Using Information Networks to Understand the Impact of Turbulence on Wake Dynamics

Coherent oscillations in wake flows manifest as a result of hydrodynamic instabilities. The wake flow behind a bluff body becomes unsteady beyond a critical Reynolds number, which leads to anti-symmetric vortex shedding. In this work, we consider the impact of freestream turbulence and acoustic forcing on the behavior of a constant-density wake flow measured using high-speed stereo particle image velocimetry. These data are analyzed using complex network analysis to identify the wavemaker and understand the impact of turbulence and acoustic forcing on the network topology, and the spatial extent and the strength of the wavemaker. For varying Reynolds numbers, nodal link strengths are quantified using statistical measures such as Pearson’s correlation coefficient, mutual information, and transfer entropy. Weighted closeness centrality is then employed to identify hubs whose spatial extent identifies the wavemaker region. Closeness centrality of transfer entropy based networks provides the most compact representation of network hubs when compared with those derived from correlation coefficients or mutual information. The presence of hubs is consistent with the presence of emergent dynamics, i.e., coherent wake oscillations. Results show that the strength of the wavemaker, as indicated by its closeness centrality, increases with increasing Reynolds number and in-flow turbulence intensity, consistent with an increasingly coherent Bérnard von Kármán street from the wake as determined from the SPOD analysis of the data. The networks based on transfer entropy more clearly identify the wavemaker when compared to the other measures. Further, the exponent of the power-law fit to the weighted-degree distribution is indicative of organized flow dynamics. More broadly, this work provides a pathway for the use of information networks on time-series sPIV data of large-scale flow instability.