Universality of extreme events in turbulent flows

TL;DR

This paper demonstrates that the statistical properties of extreme velocity gradient events in turbulent flows are universal across different flow types and Reynolds numbers, supporting the universality of small-scale turbulence structures.

Contribution

It provides evidence that extreme events in turbulence exhibit universal scaling laws and tensor structures across various flow configurations and Reynolds numbers.

Findings

Velocity gradient moments scale universally with Reynolds number.

Proportionality constants between moments are universal.

Velocity gradient tensor structure is consistent across flows.

Abstract

The universality of small scales, a cornerstone of turbulence, has been nominally confirmed for low-order mean-field statistics, such as the energy spectrum. However, small scales exhibit strong intermittency, exemplified by formation of extreme events which deviate anomalously from a mean-field description. Here, we investigate the universality of small scales by analyzing extreme events of velocity gradients in different turbulent flows, viz. direct numerical simulations (DNS) of homogeneous isotropic turbulence, inhomogeneous channel flow, and laboratory measurements in a von Karman mixing tank. We demonstrate that the scaling exponents of velocity gradient moments, as function of Reynolds number ($Re$), are universal, in agreement with previous studies at lower $Re$, and further show that even proportionality constants are universal when considering one moment order as a function of another. Additionally, by comparing various unconditional and conditional statistics across different flows, we demonstrate that the structure of the velocity gradient tensor is also universal. Overall, our findings provide compelling evidence that even extreme events are universal, with profound implications for turbulence theory and modeling.