Stochastic approach to the receptivity problem applied to bypass transition in boundary layers

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Abstract
To study the flow behavior in the presence of external disturbances of chaotic nature, a stochastic approach is pursued. In particular, transition to turbulence in boundary layers exposed to high levels of free-stream turbulence is considered. The late stages of this transition scenario, characterized by the growth and breakdown of streamwise-elongated streaks, are examined by considering the linear evolution of perturbations to a base flow consisting of the Blasius profile and the streaks. A stochastic initial condition is considered where the free-stream perturbations are described by the correlations of isotropic homogeneous turbulence. The spatial correlation of the excited flow at later times can be computed by the numerical solution of a Lyapunov equation. It is shown that free-stream turbulence has the necessary features to excite secondary energy growth, thus playing a central role in the transition to turbulence. The method proposed here can be used to examine the receptivity of other flows to external noise whose statistical properties are known or can be modeled.

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