## New Mathematical Formula Could Prevent Devastation from Tsunamis

01 November 2008 - The memories of the violent tsunami that ravaged the coastal areas of Indonesia, India, Sri Lanka, Thailand, and Malaysia in 2004 are still very vivid, with the victims still in the process of rebuilding their communities. There is, however, hope of minimizing casualties if such a disaster were to happen again, in the unlikely form of a mathematical formula. Scientists from Newcastle University, led by Professor Robin Johnson, have published their research in the academic journal Science Direct: Fluid Dynamics Research, suggesting a formula that could result in advanced warnings of where a tsunami will probably hit and the extent of destruction it may cause.

The 2004 Boxing Day tsunami disaster is said to have been caused by a deep-ocean earthquake that gave way to a long surface wave, which subsequently resulted in six colossal consecutive wave fronts. The third wave front hit the coastline with a terrifying height of 20 meters. Professor Johnson and his colleague Professor Adrian Constantin of the University of Vienna, Austria, explain that if we can learn more about the behavior of these long water waves, we might be able to obtain essential information to avoid disasters.

"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. "

The mathematical formula put forth by Johnson and his colleagues in their paper that won the Best Paper of the Year' in the journal is an alternative theory to the current Solitan' theory explaining long wave behavior. The soliton is a self-reinforcing, solitary wave which retains its shape while traveling at a steady speed. Johnson believes this Solitan theory is inaccurate. According to Johnson, it may be possible to model the behavior of a tsunami wave when it first starts deep in the ocean by monitoring seismic activity using sensors that have been placed in the Pacific and Indian Ocean. The number of troughs and peaks indicated by the measured seismic activity will reliably predict the number of wave fronts that will ultimately produce tsunami waves.

"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."

Written By: Karuna Meda

Edited by: News and Features Editor Yangguang Ou and Senior News and Features Editor Falishia Sloan