Probing the Asymptotic Link Between Eulerian Roughness and Fractional Lagrangian Diffusion in Turbulence

Abstract: The theoretical link between the Eulerian spectral roughness of a turbulent velocity field and the Lagrangian fractional diffusion exponent via the relation offers a powerful framework for understanding anomalous transport. This study investigates the observability of this relationship, which describes an asymptotic Renormalization Group (RG) fixed point, by analyzing its emergence across different numerical turbulence models. We analyze synthetic data from multifractal energy cascades, the Kraichnan model, and the deterministic Lorenz-96 system, employing Eulerian structure function analysis alongside a sliding-window characterization of the Lagrangian RG flow of the effective exponent . Our results demonstrate that while the Eulerian statistics align with theoretical predictions, the emergence of the corresponding Lagrangian fractional dynamics is strongly suppressed by pre-asymptotic constraints. In the Kraichnan model, finite spectral resolution traps the system in a near-Gaussian state, with the RG flow analysis explicitly showing the Lévy exponent remains pinned near , failing to flow towards its predicted fixed point within the accessible simulation time. Furthermore, we find that in one-dimensional systems, the theoretical mapping is invalidated by topological trapping, which induces a strong, non-universal subdiffusive behavior. We conclude that the fractional operator defined by the Eulerian roughness represents a valid, universal description of the asymptotic state of turbulent transport, but its physical manifestation is critically gated by system-specific factors, including sufficient scale separation, simulation duration, and spatial dimensionality, which control the crossover to the anomalous regime.

Subjects:	physics.flu-dyn; physics.class-ph; physics.comp-ph
Cite as:	PX:2605.00004