Optimal transient growth and very large scale structures in turbulent boundary layers

We compute the optimal energy growth sustained by a turbulent boundary using the mean flow proposed by Monkewitz et al. (Phys. Fluids 2007) and the associated eddy viscosity as recently done for channel flows (del \'Alamo \& Jim\'enez, J. Fluid Mech. 2006). Large transient energy growths are obtained for streamwise vortices evolving into streamwise streaks. For sufficiently large Reynolds numbers two distinct optimal spanwise walengths exist. The first, $\lambda^+ \sim 80 $, scales in inner units and is associated with most probable buffer layer streaks. The second, $\lambda \sim 8\,\delta$ scales in outer units and corresponds to optimal vortices centred near the boundary layer edge and to optimal streaks spreading in the whole boundary layer. These streaks scale in outer variables in the outer region and in wall units in the inner region of the boundary layer.