Structured input-output analysis of transitional Blasius boundary layer flows using a descriptor state space model.

We extend the recently proposed structured input-output analysis of channel flows (J. Fluid Mech. vol. 927, A25) to the transitional Blasius boundary layer. This approach enables the incorporation of nonlinear effects into input-output analysis through a feedback interconnection between the linear operator and modeled nonlinearity. The optimal perturbation associated with each (streamwise and spanwise) wavenumber pair can then be quantified by the structured singular value of a modified spatio-temporal frequency response operator. Our implementation employs a descriptor state space model (DSS) model that provides a more direct approach for imposing nontraditional boundary conditions (e.g., stress-free), thereby expanding the applications that can be studied. We verified the DSS model for channel flows with the previously reported results for canonical flows. As with previous observations for channel and plane Couette flow, the imposition of a model that preserves the componentwise structure of the nonlinearity in Blasius boundary layer flows weakens the streamwise elongated flow structures and uncovers the highly amplified streamwise dependent flow structures. The results are compared with nonlinear optimal perturbation and direct numerical simulation in the existing literature.