  We report that many exact invariant solutions of the Navier-Stokes equations
for both pipe and channel flows are well represented by just few modes of the
model of McKeon & Sharma J. Fl. Mech. 658, 356 (2010). This model provides
modes that act as a basis to decompose the velocity field, ordered by their
amplitude of response to forcing arising from the interaction between scales.
The model was originally derived from the Navier-Stokes equations to represent
turbulent flows and has been used to explain coherent structure and to predict
turbulent statistics. This establishes a surprising new link between the two
distinct approaches to understanding turbulence.
