  Exact coherent states of a linearly stable, plane parallel shear flow
confined between stationary stress-free walls and driven by a sinusoidal body
force (a flow first introduced by F. Waleffe, Phys. Fluids 9, 883 (1997)) are
computed using equations obtained from a large Reynolds-number asymptotic
reduction of the Navier-Stokes equations. The reduced equations employ a
decomposition into streamwise-averaged (mean) and streamwise-varying
(fluctuation) components and are characterized by an effective order one
Reynolds number in the mean equations along with a formally higher-order
diffusive regularization of the fluctuation equations. A robust numerical
algorithm for computing exact coherent states is introduced. Numerical
continuation of the lower branch states to lower Reynolds numbers reveals the
presence of a saddle-node; the saddle-node allows access to upper branch states
that, like the lower branch states, appear to be self-consistently described by
the reduced equations. Both lower and upper branch states are characterized in
detail.
