Scale locality of information flow in shell models of turbulence

TL;DR

This paper investigates how information about large-scale turbulence propagates to small scales in shell models, demonstrating that the transfer is predominantly local in scale, supporting the universality of turbulence scaling laws.

Contribution

It analytically decomposes the information flow into local and nonlocal parts and proves that the local part dominates under Kolmogorov assumptions, highlighting the scale-local nature of information transfer.

Findings

Information flow decomposes into scale-local and nonlocal parts.

Scale-nonlocal information transfer can be ignored under Kolmogorov assumptions.

Supports the scale locality of the turbulence energy cascade.

Abstract

Turbulent fluctuations exhibit universal scaling laws that are independent of large-scale statistics. It is often explained that such universality is caused by the loss of information about large-scale statistics during the cascade process. In our previous study [T. Tanogami and R. Araki, Phys. Rev. Research 6, 013090 (2024)], we applied information thermodynamics to turbulence and proved that information of large-scale turbulent fluctuations is propagated to small scales. As a first step toward understanding how universality emerges at small scales under the influence of the information flow from large scales, here we investigate the scale locality of the information flow for shell models. First, we analytically show that the information flow can be decomposed into scale-local and scale-nonlocal parts. Then, by assuming the Kolmogorov hypothesis for the Kolmogorov multiplier, we prove that the scale-nonlocal part can be ignored compared to the scale-local part. This result implies that the information transfer from large to small scales occurs mainly through scale-local interactions, which is consistent with the scale locality of the energy cascade.