The Hidden Math of Ocean Waves Crashes Into View | Quanta Magazine
Key Takeaways
- Water wave dynamics, described by Euler's equations, are mathematically complex due to their free, unrestricted surfaces.
- Stokes conjectured the existence of persistent, evenly spaced waves, which were later proven to exist and persist forever if undisturbed.
- Experiments by Benjamin and Feir in 1967 surprisingly demonstrated that Stokes waves are unstable to small perturbations.
- The instability of Stokes waves, known as 'Benjamin-Feir instabilities,' was mathematically proven in 1995.
- Current research aims to characterize the nature and extent of these instabilities to predict when and how wave patterns will be disrupted.
The mathematics governing water waves, especially those described by Euler's equations, are notoriously complex due to their free surfaces, leading to unpredictable outcomes like rogue waves from minor initial changes. Stokes sought to describe evenly spaced, unidirectional waves, a conjecture proven possible, resulting in so-called Stokes waves that should theoretically persist indefinitely without external disturbances. However, the stability of these waves against real-world complications like crossing wakes was long assumed but challenged in 1967 by Benjamin and Feir's experimental observation that Stokes waves were unstable. This instability was mathematically confirmed in 1995, leading researchers to investigate which specific disturbances cause these waves to break down and how rapidly this occurs. Current research, involving mathematicians like Deconinck and Oliveras, focuses on mapping these various instabilities that can destroy Stokes waves.
