Ocean waves and the maths behind them

For Quanta Magazine, Joseph Howlett dived into the fluid dynamics and hidden mathematics of ocean waves through the work of Italian mathematicians:

One strange phenomenon that has perplexed mathematicians for decades is that, even when friction is minimal, that steady train of gently rolling waves still eventually falls apart and becomes irregular. Mathematicians hadn’t expected to see such unstable behavior emerge from such a simple starting point. They wanted to prove it — to show that instabilities arise naturally from the Euler equations. But they couldn’t figure out how to do it.

Now Maspero and Ventura, along with their Trieste colleague Massimiliano Berti and Livia Corsi of Roma Tre University, have finally presented such a proof, showing exactly when these instabilities occur and when they don’t. The result is just the latest in a renaissance that’s starting to transform our mathematical understanding of Earth’s waves. Mathematicians have been using new computational tools to formulate conjectures about how waves behave. And they’re now developing sophisticated pen-and-paper techniques to prove those conjectures.

You can read the paper they wrote called “Infinitely many isolas of modulational instability for Stokes waves” on Arxiv.