  The spatio-temporal aspects of the transition to turbulence are considered in
the case of a boundary layer flow developing above a flat plate exposed to
free-stream turbulence. Combining results on the receptivity to free-stream
turbulence with the nonlinear concept of a transition threshold, a physically
motivated model suggests a spatial distribution of spot nucleation events. To
describe the evolution of turbulent spots a probabilistic cellular automaton is
introduced, with all parameters directly fitted from numerical simulations of
the boundary layer. The nucleation rates are then combined with the cellular
automaton model, yielding excellent quantitative agreement with the statistical
characteristics for different free-stream turbulence levels. We thus show how
the recent theoretical progress on transitional wall-bounded flows can be
extended to the much wider class of spatially developing boundary-layer flows.
