Studying wave propagation to predict tsunamis

By studying wave propagation and the creation of vortices in shallow water, scientists can predict tsunamis. Inspired by a trip to Gengi Gorge in Japan, Thi Thai Le examined the effects of side walls on the Kelvin-Helmholtz instability in a shallow water flow.

Le mathematically studied a finite width body of water at the Kelvin-Helmholtz instability, where fluid regions move with different velocities at an interface. If the flow is unstable, the interface induces vorticity. In this case, the velocity difference is a result of wind moving over water.

Le found when a body of water has a narrow width and a large velocity difference, the flow of the free surface will be stable. If the width of the body of water is very large, the flow will always be unstable. Additionally, the presence of walls effects wave propagation and kinetic energy of the system, which can further alter the Kelvin-Helmholtz instability properties at the fluid interface.

“By finding the region of stable or unstable flow, our research plays a vital role in predicting wave propagation. We can easily predict the change of wave propagation based on the value of velocity difference between fluid regions,” said Le. “Large vortices may indicate an impending tsunami. Therefore, we can predict whether one will appear or not via predicting vortices from the stability properties of interface.”

The presented research is applicable to gas, oil and other fluid flows which are contained inside a boundary. The author is in the process of expanding her model to include the effects of friction from bottom and surface walls.

Source: “Kelvin - Helmholtz instability in a shallow-water flow with a finite width,” by Thi Thai Le, Journal of Mathematical Physics (2019). The article can be accessed at https://doi.org/10.1063/1.5126321 .