Relating global and local stochastic receptivity analysis of boundary layer flows

Abstract

We utilize control-theoretic tools to study the receptivity of pre-transitional boundary layers to persistent stochastic excitation sources. White-in-time stochastic excitation is used to model the effect of free-stream turbulence on the linearized Navier-Stokes dynamics. We discuss similarities and differences resulting from local and global approaches in terms of steady-state energy amplification of velocity fluctuations and the underlying flow structures. While parallel flow analysis predicts a flow response that is dominated by the principal eigenmode of the covariance matrix, we show that global analysis yields subordinate eigenmodes that have nearly equal energetic contributions to that of the principal mode. We investigate this observation and provide a possible explanation for the disparity between the results of local and global receptivity analysis in spatially evolving flows.