Resolvent analysis of exact coherent solutions

Exact coherent solutions have been hypothesized to constitute the state-space skeleton of turbulent trajectories and thus are of interest as a means to better understand the underlying dynamics of turbulent flows. An asymptotic description of how these types of solutions self-sustain was provided by Hall \& Sherwin (JFM, 2010). Here we offer a fully-nonlinear perspective on the self-sustainment of these solutions in terms of triadic scale interactions and use the resolvent framework of McKeon \& Sharma (JFM, 2010) to interpret these results from an input/output point of view. We analyze traveling wave solutions and periodic orbits in channel flow, and demonstrate how resolvent analysis can be used to obtain low-dimensional representations of these flows.