  In this work, we prove a threshold theorem for the 2D Navier-Stokes equations
posed on the periodic channel, $\mathbb{T} \times [-1,1]$, supplemented with
Navier boundary conditions $\omega|_{y = \pm 1} = 0$. Initial datum is taken to
be a perturbation of Couette in the following sense: the shear component of the
perturbation is assumed small (in an appropriate Sobolev space) but importantly
is independent of $\nu$. On the other hand, the nonzero modes are assumed size
$O(\nu^{\frac12})$ in an anisotropic Sobolev space. For such datum, we prove
nonlinear enhanced dissipation and inviscid damping for the resulting solution.
The principal innovation is to capture quantitatively the \textit{inviscid
damping}, for which we introduce a new Singular Integral Operator which is a
physical space analogue of the usual Fourier multipliers which are used to
prove damping. We then include this SIO in the context of a nonlinear
hypocoercivity framework.
