The effect of base flow uncertainty on transitional channel flows

Abstract

We study the effect of white-in-time additive stochastic base flow perturbations on the mean-square properties of the linearized Navier-Stokes equations. Such perturbations enter the linearized dynamics as multiplicative sources of uncertainty. We adopt an input-output approach to analyze the mean-square stability and frequency response of the flow subject to additive and multiplicative uncertainty. For transitional channel flows, we uncover the Reynolds number scaling of critical base flow variances and identify length scales that are most affected by base flow uncertainty. For small-amplitude perturbations, we adopt a perturbation analysis to efficiently compute the variance amplification of velocity fluctuations around the uncertain base state. Our results demonstrate the robust amplification of streamwise elongated flow structures in the presence of base flow uncertainty and that the wall-normal shape of base flow modulations can influence the amplification of various length scales.