# Mathematicians provide new insight into tsunamis

##### Apr 01, 2009

A new mathematical formula that could be used to give advance warning of where a tsunami is likely to hit and how destructive it will be has been worked out by scientists at Newcastle University.

The research, led by Newcastle University's Professor Robin Johnson, was prompted by the 2004 Boxing Day disaster which devastated coastal communities in Indonesia, Sri Lanka, India and Thailand.

In this instance, an earthquake in the depths of the ocean triggered a long surface wave which resulted in six massive wave fronts, one after the other.

Of these it was the third and largest one that caused the most devastation, hitting the beaches with terrifying speed. Reaching a height of 20m, it is this wave that lifted a train from its tracks as it travelled along the Sri Lankan coastline, killing almost 1,000 people.

Professor Johnson and his colleague Professor Adrian Constantin, based at the University of Vienna, Austria, felt that if we could understand more about how these long water waves behave we could predict where they might hit and how devastating they might be.

Their research is published in the academic journal Science Direct: Research, and this paper has just been named the Journal's best paper of the year.

"What we found was that the number and height of the tsunami waves hitting the shoreline depends critically on the shape of the initial surface wave in deep water," explained Professor Johnson, Professor of Applied Mathematics at Newcastle University.

"From this it is possible to work out whether a 'trough' or a 'peak' is the leading wave. In the case of a trough then the familiar sight of the tide suddenly going out is the precursor to an approaching tsunami.

"If a peak is the leading wave, there is no warning except a fast-approaching wall of water.

"Potentially this could provide vital information for areas facing an impending disaster."

The maths

The primary aim of the work was to present a new theory for very long waves over variable depths, in particular tsunamis.

Until now the behaviour of this type of wave has been explained using 'Soliton theory' but Professor Johnson says he had doubted for many years this could accurately calculate the behaviour of such a large wave.

"The difficulty is that to understand in detail how a tsunami wave moves and behaves you need to know how it started in the deep ocean and we can never know that in any particular case," he said.

"However, it is possible to monitor seismic activity and then to give sufficient warning to vulnerable coastal regions that a tsunami is on its way. Automatic sensors have been in the Pacific Ocean for a number of years and sensors have now been placed in the Indian Ocean."

The research shows that the number of peaks and troughs in the initial disturbance out at sea will dictate the number of wave fronts that will steepen and eventually produce tsunami waves.

Professor Johnson said that by calculating the number of waves that will coalesce or 'join together' as the faster ones catch up the slower ones, it is possible to predict how many and how big and fast the final waves hitting the shoreline will be.

"We have shown that it is possible to use the initial wave pattern to work out how the wave will evolve and, importantly, how it might interact with the complicated motions close inshore to produce the tsunamis that we experience," he explains.

"With a time delay of maybe two or three hours between the initial wave trigger and the tsunami hitting the shore, this could prove vital."

Source: Newcastle University

Explore further: Researchers help Boston Marathon organizers plan for 2014 race

## Related Stories

#### The Math Of Deadly Waves

Feb 28, 2006

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.

#### UQ plans for the next big wave – tsunami defence

Dec 19, 2005

A new tsunami impact model developed by The University of Queensland will help emergency response teams plan what to do if the next big wave hits.

#### Cause of tsunami wave heights is studied

Aug 20, 2007

Irish-led scientists have found tsunami wave height is independent of earthquake magnitude and is instead linked to a rupture's vertical displacement.

#### Making waves: New research could minimize the impact of future tsunami

Jul 02, 2007

For the first time, a team of experts is preparing to create tsunami in a controlled environment in order to study their effects on buildings and coastlines - ultimately paving the way for the design of new ...

#### Post-tsunami Thailand yields lessons for coastal construction

Feb 25, 2005

Engineering experts see how buildings and materials fared against walls of water An inspection of Thai villages and ports struck by tsunami waves has uncovered some engineering lessons that might reduce casualties and destru ...

