The chaotic dynamics of a turbulent wake

Eliott Varon, Yoann Eulalie, Stephie Edwige, Philippe Gilotte, Jean-Luc Aider

Published 2016-07-22Version 1

The dynamics of a 3D bi-stable turbulent wake downstream 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 2D velocity field. The barycenters of the pressure distribution over the rear part of the model and the intensity recirculation are found highly correlated. Focusing on the pressure, its barycenter trajectory exhibits the same characteristics as a Lorenz dynamical system, with two well defined attractors and a 2D Poincar\'e section displaying a well-defined "butterfly-like" shape. The signal is firstly transformed and analyzed as a telegraph signal showing that its dynamics corresponds to a quasi-random telegraph signal. Then the largest Lyapunov exponent is estimated, leading to a positive value characteristic of strange attractors and chaotic systems. Finally, analyzing the autocorrelation function of the time-series, we compute the correlation dimension, slightly larger than two, very similar to the Lorenz attractor. This is the first demonstration that the dynamics of a turbulent 3D wake is not a purely stochastic process but rather a 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 dynamic of the wake's barycenter.