Linear Instability of Turbulent Channel Flow br

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

Automated summary

The formation of laminar-turbulent pattern is a distinctive feature of the intermittency regime in subcritical plane shear flows. Through extensive numerical simulations, it is shown that the pattern arises from a spatial modulation of turbulent flow due to linear instability. By sampling the linear response of turbulent field to a temporal impulse, the dispersion relation is constructed from ensemble-averaged relaxation rates. As the instability threshold is approached, the relaxation rate of the least damped modes eventually reaches zero.