Space–time dynamics of optimal wavepackets for streaks in a channel entrance flow

Abstract : Laminar/turbulent transition of a channel entrance flow for uniform inlet condition is revisited using global linear optimization analyses and direct numerical simulations. This work focuses on the region near the inlet, for a subcritical Reynolds number flow. The laminar flow developing from the entrance is linearly stable, but when perturbed by local optimal modes from the inlet section can give rise to steady nonlinear streaks, developing in the boundary layers on the walls. In this study, only the lower wall is perturbed. The boundary layers are asymptotically stable, however, a secondary linear instability analysis shows that for sufficiently high amplitude of the streaks, global optimal modes, both varicose and sinuous, taking the form of wavepackets, are amplified. It is shown that for short optimization times, varicose wavepacket grows through a combination of the Orr and lift-up effects, whereas for larger target times, both sinuous and varicose wavepackets (if exist) exhibit an instability mechanism driven by the presence of inflection points in the streaky flow. In addition, while the initial conditions for the optimal varicose modes obtained for short optimization times are localized near the inlet, where the base flow is strongly three-dimensional, the sinuous and varicose optimal modes are displaced further downstream, in the nearly parallel streaky flow, when the target time is increased. Finally, the effects of nonlinearities are highlighted by investigating the space-time evolution of the optimal wavepackets when superimposed to the streaky flow with a sufficiently high amplitude to trigger breakdown to turbulence. It is noticed that the resulting turbulent flow have the same wall-shear stress, whether the wavepackets have been obtained for short or for long time optimization.
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F. Alizard, A. Cadiou, L. Le Penven, B. Di Pierro, M. Buffat. Space–time dynamics of optimal wavepackets for streaks in a channel entrance flow. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2018, 844, pp.669-706. ⟨10.1017/jfm.2018.191⟩. ⟨hal-01951038⟩

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