  While linear non-normality underlies the mechanism of energy transfer from
the externally driven flow to the perturbation field that sustains turbulence,
nonlinearity is also known to play an essential role. The goal of this study is
to better understand the role of nonlinearity in sustaining turbulence. The
method used in this study is implementation in Couette flow of a statistical
state dynamics (SSD) closure at second order in a cumulant expansion of the
Navier-Stokes equations in which the averaging operator is the streamwise mean.
The perturbations are the deviations from the streamwise mean and two
mechanisms potentially contributing to maintaining these perturbations are
identified. These are parametric perturbation growth arising from interaction
of the perturbations with the fluctuating mean flow and transient growth of
perturbations arising from nonlinear interaction between components of the
perturbation field. By the method of comparing the turbulence maintained in the
SSD and in the associated direct numerical simulation (DNS) in which these
mechanisms have been selectively included and excluded, parametric growth is
found to maintain the perturbation field of the turbulence while the more
commonly invoked mechanism of transient growth of perturbations arising from
scattering by nonlinear interaction is found to suppress perturbation growth.
In addition to verifying that the parametric mechanism maintains the
perturbations in DNS it is also verified that the Lyapunov vectors are the
structures that dominate the perturbation energy and energetics in DNS. It is
further verified that these vectors are responsible for maintaining the roll
circulation that underlies the self-sustaining process (SSP) and in particular
the maintenance of the fluctuating streak that supports the parametric
perturbation growth.
