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

Abstract

We present experimental evidence and theoretical arguments showing that the time-evolution of freely decaying two-dimensional (2D) turbulence is governed by a 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 preferred scale factor and, as a consequence, to log-periodic oscillations. From a thorough analysis of freely decaying 2D 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 preferred scaling ratio of ≈1.2–1.3.