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Linear and nonlinear energy optimizations in a tilted domain are used tounveil the main mechanisms allowing the creation of a turbulent band in achannel flow. Linear optimization predicts an optimal growth for streamwse andspanwise wavenumbers $k_x = 1.2$, $k_z = - 1.75$, corresponding to the peakvalues of the premultiplied energy spectra of direct numerical simulations. Attarget time, the linear optimal perturbation is composed by oblique streaks,which, for a sufficiently large initial energy, induce turbulence in the wholedomain, due to the lack of spatial localization. When localization is achievedby adding nonlinear effects to the optimization, or by artificially confiningthe linear optimal to a localized region in the spanwise direction, alarge-scale flow is created, which leads to the generation of a localisedturbulent band. These results suggest that inducing transition towardsturbulent bands in a tilted domain, two main elements are needed: a linearenergy growth mechanism such as the lift-up for generating large-amplitude flowstructures which produce inflection points; large-scale vortices ensuringspatial localisation. Remarkably, these two elements alone are able to generatean isolated turbulent band also in a large, non-tilted domain.

Linear and nonlinear optimal growth mechanisms for generating turbulent bands