Effect of stochastic base flow uncertainty in transitional high speed compressible flows

We analyze the effect of persistent white-in-time structured stochastic base flow perturbations on the mean-square properties of the compressible linearized Navier-Stokes equations. We extend the input-output framework proposed by Hewawaduge and Zare (PRF, vol. 7, no. 7, 2022) to account for base flow velocity and temperature variations that enter the linearized dynamics of high speed flows as multiplicative sources of uncertainty and can alter their stability and frequency response. This allows us to investigate the stability of laminar flows near leading edges and nose tips that have been shown to undergo early transition to turbulence at supersonic and hypersonic free-stream speeds both in flight and wind tunnel conditions. Our analysis reveals that small amplitude near-wall perturbations of the base flow velocity can compromise the mean-square stability of the laminar flow. We also provide insights into how changes in different physical parameters, such as the temperature of the wall and its curvature, influence the mean-square stability of the fluctuation dynamics. We show that increasing the leading edge radius and decreasing the wall temperature can significantly deteriorate the robustness of laminar flows in the presence of base flow variations. Our approach offers a systematic framework for quantifying the influence of base flow uncertainties that can appear from stochastic sources (e.g., surface roughness and background turbulence) and are unavoidable in experiments in transitional high speed flows.