staff and tourists to clear the beach before the arrival of the larger, deadly surges.

Dr. Craig says that mathematical modelling of the Indian Ocean tsunami showed it to be close to what he calls a "classical wave packet" -- the wave behaved in a manner very close to that predicted by mathematical theory. It followed the pattern of a group of waves travelling together as well as evolving in form as they crossed the ocean basin.

Because of differences in depth, the evolution of a tsunami is different in different ocean basins. For example, the Boxing Day tsunami travelled twice as fast in the deeper Indian Ocean than in the Andaman Basin. Tsunami waves are distinguished from ordinary wind-generated ocean waves by their great length between peaks, often exceeding 200 kilometres in the deep ocean, and by the long amount of time between these peaks, ranging from 15 minutes to an hour.

It's the length and width of tsunamis, rather than their at-sea height that reveals their massive power. The Indian Ocean tsunami had a crest length of about 1,200 kilometres. The surges that inundated the Sri Lankan coast were parts of waves that were a stunning 100 kilometres from crest to trough, but in mid-ocean were less than one metre in amplitude.

"It's amazing to think about this. Even if the wave is only a metre high at mid-sea, this is a huge amount of water and it gives a sense of how much energy it's carrying," says Dr. Craig.

Another widely held belief about tsunamis that gets washed away with mathematical modelling is that the surge is always preceded by the tide going abnormally far out.

"This only happens about half the time," explains Dr. Craig. "It depends on the wavelength and whether it's the trough or crest of the wave that reaches shore first. In half the cases it's the surge that arrives first."

Dr. Craig acknowledges that for the most part geologists and tsunami experts have a strong practical understanding of how these giant waves behave. But, he says, given the paucity of real-world data on tsunamis, there are still many outstanding questions.

"To a first order of approximation the current modelling of a tsunami's evolution in mid ocean is very good," says Dr. Craig. "Nonetheless, there is much less known about the generation of tsunami waves, and about the amplification effects as they impact on coastal areas. These are not easy mathematical problems. Experimentally they're not seen very often, so it's still a question as to whether we're using the right equations to study them."

He's presently begun work with McMaster University mathematics colleagues Drs. Bartosz Protas and Nicholas Kevlahan to apply mathematical tools from meteorological forecasting to understand the generation of large tsunamis from major earthquakes. For example, some earthquakes generate large waves, while others of the same magnitude produce little or no wave response. Their approach will use hindcasting techniques -- looking back over previous patterns to understand how we arrived at present conditions -- to develop predictive computational models for tsunami sources.

While better advanced warning systems can help in many cases, Dr. Craig says his immersion in tsunami science has shown him that a tsunami's speed and power sometimes can defy an early warning system. With a wave traveling at 700 kilometres an hour, his advice is, "If you feel an earthquake, go to higher ground."

*************************************************************

Questions to explore further this topic:

What are waves?

http://www.physicsclassroom.co.....10L1a.html
http://www.physicsclassroom.co.....10L1b.html
http://id.mind.net/~zona/mstm/.....Waves.html
http://www.kettering.edu/~drus.....intro.html
http://library.thinkquest.org/10796/ch8/ch8.htm

What are the parts of a wave?

http://id.mind.net/~zona/mstm/.....eParts.htm
http://www.physicsclassroom.co.....10L2a.html
http://www.physicsclassroom.co.....10L4c.html

What are the different types of waves?

http://www.kettering.edu/~drus.....otion.html
http://www.physicsclassroom.co.....10L1c.html
http://www.physicsclassroom.co.....10L4a.html

Animations of waves

http://www.falstad.com/mathphysics.html

What properties do waves have?

http://www.physicsclassroom.co.....10L2b.html
http://www.physicsclassroom.co.....10L2c.html
http://www.physicsclassroom.co.....10L2d.html
http://www.physicsclassroom.co.....10L2e.html

Waves: A 10-day Lesson Plan

http://edweb.sdsu.edu/courses/.....eUnit.html

What are examples of waves in nature?

Light: An electromagnetic wave
http://www.colorado.edu/physic.....index.html
http://imagers.gsfc.nasa.gov/ems/radio.html
http://imagers.gsfc.nasa.gov/ems/micro.html
http://imagers.gsfc.nasa.gov/ems/infrared.html
http://imagers.gsfc.nasa.gov/ems/visible.html
http://imagers.gsfc.nasa.gov/ems/uv.html
http://imagers.gsfc.nasa.gov/ems/xrays.html
http://imagers.gsfc.nasa.gov/ems/gamma.html

Water waves
http://www.colorado.edu/physic.....waves.html
http://www.pbs.org/wnet/savageearth/tsunami/

Seismic waves
http://www.thetech.org/exhibit.....waves.html
http://www.seismo.unr.edu/ftp/.....waves.html
http://www.geo.mtu.edu/UPSeis/waves.html

