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Successive bifurcations in a fully three-dimensional open cavity flow

Published online by Cambridge University Press:  12 April 2018

F. Picella Open the ORCID record for F. Picella [Opens in a new window] ,
J.-Ch. Loiseau Open the ORCID record for J.-Ch. Loiseau [Opens in a new window] ,
F. Lusseyran ,
J.-Ch. Robinet ,
S. Cherubini Open the ORCID record for S. Cherubini [Opens in a new window]  and
L. Pastur
F. Picella
Affiliation:
DynFluid – Arts et Métiers ParisTech, 151Bd. de l’Hôpital, 75013 Paris, France
J.-Ch. Loiseau
Affiliation:
DynFluid – Arts et Métiers ParisTech, 151Bd. de l’Hôpital, 75013 Paris, France
F. Lusseyran
Affiliation:
LIMSI, CNRS, Université Paris-Saclay, Bat. 508, Rue John Von Neumann, Campus Universitaire, 91403 Orsay, France
J.-Ch. Robinet*
Affiliation:
DynFluid – Arts et Métiers ParisTech, 151Bd. de l’Hôpital, 75013 Paris, France
S. Cherubini
Affiliation:
DMMM, Politecnico di Bari, Via Re David 200, 70126 Bari, Italy
L. Pastur
Affiliation:
LIMSI, CNRS, Université Paris-Sud, Université Paris-Saclay, Bat. 508, Rue John Von Neumann, 91403 Orsay, France
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Instability: Instability Nonlinear Dynamical Systems: Nonlinear Dynamical Systems
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 844 , 10 June 2018 , pp. 855 - 877
Copyright
© 2018 Cambridge University Press 

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