  In this work, we study the transient growth of the principal resolvent modes
in the minimal flow unit using a reformulation of resolvent analysis in a
time-localized wavelet basis. We target the most energetic spatial wavenumbers
for the minimal flow unit and obtain modes that are constant in the streamwise
direction and once-periodic in the spanwise direction. The forcing modes are in
the shape of streamwise rolls, though pulse-like in time, and the response
modes are in the form of transiently growing streaks. We inject the principal
transient forcing mode at different intensities into a simulation of the
minimal flow unit and compare the resulting nonlinear response to the linear
one. The peak energy amplification scales quadratically with the intensity of
the injected mode, and this peak occurs roughly at the same time for all
forcing intensities. However, the larger energy amplification intensifies the
magnitude of the nonlinear terms, which play an important role in damping the
energy growth and accelerating energy decay of the principal resolvent mode. We
also observe that the damping effect of the nonlinearities is less prominent
close to the wall. Finally, we find that the principal resolvent forcing mode
is more effective than other structures at amplifying the streak energy in the
turbulent minimal-flow unit. In addition to lending support to the claim that
linear mechanisms are important to near-wall turbulence, this work identifies
time scales for the nonlinear breakdown of linearly-generated streaks.
