  S3T (Stochastic Structural Stability Theory) employs a closure at second
order to obtain the dynamics of the statistical mean turbulent state. When S3T
is implemented as a coupled set of equations for the streamwise mean and
perturbation states, nonlinearity in the dynamics is restricted to interaction
between the mean and perturbations. The S3T statistical mean state dynamics can
be approximately implemented by similarly restricting the dynamics used in a
direct numerical simulation (DNS) of the full Navier-Stokes equations (referred
to as the NS system). Although this restricted nonlinear system (referred to as
the RNL system) is greatly simplified in its dynamics in comparison to the
associated NS, it nevertheless self-sustains a turbulent state in wall-bounded
shear flow with structures and dynamics comparable to that in observed
turbulence. Moreover, RNL turbulence can be analyzed effectively using
theoretical methods developed to study the closely related S3T system. In order
to better understand RNL turbulence and its relation to NS turbulence, an
extensive comparison is made of diagnostics of structure and dynamics in these
systems. Although quantitative differences are found, the results show that
turbulence in the RNL system closely parallels that in NS and suggest that the
S3T/RNL system provides a promising reduced complexity model for studying
turbulence in wall-bounded shear flows.
