How do laminar-turbulent patterns emerge from turbulent shear flow ?
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On one hand, the issue of the stability of turbulent shear flows to small perturbations is a long-debate questions in turbulence theory. On the other hand large-scale laminar-turbulent patterns have long been reported in planar or circular shear flows, and are found at marginally low Reynolds numbers close to turbulence becomes transient (see Figure 1). We reconcile these two concerns here by demonstrating, in the context of plane channel flow, that these laminar-turbulent patterns come from spatial modulations of the fully turbulent flow, themselves explained by a linear instability of the turbulent flow at sufficiently low Reynolds number. This numerical perturbative approach leads to the determination of an effective dispersion relation for the instability modes. The status of this linear instablity will be discussed for other wall-bounded flows and in the presence of turbulence closure models.