A team of mathematicians at the University of California, Santa Barbara, has published a paper that may help to shed some light on the mystery of why tsunamis can be so destructive. The researchers developed a mathematical model that shows how the shallow water near a coastline can amplify the energy carried by a tsunami, leading to higher waves and greater destruction.

The researchers used a mathematical technique called "wave action conservation" to derive a non-linear equation that accurately describes the evolution of a tsunami wave in shallow water. The equation shows how the wave height increases as the water depth decreases, due to the conservation of energy carried by the wave.

To validate their model, the researchers compared the results of the non-linear equation to data from a laboratory experiment. The experiment involved generating a tsunami wave in a long tank, with a variable water depth. The results of the comparison showed that the model agreed well with the experimental data, with a relative error of only about 10%.

The research team also compared their model to a linear model, which is commonly used to describe tsunamis in deep water. The researchers found that the linear model does not accurately predict the wave height in shallow water, and that the non-linear model provides a much more accurate description.

The researchers believe that their model can provide insights into the physics of tsunamis and help to better understand and predict the potential risks and damage caused by tsunamis. This could lead to improved early warning systems and mitigation strategies, helping to reduce the impact of future tsunami events.