Superstatistical Approach to Turbulent Circulation Fluctuations

TL;DR

This paper demonstrates that superstatistics, particularly q-exponentials, accurately models circulation fluctuations in homogeneous isotropic turbulence, linking turbulence statistics to non-extensive statistical mechanics.

Contribution

It introduces a superstatistical framework for turbulence circulation fluctuations, connecting geometric features and intermittency to non-extensive entropy models.

Findings

Circulation PDFs are well described by q-exponentials.

Superstatistics captures the correlation between dissipation and vortex structures.

The approach links turbulence statistics to non-extensive statistical mechanics.

Abstract

Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular interest here is the observation that circulation probability distribution functions admit a superstatistical representation, namely a description based on "ensembles of Boltzmann-Gibbs ensembles". A fundamental phenomenological ingredient of this approach, which serves as a natural starting point for modeling, relies on the strong correlation between the dissipation field and the spatial distribution of elementary circulation-carrying structures, i.e., small-scale vortices. Within the language of superstatistics, this corresponds to characterizing circulation statistics through an appropriate choice of conditioned (Boltzmann-like) distributions and mixing distributions. We show that the superstatistical class of q-exponentials, known to have broad applicability in a wide range of multiscale and non-equilibrium systems, provides an accurate description of the observed circulation statistics in homogeneous and isotropic turbulence. This finding opens avenues for exploring the statistical structure of the turbulent cascade in the context of non-extensive statistical mechanics, rooted in the concept of non-additive entropies.