New shallow water wave patterns observed

Many people are still haunted by images of the devastating earthquake and tsunami which occurred just over a year ago in Tohoku, Japan.

The 20-foot high tsunami hit the Pacific coastline of Japan, destroying many lives and much property. A recent study by Mark Ablowitz and Douglas Baldwin, mathematicians at the University of Colorado at Boulder, offers new insight into the causes of tsunamis based on satellite images taken during the calamity.

Tsunamis are series of water waves that displace large volumes of water and often reach extraordinary heights, endangering coastal structures and people. Large disturbances, such as explosions, volcanoes, and earthquakes, are typically the causes of a tsunami.

Underwater earthquakes, for instance, are a common tsunami trigger – including the Tohoku incident. The lithosphere of the earth is broken into many tectonic plates, which constantly move in various directions relative to each other. However, once two plates “lock” in place due to frictional resistance, continued attempted movement between the two plates will lead to a gradual build up of tension.

This tension stores more potential energy. Eventually, the amount of energy will be so great that the two plates will suddenly break free of each other, causing an earthquake.

The release of all that built up energy displaces the water above, generating the start of a tsunami. It is often difficult to recognize a tsunami as it travels through deep waters of the ocean because of its small amplitude and long wavelength.

However, as the waves enter shallow waters, they become compressed, increasing the amplitude and shortening the wavelength. This eventually results in the characteristic tall waves known to bring tragedy to coastal cities.

In addition to these well-known qualities of tsunami waves, Ablowitz and Baldwin found straight waves in shallow waters that interact to form X and Y shapes and other more complex wave forms.

Normally when two waves collide, the resulting amplitude is the sum of the heights of the two incoming waves. However, these interactions led to waves with heights much taller than predicted, suggesting what mathematicians called nonlinear collisions.

Satellite images of the 2011 tsunami in Japan revealed X-shaped wave patterns similar to the ones Ablowitz and Baldwin observed, and they suggest that this nonlinear interaction significantly added to the tsunami’s destructive power.

According to the mathematicians, these interesting wave interactions are relatively easy to identify with just the naked eye and a few hours on a low-tide beach.

Hopefully, this finding will add to the ways in which scientists can predict tsunamis, potentially reducing casualties in the future.