Punctuated vortex coalescence and discrete scale invariance in two-dimensional turbulence

TL;DR

This paper provides experimental and theoretical evidence that two-dimensional turbulence evolves through punctuated vortex merging, exhibiting discrete scale invariance and log-periodic oscillations rather than continuous scaling.

Contribution

It demonstrates that 2D turbulence dynamics are governed by discrete time scale invariance, revealing punctuated vortex coalescence and associated log-periodic oscillations.

Findings

Vortex number, radius, and separation show log-periodic oscillations over time.

The preferred scale factor is approximately 1.2-1.3.

The average log-frequency of oscillations is about 4-5.

Abstract

We present experimental evidence and theoretical arguments showing that the time-evolution of freely decaying 2-d turbulence is governed by a {\it discrete} time scale invariance rather than a continuous time scale invariance. Physically, this reflects that the time-evolution of the merging of vortices is not smooth but punctuated, leading to a prefered scale factor and as a consequence to log-periodic oscillations. From a thorough analysis of freely decaying 2-d turbulence experiments, we show that the number of vortices, their radius and separation display log-periodic oscillations as a function of time with an average log-frequency of ~ 4-5 corresponding to a prefered scaling ratio of ~ 1.2-1.3