Statistics of Extreme Turbulent Circulation Events from Multifractality Breaking

TL;DR

This paper investigates the extreme fluctuations in turbulent circulation at high Reynolds numbers, revealing that multifractality breaking is crucial for understanding the tails of circulation probability distributions, with analytical results aligning with instanton theory.

Contribution

It extends vortex gas models by highlighting multifractality breaking as essential for predicting circulation distribution tails, connecting phenomenological and analytical approaches.

Findings

Analytical agreement with instanton approach results.

Multifractality breaking influences circulation PDF tails.

Enhanced understanding of turbulence intermittency.

Abstract

Recent numerical explorations of extremely intense circulation fluctuations at high Reynolds number flows have brought to light novel aspects of turbulent intermittency. Vortex gas modeling ideas, introduced alongside such developments, have led to accurate descriptions of the core and the intermediate tails of circulation probability distribution functions (cPDFs), as well as the scaling exponents associated to statistical moments of circulation. We extend the predictive reach of the vortex gas picture of turbulence, by emphasizing that multifractality breaking, one of its salient phenomenological ingredients, is the key concept to disclose the asymptotic form of cPDF tails. A remarkable analytical agreement is found with previous results derived within the framework of the instanton approach to circulation intermittency.