Linear instability of turbulent channel flow

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.

5 pages, 4 figures

References in corpus (2)

• The phase transition to turbulence in spatially extended shear flows
• Flow Statistics in the Transitional Regime of Plane Channel Flow

Cited by in corpus (11)

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• Characterizing Data Assimilation in Navier-Stokes Turbulence with Transverse Lyapunov Exponents
• Patterns in transitional shear turbulence. Part 2: Emergence and optimal wavelength
• Improved assessment of the statistical stability of turbulent flows using extended Orr-Sommerfeld stability analysis
• Energy stability of magnetohydrodynamic flow in channels and ducts
• Linear stability of turbulent channel flow with one-point closure
• Model for transitional turbulence in a planar shear flow
• A cascade model for the discontinuous absorbing phase transition between turbulent and laminar flows
• Large-scale streak instabilities of transitional channel flow