Information-Thermodynamic Bound on Information Flow in Turbulent Cascade

TL;DR

This paper explores the transfer of information in turbulent flows using an information-thermodynamic framework, revealing that information cascades from large to small scales with low efficiency, offering new insights into turbulence universality.

Contribution

It introduces an information-thermodynamic perspective to turbulence, proving information transfer along the energy cascade and analyzing its efficiency through numerical simulations.

Findings

Information of large-scale eddies transfers to small scales.

Information flow intensity remains nearly constant in the inertial range.

Information-thermodynamic efficiency is low compared to other systems.

Abstract

We investigate the nature of information flow in turbulence from an information-thermodynamic viewpoint. For the fully developed three-dimensional fluid turbulence described by the fluctuating Navier-Stokes equation, we prove that information of large-scale eddies is transferred to small scales along with the energy cascade. We numerically illustrate our findings using a shell model and further show that in the inertial range, the intensity of the information flow is nearly constant and can be scaled by the large-eddy turnover time. Our numerical results also suggest that the corresponding information-thermodynamic efficiency is quite low compared to other typical information processing systems such as Maxwell's demon. These findings provide a new perspective on how universality and intermittency of turbulent fluctuations emerge at small scales.