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PreprintCC BY 4.0HAL

Stochastic interpretation of the Water Waves equations

  • Antoine Moneyron
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Abstract

The aim of this article is to derive a stochastic interpretation of the Water Waves equations, based on the location uncertainty principle (LU). Next, these equations are used to infer simpler models from scaling limits, such as the Saint-Venant, Boussinesq and Serre-Green-Naghdi ones. Once adapted to the stochastic setting, these models have been successfully implemented numerically, and we show several experiments to assess their properties – for example the breaking of the wave symmetry, and the influence of time correlated noises.

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Cite

BibTeXRIS
BibTeX
@misc{moneyron2026stochastic,
  title = {{Stochastic interpretation of the Water Waves equations}},
  author = {Antoine Moneyron},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2611.04739},
  eprint = {2611.04739},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05848104v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Stochastic interpretation of the Water Waves equations
AU  - Antoine Moneyron
PY  - 2026
DA  - 2026/10/25
PB  - HAL
DO  - 10.48550/arxiv.2611.04739
UR  - https://hal.science/hal-05848104v1
AB  - The aim of this article is to derive a stochastic interpretation of the Water Waves equations, based on the location uncertainty principle (LU). Next, these equations are used to infer simpler models from scaling limits, such as the Saint-Venant, Boussinesq and Serre-Green-Naghdi ones. Once adapted to the stochastic setting, these models have been successfully implemented numerically, and we show several experiments to assess their properties – for example the breaking of the wave symmetry, and the influence of time correlated noises.
ER  -