Coherent streaky structures and optimal perturbations of turbulent boundary layers
Résumé
The presence of persistent streaky structures is a well established robust feature of turbulent shear flows . A large amount of research has been dedicated to the understanding of the mechanisms by which streaks are generated and of their relevance on the turbulent dynamics. In the near wall region of the boundary layer these streaks, with characteristic mean spacing of about one hundred wall units, are thought to play an essential role in a turbulent self sustained mechanism. The 'lift-up' effect by which low energy streamwise vortices can induce large energy streaks is an important process embedded in this self sustained mechanism. Recent studies have also demonstrated that the well controlled optimal transient growth of artificially forced streaks can be efficiently used to manipulate at leading order laminar shear flows. Such a paradigm has been successfully applied to stabilize Tollmien-Schlichting waves in a laminar boundary layer [1] and to effectively delay transition to turbulence [4]. In these investigations, roughness elements were used to create nearly optimal vortices in the upstream part of the boundary layer that induced well controlled streamwise streaks downstream. A still not addressed extension of such a kind of approach would consist in the manipulation of turbulent boundary layers with optimal or nearly optimal vortices and streaks, the first step in this direction being to compute the optimal perturbations of the turbulent boundary layer.