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PreprintCC BY 4.0arXiv

Ekman Boundary Layers Under Transport Noise

  • Daniel Goodair
  • Szymon Sobczak
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Abstract

We consider a 3D rotating Navier-Stokes equation with transport-stretching noise, posed between two horizontal plates, and study the joint limit of vanishing vertical viscosity and rapid rotation. Our driving noise depends only on the horizontal coordinates and its vertical component vanishes with the viscosity. Provided that the initial data is purely horizontal, we construct martingale weak solutions which converge in L2ωL∞tL2x to the layered strong solution of a 2D stochastic Navier-Stokes equation with damping. The damping coefficient is dependent on the limit of the ratio between vertical viscosity and inverse rotation rate.

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Cite

BibTeXRIS
BibTeX
@misc{goodair2026ekman,
  title = {{Ekman Boundary Layers Under Transport Noise}},
  author = {Daniel Goodair and Szymon Sobczak},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.22011},
  eprint = {2609.22011},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.22011},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Ekman Boundary Layers Under Transport Noise
AU  - Daniel Goodair
AU  - Szymon Sobczak
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.22011
UR  - https://arxiv.org/abs/2609.22011
AB  - We consider a 3D rotating Navier-Stokes equation with transport-stretching noise, posed between two horizontal plates, and study the joint limit of vanishing vertical viscosity and rapid rotation. Our driving noise depends only on the horizontal coordinates and its vertical component vanishes with the viscosity. Provided that the initial data is purely horizontal, we construct martingale weak solutions which converge in L^2_ωL^∞_tL^2_x to the layered strong solution of a 2D stochastic Navier-Stokes equation with damping. The damping coefficient is dependent on the limit of the ratio between vertical viscosity and inverse rotation rate.
ER  -