The chaotic dynamics of large-scale structures in a turbulent wake

TL;DR

This study reveals that the low-frequency dynamics of a turbulent wake behind a bluff body exhibit weak chaotic behavior with strange attractors, challenging the notion of purely stochastic turbulence.

Contribution

It demonstrates that the large-scale structures in a turbulent wake follow weak chaotic dynamics with strange attractors, providing new insights into flow control strategies.

Findings

Low positive Lyapunov exponent indicates weak chaos.

Correlation dimension exceeds two, confirming complex dynamics.

Dynamics resemble a quasi-random telegraph signal.

Abstract

The dynamics of a 3D bimodal 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. Both described the most energetic large-scale structures dynamics, confirming the relation between the large-scale recirculation bubble and its wall pressure foot-print. Focusing on the pressure, its barycenter trajectory has a stochastic behavior but its low frequencies dynamics exhibit the same characteristics as a weak strange chaotic attractor system, with two well defined attractors. The low frequencies 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 time-series, 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 quasi-random telegraph signal. This is the first demonstration that the low frequencies 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.