Low-Dimensional Modal Description of Optimal Streaks

Streaky perturbations play an essential role in the destabilization of boundary layers, especially in the presence of free-stream turbulence. These perturbations are calculated in terms of a streamwise evolving parabolic problem. Using the asymptotic behaviour of the solutions near the leading edge singularity, we obtain a low-dimensional modal description of the streaks in the case of a boundary layer attached to a flat plate. Comparison with optimal streaks obtained via the adjoint gradient (Luchini, JFM 2000), seems to indicate that the development of the instability may be understood on the basis of appropriate amplitude equations giving the streamwise evolution of the amplitudes of the relevant modes.