It is rare to have mathematicians publish in The Proceedings of the National Academy of Sciences (PNAS), when it happens is a great honor. One of our Distinguished Professors and two alumni just did exactly that!
An origin of breaking of oceanic waves was identified in a recent publication in The Proceedings of the National Academy of Sciences (PNAS) https://doi.org/10.1073/pnas.230893512 by a team of researchers consisting of two UNM Department of Mathematics and Statistics alumni Sergey Dyachenko (PhD 2014, now Assistant Professor at the Department of Mathematics, University of Buffalo) and Anastassiya Semenova (PhD 2020, now a postdoctoral researcher at the Department of Applied Mathematics, University of Washington) together with Professor Bernard Deconinck (Department of Applied Mathematics, University of Washington) and our own Distinguished Professor Pavel Lushnikov (Department of Mathematics and Statistics, UNM).
Steady propagating surface gravity waves found in 19th century by Stokes is the key structure of ocean swell easily seen from beaches, airplanes and ocean liners. The dominant instability of these waves depends on their steepness. It is well known since 1960s that the Benjamin-Feir or modulational instability dominates the dynamics of a small amplitude waves resulting in a slow variation of the swell. The team demonstrated that for steeper waves another instability caused by disturbances localized at the wave crest vastly surpasses the growth rate of the modulational instability. These dominant localized disturbances are either co-periodic with the Stokes wave or have twice its period. In either case, the nonlinear evolution of the instability leads to very fast formation of plunging breakers destroying steep waves. This phenomenon explains why long propagating ocean swell consists of small-amplitude waves. A breaking of oceanic waves provides a key mechanism of the exchange of the energy between atmosphere and oceans strongly affecting the global climate dynamics.
The paper is titled "The dominant instability of near-extreme Stoke waves" and it appeared on July 31st, 2023.
Congratulation Pavel, Anastassiya and Sergey!!! You make us proud!
