  This is the second in a pair of works which study small disturbances to the
plane, periodic 3D Couette flow in the incompressible Navier-Stokes equations
at high Reynolds number $\textbf{Re}$. In this work, we show that there is
constant $0 < c_0 \ll 1$, independent of $\textbf{Re}$, such that sufficiently
regular disturbances of size $\epsilon \lesssim \textbf{Re}^{-2/3-\delta}$ for
any $\delta > 0$ exist at least until $t = c_0\epsilon^{-1}$ and in general
evolve to be $O(c_0)$ due to the lift-up effect. Further, after times $t
\gtrsim \textbf{Re}^{1/3}$, the streamwise dependence of the solution is
rapidly diminished by a mixing-enhanced dissipation effect and the solution is
attracted back to the class of "2.5 dimensional" streamwise-independent
solutions (sometimes referred to as "streaks"). The largest of these streaks
are expected to eventually undergo a secondary instability at $t \approx
\epsilon^{-1}$. Hence, our work strongly suggests, for all (sufficiently
regular) initial data, the genericity of the "lift-up effect $\Rightarrow$
streak growth $\Rightarrow$ streak breakdown" scenario for turbulent transition
of the 3D Couette flow near the threshold of stability forwarded in the applied
mathematics and physics literature.
