  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 this forcing 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 not only the identification of the streamwise coherent
structures predicted through traditional input-output approaches, but also the
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 weakening
of the lift-up mechanism, which is known to dominate the linear operator.
Capturing this key nonlinear effect enables the prediction of the wider range
of known transitional flow structures within the analytical input-output
modeling paradigm.
