Aging and memory of transitional turbulence

TL;DR

This paper challenges the application of directed percolation models to channel flow turbulence, showing that turbulent stripes exhibit aging and memory effects near the critical point, unlike in other shear flows.

Contribution

It demonstrates that the memoryless assumption of turbulent sites in directed percolation models does not hold for channel flow, revealing flow-specific transition mechanisms.

Findings

Turbulent stripes in channel flow age near the critical point.

Memoryless property of turbulence does not apply to channel flow.

Differences in flow geometry affect transition dynamics.

Abstract

The recent classification of the onset of turbulence as a directed percolation (DP) phase transition has been applied to all major shear flows including pipe, channel, Couette and boundary layer flows. A cornerstone of the DP analogy is the memoryless (Poisson) property of turbulent sites. We here show that, for the classic case of channel flow, neither the decay nor the proliferation of turbulent stripes is memoryless. As demonstrated by a standard analysis of the respective survival curves, isolated channel stripes, in the immediate vicinity of the critical point, age. Consequently, the one to one mapping between turbulent stripes and active DP-sites is not fulfilled in this low Reynolds number regime. In addition, the interpretation of turbulence as a chaotic saddle with supertransient properties, the basis of recent theoretical progress, does not apply to individual localized stripes. The discrepancy between channel flow and the transition models established for pipe and Couette flow, illustrates that seemingly minor geometrical differences between flows can give rise to instabilities and growth mechanisms that fundamentally alter the nature of the transition to turbulence.