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An Obukhov-Corrsin-Yaglom law for a kinematic model of turbulence

  • Camillo De Lellis
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Abstract

We prove an Obukhov-Corrsin-Yaglom-type law for passive scalars advected by a family of random Cα velocity field proposed in \cite{JDEMS} as a kinematic model of turbulent fluids. Up to a technical assumption on one parameter, the expectation of the squared L2t Hγx norm of solutions to the passive scalar equation is bounded by the squared L2 norm of the deterministic initial datum, uniformly in the viscosity, whenever α+ 2γ< 1. The proof is based on a new insight in the theory developed by \cite{FM} to prove Richardson's dispersion and anomalous dissipation for the same model.

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Cite

BibTeXRIS
BibTeX
@misc{lellis2026obukhovcorrsinyaglom,
  title = {{An Obukhov-Corrsin-Yaglom law for a kinematic model of turbulence}},
  author = {Camillo De Lellis},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.07076},
  eprint = {2611.07076},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.07076},
}
RIS
TY  - UNPB
TI  - An Obukhov-Corrsin-Yaglom law for a kinematic model of turbulence
AU  - Camillo De Lellis
PY  - 2026
DA  - 2026/11/04
PB  - arXiv
DO  - 10.48550/arxiv.2611.07076
UR  - https://arxiv.org/abs/2611.07076
AB  - We prove an Obukhov-Corrsin-Yaglom-type law for passive scalars advected by a family of random C^α velocity field proposed in \cite{JDEMS} as a kinematic model of turbulent fluids. Up to a technical assumption on one parameter, the expectation of the squared L^2_t H^γ_x norm of solutions to the passive scalar equation is bounded by the squared L^2 norm of the deterministic initial datum, uniformly in the viscosity, whenever α+ 2γ< 1. The proof is based on a new insight in the theory developed by \cite{FM} to prove Richardson's dispersion and anomalous dissipation for the same model.
ER  -