Abstract
This paper analyses the turbulent energy cascade from the perspective of statistical mechanics, and relates interscale energy fluxes to statistical irreversibility and information entropy production. The microscopical reversibility of the energy cascade is tested by constructing a reversible three-dimensional 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 on the dynamics of the rate-of-strain tensor, which is identified as the most important source of statistical irreversibility in the energy cascade.
Highlights
The turbulence cascade is a scientific paradigm that dates back to the beginning of the 20th century
We have studied a microscopically reversible turbulent system constructed using a reversible sub-grid scale (SGS) model to explore the energy cascade as an entropydriven process
We explain the origin of this irreversibility by focusing on the dynamics of the energy cascade in physical space
Summary
The turbulence cascade is a scientific paradigm that dates back to the beginning of the 20th century. A meaningful description of the energy cascade must first identify the dynamically relevant mechanisms related to energy transfer, and subsequently establish the causes of the prevalence of the direct mechanisms over the inverse ones We address both by analysing the filtered velocity gradient tensor through its invariants (Naso & Pumir 2005; Lozano-Duran et al 2016; Danish & Meneveau 2018), and by determining their relation to the local energy fluxes in physical space. In this frame, we justify the higher probability of direct over inverse cascades by noting that the latter require the organisation of a large number of spatial degrees of freedom, whereas the direct cascade results from space-local dynamics.
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