#### Scientists study 'stealth' tsunami that killed 600 in Java last summer

Jun 18, 2007

Though categorized as magnitude 7.8, the earthquake could scarcely be felt by beachgoers that afternoon. A low tide and wind-driven waves disguised the signs of receding water, so when the tsunami struck, ...

## Recommended for you

#### Changing dinosaur tracks spurs novel approach

6 hours ago

Paleontologists are using a range of old and new techniques to map the Broome Sandstone dinosaur trackways.

#### Newlyweds, be careful what you wish for

8 hours ago

A statistical analysis of the gift "fulfillments" at several hundred online wedding gift registries suggests that wedding guests are caught between a rock and a hard place when it comes to buying an appropriate gift for the ...

#### Can new understanding avert tragedy?

11 hours ago

As a boy growing up in Syracuse, NY, Sol Hsiang ran an experiment for a school project testing whether plants grow better sprinkled with water vs orange juice. Today, 20 years later, he applies complex statistical ...

#### Crowd-sourcing Britain's Bronze Age

11 hours ago

A new joint project by the British Museum and the UCL Institute of Archaeology is seeking online contributions from members of the public to enhance a major British Bronze Age archive and artefact collection.

#### Roman dig 'transforms understanding' of ancient port

11 hours ago

(Phys.org) —Researchers from the universities of Cambridge and Southampton have discovered a new section of the boundary wall of the ancient Roman port of Ostia, proving the city was much larger than previously ...

#### Study looks at stock market performance of polarizing brands

12 hours ago

Are you a big fan of Apple or Nike, or a hater of McDonald's? A new study from the W. P. Carey School of Business at Arizona State University shows love-it or hate-it brands probably won't perform exceptionally ...

## More news stories

#### Changing dinosaur tracks spurs novel approach

Paleontologists are using a range of old and new techniques to map the Broome Sandstone dinosaur trackways.

#### Newlyweds, be careful what you wish for

A statistical analysis of the gift "fulfillments" at several hundred online wedding gift registries suggests that wedding guests are caught between a rock and a hard place when it comes to buying an appropriate gift for the ...

#### Can new understanding avert tragedy?

As a boy growing up in Syracuse, NY, Sol Hsiang ran an experiment for a school project testing whether plants grow better sprinkled with water vs orange juice. Today, 20 years later, he applies complex statistical ...

#### Roman dig 'transforms understanding' of ancient port

(Phys.org) —Researchers from the universities of Cambridge and Southampton have discovered a new section of the boundary wall of the ancient Roman port of Ostia, proving the city was much larger than previously ...

#### Crowd-sourcing Britain's Bronze Age

A new joint project by the British Museum and the UCL Institute of Archaeology is seeking online contributions from members of the public to enhance a major British Bronze Age archive and artefact collection.

#### Hackathon team's GoogolPlex gives Siri extra powers

(Phys.org) —Four freshmen at the University of Pennsylvania have taken Apple's personal assistant Siri to behave as a graduate-level executive assistant which, when asked, is capable of adjusting the temperature ...

#### Better thermal-imaging lens from waste sulfur

Sulfur left over from refining fossil fuels can be transformed into cheap, lightweight, plastic lenses for infrared devices, including night-vision goggles, a University of Arizona-led international team ...

#### Is UK shale gas extraction posing a risk to public health?

More needs to be done to investigate the risks to human health that extracting shale gas poses, suggests a personal view published in BMJ today.

#### Experts call for higher exam pass marks to close performance gap between international and UK medical graduates

The pass mark for a two-part test that international medical graduates must pass to work as a doctor in the UK should be raised to reduce differences in performance between international and UK medical graduates, suggest ...

#### Vitamin B3 might have been made in space, delivered to Earth by meteorites

Ancient Earth might have had an extraterrestrial supply of vitamin B3 delivered by carbon-rich meteorites, according to a new analysis by NASA-funded researchers. The result supports a theory that the origin ...