  The nonlinear mechanism in the self-sustaining process (SSP) of wall-bounded
turbulence is investigated. Resolvent analysis is used to identify the
principal forcing mode which produces the maximum amplification of the
velocities in numerical simulations of the minimal channel for the buffer layer
and a modified logarithmic (log) layer. The wavenumbers targeted in this study
are those of the fundamental mode that is infinitely long in the streamwise
direction and once periodic in the spanwise direction. The identified mode is
then projected out from the nonlinear term of the Navier-Stokes equations at
each time step from the simulation of the corresponding minimal channel. The
results show that the removal of the principal forcing mode of the fundamental
wavenumber can inhibit turbulence in both the buffer and log layer, with the
effect being greater in the buffer layer. Removing other modes instead of the
principal mode of the fundamental wavenumber only marginally affects the flow.
Closer inspection of the dyadic interactions in the nonlinear term shows that
contributions toward the principal forcing mode come from a limited set of
wavenumber interactions. Using conditional averaging, the flow structures that
are responsible for generating the nonlinear interaction to self-sustain
turbulence are identified as spanwise rolls interacting with oblique streaks.
This method, based on the equations of motion, validates the similarities in
the SSP of the buffer and log layer, and characterises the underlying quadratic
interactions in the SSP of the minimal channel.
