Input-output analysis of stochastic base flow uncertainty in channel flows

We adopt an input-output approach to study the effect of base flow perturbations on the stability and receptivity properties of transitional and turbulent channel flows. Base flow perturbations are modeled as persistent white-in-time stochastic excitations that enter the linearized dynamics as multiplicative sources of uncertainty that can alter the mean-square properties of state. We provide verifiable conditions for mean-square stability and study the frequency response of the flow subject to additive and multiplicative sources of uncertainty. Our approach does not rely on costly stochastic simulations or adjoint-based sensitivity analyses. We use our framework to uncover the Reynolds number scaling of critically destabilizing variance levels of the base flow uncertainty and identify the length-scales that are predominantly affected by perturbations of various shapes and sizes.