Scale locality of information flow in shell models of turbulence

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.