Linear instability of turbulent channel flow

TL;DR

This paper demonstrates that laminar-turbulent pattern formation in channel flow arises from a linear instability, identified through numerical simulations and analysis of the turbulent flow's linear response.

Contribution

It reveals that the pattern formation results from a linear instability in turbulent channel flow, providing a new understanding of the transition mechanism.

Findings

Pattern emerges from spatial modulation due to linear instability.

Relaxation rate of modes approaches zero at instability threshold.

Method estimates wavevector of modulation without closure models.

Abstract

Laminar-turbulent pattern formation is a distinctive feature of the intermittency regime in subcritical plane shear flows. By performing extensive numerical simulations of the plane channel flow, we show that the pattern emerges from a spatial modulation of the turbulent flow, due to a linear instability. We sample over many realizations the linear response of the fluctuating turbulent field to a temporal impulse, in the regime where the turbulent flow is stable, just before the onset of the instability. The dispersion relation is constructed from the ensemble-averaged relaxation rates. As the instability threshold is approached, the relaxation rate of the least damped modes eventually reaches zero. The method allows, despite the presence of turbulent fluctuations and without any closure model, for an accurate estimation of the wavevector of the modulation at onset.