  Input-output analysis of transitional channel flows has proven to be a
valuable analytical tool for identifying important flow structures and
energetic motions. The traditional approach abstracts the nonlinear terms as
forcing that is unstructured, in the sense that is not directly tied to the
underlying nonlinearity in the dynamics. This paper instead employs a
structured singular value-based approach that preserves certain input-output
properties of the nonlinear forcing function in an effort to recover the larger
range of key flow features identified through nonlinear analysis, experiments,
and direct numerical simulation (DNS) of transitional channel flows.
Application of this method to transitional plane Couette and plane Poiseuille
flows leads to identification of not only the streamwise coherent structures
predicted through traditional input-output approaches but also characterization
of the oblique flow structures as those requiring the least energy to induce
transition in agreement with DNS studies, and nonlinear optimal perturbation
analysis. The proposed approach also captures the recently observed oblique
turbulent bands that have been linked to transition in experiments and DNS with
very large channel size. The ability to identify the larger amplification of
the streamwise varying structures predicted from DNS and nonlinear analysis in
both flow regimes suggests that the structured approach allows one to maintain
the nonlinear effects associated with the saturation of the lift-up mechanism,
which is known to dominate the linear operator. Capturing this key nonlinear
mechanism enables the prediction of the wider range of known transitional flow
structures within the analytical input--output modeling paradigm.
