Scientists Shed New Light on Mysteriously Large Rogue Waves That Can Threaten Large Ships

Extreme Nonlinear Wave Group Dynamics in Directional Wave States

Understanding the unexpected nature of ocean waves can be a matter of survival for seafarers. Deep-water wave groups have been known to be unstable and become rogue. These rogue waves are abnormally large, unpredictable, and suddenly appearing surface waves that can be incredibly dangerous to even large ships. 

This rogue wave behavior is caused by modulation instability, which happens only in unidirectional waves. When interacting with other wave systems, wave focusing (wave amplification) is also expected to weaken.

Independent Propagation of Unstable Wave Groups

A team led by Kyoto University has now shown that such unstable wave groups propagate independently of interference. Their findings were recently published in the journal Physical Review Letters. 

Demonstration of an unperturbed nonlinear water wave group focusing in the presence of counter-propagating waves, implying directional wave states. Credit: KyotoU / Amin Chabchoub

“Our results seem to support the concept of an unperturbed nonlinear water wave group focusing in the presence of counter-propagating waves, implying that the wave states are directional,” says lead author Amin Chabchoub.

Using a water wave tank, the team performed experiments validating results from computer simulations based on the coupled nonlinear Schrödinger equation. This nonlinear wave equation model accounts for complex interactions of waves propagating from two different directions.

The team’s findings demonstrate that the model agrees well with the experiments, including rogue and counter-propagating wave dynamics.

Broader Applications of Nonlinear Wave Research

Fields such as offshore engineering, nonlinear optics, electrical engineering, and plasma physics, as well as the study of extreme ocean waves, stand to benefit from a better understanding of the role of nonlinearity.

“Our study may further motivate theoretical and experimental studies to improve our understanding of such dynamics in the cacophony of different wave systems,” Chabchoub concludes.

Reference: “Experimental Evidence of Nonlinear Focusing in Standing Water Waves” by Yuchen He, Alexey Slunyaev, Nobuhito Mori and Amin Chabchoub, 28 September 2022, Physical Review Letters.
DOI: 10.1103/PhysRevLett.129.144502

The study was funded by the RFBR and the Laboratory of Dynamical Systems and Applications NRU HSE. 

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