Water waves can be a total chaotic mess on the inside while looking perfectly calm and smooth on top.
Mathematically, it was long thought that waves needed to break or crash to transfer energy. This proof shows that energy can shift into high-frequency 'turbulence' even in calm-looking water, changing our fundamental understanding of how oceans dissipate energy.
Transfer of energy for pure-gravity water waves with constant vorticity
arXiv · 2604.08343
We consider two-dimensional periodic gravity water waves with constant nonzero vorticity $\gamma$, in infinite depth and with periodic boundary conditions. We prove that, if the characteristic wave number $\frac{\gamma^2}{g}$ is rational, the system admits smooth small-amplitude solutions whose high Sobolev norms grow arbitrarily large while lower-order norms remain arbitrarily small, thereby exhibiting a genuine transfer of energy toward high frequencies. This yields the first rigorous construc