Extreme events in a random set of nonlinear elastic bending waves

Summary

Researchers studied extreme events in nonlinear elastic bending waves, similar to rogue waves on the ocean surface. They used an experimental setup with a thin stainless steel plate and an electromagnetic shaker to generate bending waves. The study aimed to investigate the statistics of extreme events and their correlations with wave characteristics.

Highlights

• Extreme events in bending waves were found to occur more frequently than rogue waves in ocean waves.
• The researchers used a new criterion to define extreme events, as the traditional definition was insufficient.
• The study found that extreme events in bending waves are correlated with the fundamental modes of the plate.
• The steepness of rare events was found to be slightly higher than that of other waves.
• The kinetic energy per unit mass during rare events was similar to the time-averaged value.
• The local periods of extreme events were concentrated around the highest periods.
• The study raises questions about the mechanisms behind rogue wave formation and the role of inverse cascade.

Key Insights

• The study highlights the differences between extreme events in bending waves and rogue waves in ocean waves, suggesting that the mechanisms behind their formation may be distinct.
• The correlation between extreme events and the fundamental modes of the plate suggests that the plate's geometry plays a crucial role in the formation of these events.
• The finding that the steepness of rare events is only slightly higher than that of other waves challenges the common perception of rogue waves as "walls of water."
• The study's results imply that the traditional definition of rogue waves may not be applicable to bending waves, and a new criterion is needed to capture the unique characteristics of these events.
• The similarity between the kinetic energy per unit mass during rare events and the time-averaged value suggests that these events may not be as energetic as previously thought.
• The concentration of local periods around the highest periods suggests that the plate's resonant frequencies play a key role in the formation of extreme events.
• The study's findings raise questions about the role of inverse cascade in the formation of rogue waves and whether it is a necessary condition for their occurrence.

Mindmap

Citation

Muralidhar, M., Naert, A., & Aumaître, S. (2024). Extreme events in a random set of nonlinear elastic bending waves (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.15786