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The spatio-temporal aspects of the transition to turbulence are considered inthe case of a boundary layer flow developing above a flat plate exposed tofree-stream turbulence. Combining results on the receptivity to free-streamturbulence with the nonlinear concept of a transition threshold, a physicallymotivated model suggests a spatial distribution of spot nucleation events. Todescribe the evolution of turbulent spots a probabilistic cellular automaton isintroduced, with all parameters directly fitted from numerical simulations ofthe boundary layer. The nucleation rates are then combined with the cellularautomaton model, yielding excellent quantitative agreement with the statisticalcharacteristics for different free-stream turbulence levels. We thus show howthe recent theoretical progress on transitional wall-bounded flows can beextended to the much wider class of spatially developing boundary-layer flows.

Bypass transition and spot nucleation in boundary layers