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arXiv · 2611.07076

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 $C^α$ 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.

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Camillo De Lellis. 2026-11-04. An Obukhov-Corrsin-Yaglom law for a kinematic model of turbulence. https://arxiv.org/abs/2611.07076

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