Boundary layer receptivity analysis via the algebraic Lyapunov equation

摘要

We use the algebraic Lyapunov equation to study the receptivity of pre-transitional boundary layers to persistent sources of stochastic excitation. The effect of exogenous disturbances is modeled using an additive stochastic forcing that enters at various wall-normal locations and the fluctuation dynamics are studied via linearized models that arise from locally parallel and global perspectives. Even though locally parallel analysis does not account for the effect of the spatially evolving base flow, we demonstrate that it captures the essential mechanisms and the prevailing length-scales. On the other hand, global analysis, which accounts for the spatially evolving nature of the boundary layer flow, predicts the amplification of a cascade of streamwise scales throughout the streamwise domain. We show that the flow structures that are extracted from a modal decomposition of the resulting velocity covariance matrix, can be closely captured by conducting locally parallel analysis at various streamwise locations and over different wall-parallel wavenumber pairs. Our approach does not rely on costly stochastic simulations and it provides insight into mechanisms for perturbation growth, including the interaction of the slowly varying base flow with streaks and Tollmien-Schlichting waves.