Entropy, irreversibility and cascades in the inertial range of isotropic turbulence

Alberto Vela-Martin, Javier Jimenez

Published 2020-05-07Version 1

This paper analyses the turbulent energy cascade from the perspective of statistical mechanics, and relates inter-scale energy fluxes to information-entropy production. The microscopical reversibility of the energy cascade is tested by constructing a reversible 3D turbulent system using a dynamic model for the sub-grid stresses. This system, when reversed in time, develops a sustained inverse cascade towards the large scales, evidencing that the characterization of the inertial energy cascade must consider the possibility of an inverse regime. This experiment suggests the introduction of a probabilistic concept, namely the entropy, to explain statistical irreversibiliy or the prevalence of direct over inverse energy cascades. Entropy production, a statistical property of ensembles in phase space, is connected to the dynamics of the energy cascade in physical space by considering the space locality of the energy fluxes and their relation to the local structure of the flow. An entropic mechanism for the prevalence of direct energy transfer is proposed based on the dynamics of the rate-of-strain tensor, which is identified as the most important source of statistical irreversibility in the energy cascade.