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Chaotic dynamics of large-scale structures in a turbulent wake

Eliott Varon1,2,*, Yoann Eulalie3, Stephie Edwige3, Philippe Gilotte3, and Jean-Luc Aider1,2,†

  • 1Laboratoire PMMH, CNRS UMR7636, ESPCI Paris, PSL Research University, 10 rue Vauquelin, Paris, France
  • 2Laboratoire PMMH, CNRS UMR7636, Université Pierre et Marie Curie, 10 rue Vauquelin, Paris, France
  • 3Plastic Omnium Auto Extérieur Services (POAES), Parc Industriel de la Plaine de l'Ain, Sainte-Julie, France

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Phys. Rev. Fluids 2, 034604 – Published 17 March, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.034604

Abstract

The dynamics of a three-dimensional (3D) bimodal turbulent wake downstream of a square-back Ahmed body are experimentally studied in a wind tunnel through high-frequency wall-pressure probes mapping the rear of the model and a horizontal two-dimensional (2D) velocity field. The barycenters of the pressure distribution over the rear part of the model and the intensity recirculation are found highly correlated. Both described the most energetic large-scale structures dynamics, confirming the relation between the large-scale recirculation bubble and its wall-pressure footprint. Focusing on the pressure, its barycenter trajectory has a stochastic behavior but its low-frequency dynamics exhibit the same characteristics as a weak strange chaotic attractor system, with two well-defined attractors. The low-frequency dynamics associated to the large-scale structures are then analyzed. The largest Lyapunov exponent is first estimated, leading to a low positive value characteristic of strange attractors and weak chaotic systems. Afterwards, analyzing the autocorrelation function of the timeseries, we compute the correlation dimension, larger than two. The signal is finally transformed and analyzed as a telegraph signal, showing that its dynamics correspond to a quasirandom telegraph signal. This is the first demonstration that the low-frequency dynamics of a turbulent 3D wake are not a purely stochastic process but rather a weak chaotic process exhibiting strange attractors. From the flow control point of view, it also opens the path to more simple closed-loop flow-control strategies aiming at the stabilization of the wake and the control of the dynamics of the wake barycenter.

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Phys. Rev. Fluids 2, 034604– Published 17 March, 2017
  • Received 26 July 2016

©2017 American Physical Society

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