The wave nature of matter
http://www.colorado.edu/physic.....oglie.html

Sound waves
http://www.glenbrook.k12.il.us.....ndtoc.html
http://www.kettering.edu/~drus.....2/mdq.html
http://www.kettering.edu/~drus.....ation.html
http://www.kettering.edu/~drussell/forkanim.html
http://www.kettering.edu/~drus.....iston.html
http://www.kettering.edu/~drus...../RT60.html

Swinging motion
http://www.kettering.edu/~drus.....Chain.html

Strings
http://www.kettering.edu/~drus.....Fixed.html

Membranes
http://www.kettering.edu/~drus.....quare.html

Drums
http://www.kettering.edu/~drus.....ircle.html

Acoustic guitar
http://www.kettering.edu/~drus.....gbird.html

The Mathematics of Waves

http://www.math.ubc.ca/~cass/c.....ves1d.html
http://www.visionlearning.com/.....l=&c3=
http://fas.rutgers.edu/home/be.....vesL1.html
http://fas.rutgers.edu/home/be.....vesL2.html
http://fas.rutgers.edu/home/be.....vesL3.html
http://fas.rutgers.edu/home/be.....vesL4.html
http://fas.rutgers.edu/home/be.....vesL5.html

Trigonometric Functions

http://people.hofstra.edu/facu.....intro.html
http://www.ies.co.jp/math/products/trig/menu.html
http://aleph0.clarku.edu/~djoyce/java/trig/
http://people.hofstra.edu/facu.....trig2.html

What are the mathematical properties of waves?

Superposition
http://www.physicsclassroom.co.....10L3c.html
http://www.kettering.edu/~drus.....ition.html

Doppler
http://www.physicsclassroom.co.....10L3d.html
http://www.kettering.edu/~drus.....ppler.html

Fourier
http://www.kettering.edu/~drus.....urier.html

Reflection
http://www.physicsclassroom.co.....10L3a.html
http://www.physicsclassroom.co.....10L3b.html
http://www.kettering.edu/~drus.....flect.html

Refraction
http://www.kettering.edu/~drus.....fract.html

What is the wave equation?

http://mathworld.wolfram.com/WaveEquation.html

The Mathematics of Tsunamis

http://mathworld.wolfram.com/n...../tsunamis/
http://plus.maths.org/issue34/.....-gifd.html

GAMES

http://faculty.washington.edu/.....aring.html
http://www.cbc.ca/kids/games/tallships/
http://www.classicsforkids.com/games/index.asp
http://library.thinkquest.org/.....index.html
http://pbskids.org/arthur/games/index.html


Last edited by adedios on Sat Jan 27, 2007 3:13 pm; edited 1 time in total
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adedios
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Joined: 06 Jul 2005
Posts: 5060
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PostPosted: Wed Jul 19, 2006 5:55 pm    Post subject: Surf Watch Reply with quote

Surf Watch
26 July 2006
Emily Sohn

I usually hate getting up early. But during a recent surfing trip to Mexico, I was up with the sun. I couldn't wait to get to the beach.
Even so, I didn't plunge into the water right away. I watched the waves and studied surfers in action. I tried to figure out how big the swells were, which way the wind was blowing, and where the waves were breaking.

For the full article, links and illustrations:

http://www.sciencenewsforkids......ature1.asp
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adedios
SuperPoster


Joined: 06 Jul 2005
Posts: 5060
Location: Angel C. de Dios

PostPosted: Thu Oct 05, 2006 8:28 pm    Post subject: Waves from Top of the World Destroy Huge Iceberg at Bottom Reply with quote

Waves from Top of the World Destroy Huge Iceberg at Bottom

By Robert Roy Britt
LiveScience Managing Editor
posted: 02 October 2006
05:06 pm ET

On a calm, clear day in October 2005, a huge Antarctic iceberg broke into half a dozen pieces. Today, scientists said the event was triggered by ocean swells kicked up during an Alaskan storm—half a world away.

At 60 miles long and 18.5 miles wide, the iceberg called B15A was half of a larger iceberg called B15, which was for a time the world's largest iceberg after breaking away from the Antarctic's in Ross Ice Shelf in 2000. Over the years, scientists put seismic monitors on B15A to better understand strange sounds called "iceberg songs."

For the full article:

http://www.livescience.com/for....._wave.html
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adedios
SuperPoster


Joined: 06 Jul 2005
Posts: 5060
Location: Angel C. de Dios

PostPosted: Fri Jul 13, 2007 12:22 pm    Post subject: On a Wire or in a Fiber, a Wave is a Wave Reply with quote

Plasmonics


On a Wire or in a Fiber, a Wave is a Wave
Brown University
13 July 2007

Around the world, students learn about the wave nature of light through the interference patterns of “Young’s double-slit experiment,” first performed more than 200 years ago and still considered among the most beautiful physics experiments. Using an analogous experiment, researchers at Brown and Stanford have shown that a simple analytical model can describe the wave nature of surface plasmon polaritons. Their work suggests that plasmonic devices cannot easily circumvent the limitations of electromagnetic waves.

For the full article:

http://www.brown.edu/Administr.....7-005.html
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