Low-frequency dynamics of separated boundary-layer Stefania Cherubini 1,2 , Jean-Christophe Robinet 1 & Pietro De Palma 2 1 Laboratoire DYNFLUID - Arts & M´ etiers ParisTech - 151 Bd. de l’Hˆ opital - 75013 Paris - France, 2 DIMeG, CEMeC, Politecnico di Bari - Via Re David 200 - 70125 Bari - Italie Jean-Christophe.Robinet@paris.ensam.fr R´ esum´ e: Dans ce papier nous nous int´ eressons ` a la dynamique transitoire et asymptotique d’une couche limite de plaque plane fortement d´ ecoll´ ee. Seul le r´ egime supercritique (lin´ eairement globale- ment instable) est abord´ e. Les effets de la non-normalit´ e de l’op´ erateur lin´ earis´ e sont ´ etudi´ es en d´ etail ainsi que l’influence des non-lin´ earit´ es pour des perturbations d’amplitude finie. L’´ etude de la dynamique est d’une part r´ ealis´ ee par la r´ esolution d’un probl` eme aux valeurs propres de grande dimension et la r´ esolution des ´ equations de Navier-Stokes directes. Les analyses de stabilit´ e globale ainsi que les simulations num´ eriques initialis´ ees par des perturbations d’ampli- tude croissante montrent que l’´ ecoulement est globalement instable et se comporte comme un oscillateur engendrant des oscillations auto-entretenues de basses fr´ equences ` a temps longs. Abstract : The effects of non-normality and non-linearity of the two-dimensional differential Navier- Stokes operator on the dynamics of a large laminar separation bubble over a flat plate have been studied in a slightly supercritical conditions. The global eigenvalue analysis together with direct numerical simulations have been employed in order to investigate the linear and non- linear stability of the flow. For supercritical conditions, the non-normality of the modes has been found to generate low-frequency oscillations (flapping) at large times. Mots-clefs : global eigenvalue analysis, direct numerical simulation, optimal response, flapping fre- quency 1 Introduction In many engineering applications the boundary layer undergoes separation and reattach- ment, thus forming recirculation bubbles whose stability and control may be crucial for the performance of the device under consideration. This may happen, for example, over the surface of turbomachinery blades or of airplane wings. Separation may be triggered by the geometry of the body or by the adverse pressure gradient. In both cases the aerodynamic load may be strongly affected by the behavior of the bubble which changes its characteristics depending on the operating conditions. Often, the presence of a bubble is associated with a laminar-turbulent transition of the boundary layer since flow separation occurs in the laminar part of the bubble and, after transition, the flow reattaches. Such a transition is governed by the amplification of flow perturbations which may be due either to a linear process based on transient growth or to a non-linear one in the presence of high free-stream disturbance levels (bypass transition) [1]. 1