Stokes wave. High precision Padé data.


Three different Stokes waves.

Authors of the web-site in alphabetical order:
Sergey A. Dyachenko Alexander O. Korotkevich Pavel M. Lushnikov Denis A. Silantyev
Sergey A. Dyachenko Alexander O. Korotkevich Pavel M. Lushnikov Anastassiya A. Semenova Denis A. Silantyev
In our recent works we computed with very high accuracy (at least 10e-26) Stokes' waves of different amplitude and provided a new, more accurate, estimation for the maximum amplitude of the Stokes' wave. We were able to compute Stokes' waves with amplitudes which differs from the maximum one less than by 0.003%.
These results were published in the following articles:
  1. S.A. Dyachenko, P.M. Lushnikov, and A.O. Korotkevich, The complex singularity of a Stokes' wave, JETP Letters, 98 (11), 767-771 (2013) arXiv:1311.1882 DOI: 10.7868/S0370274X13230070
  2. S.A. Dyachenko, P.M. Lushnikov, and A.O. Korotkevich, Branch cuts of Stokes' wave on deep water. Part I: Numerical solution and Padé approximation, Studies in Applied Mathematics 137 (4), 419-472 (2016) arXiv:1507.02784 DOI: 10.1111/sapm.12128
  3. P.M. Lushnikov, Structure and location of branch point singularities for Stokes' waves on deep water, Journal of Fluid Mechanics, 800, 557-594 (2016) arXiv:1509.03393
  4. S.A. Dyachenko, P.M. Lushnikov, and D.A. Silantyev, New conformal mapping for adaptive resolving of the complex singularities of Stokes wave, Proc. Roy. Soc. A 473, 20170198 (2017) arXiv:1703.06343
  5. A.O. Korotkevich, P.M. Lushnikov, A.A. Semenova, and S.A. Dyachenko, On Superharmonic Instability of Stokes' Waves , In progress (2021)
Here you can find library of computed Stokes' waves represented as data for Padé approximation (see Appendix C in the article 2 above for full description):
ZIP-Archive of the library of Stokes' waves (quadruple precision)
ZIP-Archive of the few Stokes' waves (200 decimal digits precision)
Here we provide several examples of the first three unstable eigenmodes for different values of steepness (see Appendix C in the article 5 above for full description):
ZIP-Archive of the library of elevation profiles of the the first three unstable eigenmodes for perturbations of Stokes' waves (double precision)
This research was performed under support of National Science Foundation grant OCE1131791, work on Padé approximation was supported by Russian Scientific Foundation grant 14-22-00259.