Energy amplification in a parallel Blasius boundary layer flow subject to free-stream turbulence

We perform an input-output analysis of transition in boundary layers subject to free-stream turbulence, which is modeled as a stochastic excitation to the Navier-Stokes equations linearized around a parallel Blasius base flow. The second order statistics of this excitation are determined by modeling energy spectrum of the homogeneous isotropic turbulence using the linearized Navier-Stokes equations. Our variance-amplification analysis identifies the near-plate streamwise streaks as the most energetic flow structures and theoretically predicts prevailing length-scales. The results of our analysis are in good agreement with the experimental and numerical studies of the free-stream-turbulence-induced boundary layer transition.