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PreprintCC BY 4.0arXiv

A windy sea surface with Stokes waves

  • Nikhil Yewale
  • Anil Kumar
  • Vinod Kumar Kadari
  • Ratul Dasgupta
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Abstract

Predicting the transition of wind-forced, gravito-capillary surface waves from smooth to corrugated states remains a longstanding problem in nonlinear surface wave mechanics. Solving driven-dissipative, nonlinear potential flow equations we map these waves (4−13 cm) onto a Reynolds number -- wave energy phase-space. We identify a transition band separating smooth from corrugated wave states - the wave steepness exhibits a non-monotonic dependence on Reynolds number within this. Subharmonic (in)stability analysis reveals that the fastest-growing mode intensifies corrugations on alternate faces of the carrier wave. Our results offer insights into parasitic capillary wave formation on steep carrier waves and are of interest to ocean remote-sensing.

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Cite

BibTeXRIS
BibTeX
@misc{yewale2026windy,
  title = {{A windy sea surface with Stokes waves}},
  author = {Nikhil Yewale and Anil Kumar and Vinod Kumar Kadari and Ratul Dasgupta},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.03657},
  eprint = {2608.03657},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.03657},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A windy sea surface with Stokes waves
AU  - Nikhil Yewale
AU  - Anil Kumar
AU  - Vinod Kumar Kadari
AU  - Ratul Dasgupta
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2608.03657
UR  - https://arxiv.org/abs/2608.03657
AB  - Predicting the transition of wind-forced, gravito-capillary surface waves from smooth to corrugated states remains a longstanding problem in nonlinear surface wave mechanics. Solving driven-dissipative, nonlinear potential flow equations we map these waves (4−13 cm) onto a Reynolds number -- wave energy phase-space. We identify a transition band separating smooth from corrugated wave states - the wave steepness exhibits a non-monotonic dependence on Reynolds number within this. Subharmonic (in)stability analysis reveals that the fastest-growing mode intensifies corrugations on alternate faces of the carrier wave. Our results offer insights into parasitic capillary wave formation on steep carrier waves and are of interest to ocean remote-sensing.
ER  -