  We utilize the externally forced linearized Navier-Stokes equations to study
the receptivity of pre-transitional boundary layers to persistent sources of
stochastic excitation. Stochastic forcing is used to model the effect of
free-stream turbulence that enters at various wall-normal locations and the
fluctuation dynamics are studied via linearized models that arise from locally
parallel and global perspectives. In contrast to the widely used resolvent
analysis that quantifies the amplification of deterministic disturbances at a
given temporal frequency, our approach examines the steady-state response to
stochastic excitation that is uncorrelated in time. In addition to stochastic
forcing with identity covariance, we utilize the spatial spectrum of
homogeneous isotropic turbulence to model the effect of free-stream turbulence.
Even though locally parallel analysis does not account for the effect of the
spatially evolving base flow, we demonstrate that it captures the essential
mechanisms and the prevailing length-scales in stochastically forced boundary
layer flows. On the other hand, global analysis, which accounts for the
spatially evolving nature of the boundary layer flow, predicts the
amplification of a cascade of streamwise scales throughout the streamwise
domain. We show that the flow structures that can be extracted from a modal
decomposition of the resulting velocity covariance matrix, can be closely
captured by conducting locally parallel analysis at various streamwise
locations and over different wall-parallel wavenumber pairs. Our approach does
not rely on costly stochastic simulations and it provides insight into
mechanisms for perturbation growth including the interaction of the slowly
varying base flow with streaks and Tollmien-Schlichting waves.
