| Abstract: |
| The long-standing problem of stability of surface waves on 2D fluid is solved in conformal
variables for Stokes up to nearly extreme steepness. The stability spectrum of Stokes waves exhibits
recurrent transitions, multiple modulation, or Benjamin-Feir instability branches. We show that all
Stokes waves are, in fact, unstable, but the nature of these instabilities varies -- in some cases it leads
directly to wave-breaking, and, in others, to modulational disturbance and appearance of rogue waves in
the ocean swell. We discuss the profound change in the numerical approach that allowed us to consider
nearly extreme Stokes waves. |
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