Non modal subcritical transition of channel entry flow

Abstract

International audienceDeveloping channel flows are of interest in a large number of application areas. Many aspects of these flows are not yet fully understood, such as the stability characteristics at subcritical Reynolds number. Using massively parallel supercomputers, it is now possible to device new numerical experiments to study this kind of flow, that would have been impossible a few years ago. This work presents DNS of bypass transition of a subcritical channel entrance flow where transition occurs inside the boundary layers of the developing entry flow. The two boundary layers are perturbed near the entrance and streaks are generated inside the boundary layers through the classical linear lift-up mechanism (transient growth). The streaks strongly modify the velocity profile, which become inflectional at some distant downstream in the low-speed regions of the streaks. It is generally expected that the local inflectional velocity profiles associated with the low-speed streak are unstable with two kind of instability modes: a symmetric varicose mode and an antisymmetric sinuous mode [1]. In zero pressure gradient boundary layer, the low-speed streaks are more unstable with respect to the latter. On the contrary, in the present channel entrance flow, the varicose mode is favored. The streaks occupy almost half of the channel height when they are subjected at their top head to a Kelvin-Helmholtz instability. Furthermore, instabilities at the top of a low speed streak on one wall are found to be coupled with the instabilities of the streaks on the opposite wall. This observation is confirmed by a local linear stability analysis of the streaky velocity profile. Further downstream, a turbulent transition is observed and the flow evolves towards a fully turbulent channel flow. Simulations corresponding to a larger channel height have also been performed with an inlet perturbation located at the same position. In that case the boundary layers are thinner respectively to the channel height, and a sinuous mode precedes the streaks breakdown and the turbulent transition of the boundary layers