  A resolvent-based reduced-order representation is used to capture
time-averaged second-order statistics in turbulent channel flow. The
recently-proposed decomposition of the resolvent operator into two distinct
families related to the Orr-Sommerfeld and Squire operators [K. Rosenberg and
B. J. McKeon, Efficient representation of exact coherent states of the
Navier-Stokes equations using resolvent analysis, Fluid Dynamics Research 51,
011401 (2019)] results in dramatic improvement in the ability to match all
components of the energy spectra and the $uv$ cospectrum. The success of the
new representation relies on the ability of the Squire modes to compete with
the vorticity generated by Orr-Sommerfeld modes, which is demonstrated by
decomposing the statistics into contributions from each family. It is then
shown that this competition can be used to infer a phase relationship between
the two sets of modes. Additionally, the relative Reynolds number scalings for
the two families of resolvent weights are derived for the universal classes of
resolvent modes presented by Moarref et al. [R. Moarref, A. S. Sharma, J. A.
Tropp, and B. J. McKeon, Model-based scaling of the streamwise energy density
in high-Reynolds-number turbulent channels, Journal of Fluid Mechanics 734, 275
(2013)]. These developments can be viewed as a starting point for further
modeling efforts to quantify nonlinear interactions in wall-bounded turbulence.
