  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.
