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

Abstract

This paper analyses the turbulent energy cascade from the perspective of statistical mechanics, and relates inter-scale energy fluxes to statistical irreversibility and 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 characterisation of the inertial energy cascade must consider the possibility of an inverse regime. This experiment is used to study the origin of statistical irreversibility and the prevalence of direct over inverse energy cascades in isotropic turbulence. Statistical irreversibility, a property of statistical ensembles in phase space related to entropy production, 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. A mechanism to explain the probabilistic prevalence of direct energy transfer is proposed based the dynamics of the rate-of-strain tensor, which is identified as the most important source of statistical irreversibility in the energy cascade.

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Cited by in corpus (12)

• Decomposing causality into its synergistic, unique, and redundant components
• On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade
• Comparing local energy cascade rates in isotropic turbulence using structure function and filtering formulations
• Coherent structures at the origin of time irreversibility in wall turbulence
• Causal features in turbulent channel flow
• Identifying causal significance in three-dimensional isotropic turbulence
• Chaos, coherence and turbulence
• Entropy and fluctuation relations in isotropic turbulence
• Experimental measurement of the vorticity-strain alignment around extreme energy transfer events
• Space-local Navier--Stokes turbulence
• Fluctuations around Turbulence Models
• Velocity alignment explains Lagrangian irreversibility in turbulence