Geometric Intermittency in Turbulence

TL;DR

This paper reveals multiscaling phenomena in turbulence by analyzing velocity vector components, uncovering complex statistical structures and flow geometry interactions in both 2D and 3D turbulence cascades.

Contribution

It demonstrates multiscaling in velocity magnitude and orientation increments, extending understanding beyond traditional scalar velocity increment analysis.

Findings

Multiscaling appears in velocity vector components in turbulence.

Decomposition reveals multiscaling in 2D inverse cascade.

Flow geometry and velocity amplitude are statistically decoupled.

Abstract

Equal-time scaling exponents in fully developed turbulence typically exhibit non anomalous scaling in the inverse cascade of two-dimensional (2D) turbulence and anomalous scaling in three dimensions. We demonstrate that multiscaling is not confined to longitudinal, scalar velocity increments, but also emerges in increments associated with the magnitude and orientation of the velocity vector. This decomposition uncovers a multiscaling in the 2D inverse cascade, which remains obscured when using conventional structure functions. Our results highlight a decoupling between velocity amplitude and flow geometry, offering new insight into the statistical structure of turbulent cascades as well as showing how different classes of multiscaling emerge.