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

Anders Johansen·Didier Sornette·Adam Espe Hansen
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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

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Anders Johansen, Didier Sornette, Adam Espe Hansen. 1999-02-17. Punctuated vortex coalescence and discrete scale invariance in two-dimensional turbulence. https://doi.org/10.1016/s0167-2789(99)00204-3

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