Successive bifurcations in a fully three-dimensional open cavity flow

F Picella (1) , J.-Ch Loiseau (1) , F. Lusseyran (2) , J.-Ch Robinet (1) , S Cherubini (3) , L. Pastur (2)

1 DynFluid - Laboratoire de Dynamique des Fluides
2 LIMSI - Laboratoire d'Informatique pour la Mécanique et les Sciences de l'Ingénieur
3 Polytechnic University of Bari / Politecnico di Bari

The transition to unsteadiness of a three-dimensional open cavity flow is investigated using the joint application of direct numerical simulations and fully three-dimensional linear stability analyses, providing a clear understanding of the first two bifurcations occurring in the flow. The first bifurcation is characterized by the emergence of Taylor–Görtler-like vortices resulting from a centrifugal instability of the primary vortex core. Further increasing the Reynolds number eventually triggers self-sustained periodic oscillations of the flow in the vicinity of the spanwise end walls of the cavity. This secondary instability causes the emergence of a new set of Taylor–Görtler vortices experiencing a spanwise drift directed toward the spanwise end walls of the cavity. While a two-dimensional stability analysis would fail to capture this secondary instability due to the neglect of the lateral walls, it is the first time to our knowledge that this drifting of the vortices can be entirely characterized by a three-dimensional linear stability analysis of the flow. Good agreements with experimental observations and measurements strongly support our claim that the initial stages of the transition to turbulence of three-dimensional open cavity flows are solely governed by modal instabilities.

Mots clés: bifurcation; nonlinear dynamical systems; instability

Domaines: Mécanique des fluides [physics.class-ph]

F Picella, J.-Ch Loiseau, F. Lusseyran, J.-Ch Robinet, S Cherubini, et al.. Successive bifurcations in a fully three-dimensional open cavity flow. Journal of Fluid Mechanics, 2018, 844, pp.855-877. ⟨10.1017/jfm.2018.169⟩. ⟨hal-01770084⟩