New singularities for Stokes waves

@article{Crew2016NewSF,
  title={New singularities for Stokes waves},
  author={Samuel Crew and Philippe H. Trinh},
  journal={Journal of Fluid Mechanics},
  year={2016},
  volume={798},
  pages={256 - 283}
}
In 1880, Stokes famously demonstrated that the singularity that occurs at the crest of the steepest possible water wave in infinite depth must correspond to a corner of $120^{\circ }$ . Here, the complex velocity scales like $f^{1/3}$ where $f$ is the complex potential. Later in 1973, Grant showed that for any wave away from the steepest configuration, the singularity $f=f^{\ast }$ moves into the complex plane, and is of order $(f-f^{\ast })^{1/2}$ (Grant J. Fluid Mech., vol. 59, 1973, pp. 257… Expand
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