Continuous Spectrum Analysis of Suboptimal Roughness-Induced Growth in Experiments and DNS

Transient growth theory provides a framework for addressing stability and transition in the absence of unstable eigenmodes. To make use of the theory for stationary, roughness-induced disturbances, the wake flow behind roughness elements must be decomposed into a sum of the continuous spectrum modes of the Orr-Sommerfeld equation. The amplitude of the continuous spectrum modes provides a quantitative measure of the receptivity process. This presentation briefly covers the background of the biorthogonal decomposition procedure and its application to flow behind an array of discrete, periodic, roughness elements in a flat-plate boundary layer. The decomposition of the results into the continuous spectrum modes is given for a test case where both experimental and DNS data is available. These results are compared to solutions for optimal disturbances and linear receptivity models, providing a basis for characterizing flow response in terms of excitation of continuous spectrum wavenumbers.