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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
PHYSICAL REVIEW LETTERS
By: Kashyap, Pavan V. / Duguet, Yohann / Dauchot, Olivier
Volume 129, Issue 24, Article Number 244501
DOI: https://doi.org/10.1103/PhysRevLett.129.244501
Published DEC 2022