The Math of Ocean Waves
14 days ago
- #Fluid Dynamics
- #Mathematics
- #Wave Theory
- Alberto Maspero enjoys a beautiful view of the Adriatic Sea from his office in Trieste, Italy.
- Trieste is known for its 'bora' wind, which can reverse the direction of waves in the bay.
- Euler's equations describe fluid flow but are notoriously difficult to solve, even for simple wave patterns.
- Mathematicians have long struggled to prove instabilities in wave patterns, known as Benjamin-Feir instabilities.
- Maspero, Ventura, Berti, and Corsi have provided a proof showing when these instabilities occur.
- Stokes waves, once thought stable, can be disrupted by certain disturbances, leading to instability.
- Deconinck and Oliveras discovered alternating intervals of stability and instability in wave patterns, called 'isole'.
- Maspero's team used computational and theoretical techniques to prove the existence of these instabilities.
- The findings open new avenues for understanding wave behavior and solving other problems in fluid dynamics.
- The research enhances the mathematical understanding of water waves, combining computational tools with pen-and-paper proofs.