Input-output analysis of stochastic base flow uncertainty

We adopt an input-output approach to analyze the effect of persistent white-in-time structured stochastic base flow perturbations on mean-square properties linearized Navier-Stokes equations. Such variations enter dynamics as multiplicative sources uncertainty that can alter stability and their receptivity exogenous excitations. Our does not rely costly simulations or adjoint-based sensitivity analysis. provide verifiable conditions for study frequency response subject additive using solution generalized Lyapunov equation. For small-amplitude perturbations, we bypass need solve large equations by adopting a perturbation use our framework destabilizing effects in transitional parallel flows, reliability numerically estimated mean velocity profiles turbulent channel flows. uncover Reynolds number scaling critically variances demonstrate how wall-normal shape modulations influence amplification various length scales. Furthermore, explain robust streamwise streaks presence analyzing dynamical structure governing well dependence energy spectrum.