Susceptibility divergence, phase transition and multistability of a highly turbulent closed flow

Abstract

Using time-series of stereoscopic particle image velocimetry data, we study the response of a turbulent von Kármán swirling flow to a continuous breaking of its forcing symmetry. Experiments are carried over a wide Reynolds number range, from laminar regime at $Re=10^2$ to highly turbulent regime near $Re=10^6$. We show that the flow symmetry can be quantitatively characterized by two scalars, the global angular momentum $I$ and the mixing layer altitude $z_s$, which are shown to be statistically equivalent. Furthermore, we report that the flow response to small forcing dissymetry is linear, with a slope depending on the Reynolds number: this response coefficient increases non monotonically from small to large Reynolds number and presents a divergence at a critical Reynolds number $R{e}_c=40000\pm 5000$. This divergence coincides with a change in the statistical properties of the instantaneous flow symmetry $I(t)$: its pdf changes from Gaussian to non-Gaussian with multiple maxima, revealing metastable non-symmetrical states. For symmetric forcing, a peak of fluctuations of $I(t)$ is also observed at $R{e}_c$: these fluctuations correspond to time-intermittencies between metastable states of the flow which, contrary to the very-long-time-averaged mean flow, spontaneously and dynamically break the system symmetry. We show that these observations can be interpreted in terms of divergence of the susceptibility to symmetry breaking, revealing the existence of a phase transition. An analogy with the ferromagnetic-paramagnetic transition in solid-state physics is presented and discussed.

to appear in Journal of Statistical Mechanics

References in corpus (9)

• Generation of magnetic field by dynamo action in a turbulent flow of liquid sodium
• Random changes of flow topology in two dimensional and geophysical turbulence
• Slow dynamics in a turbulent von Kármán swirling flow
• Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh-Bénard convection
• Experimental evidence of a phase transition in a closed turbulent flow
• Statistical mechanics of Beltrami flows in axisymmetric geometry: Theory reexamined
• Fluctuation-Dissipation Relations and statistical temperatures in a turbulent von Kármán flow
• Statistical mechanics of Beltrami flows in axisymmetric geometry: Equilibria and bifurcations
• Fluctuation-dissipation relation on a Melde string in a turbulent flow, considerations on a "dynamical temperature"

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• Probing turbulence intermittency via Auto-Regressive Moving-Average models
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