  In this paper, we study the transition threshold problem for the 2-D
Navier-Stokes equations around the Poiseuille flow $(1-y^2,0)$ in a finite
channel with Navier-slip boundary condition. Based on the resolvent estimates
for the linearized operator around the Poiseuille flow, we first establish the
enhanced dissipation estimates for the linearized Navier-Stokes equations with
a sharp decay rate $e^{-c\sqrt{\nu}t}$. As an application, we prove that if the
initial perturbation of vortiticy satisfies $$\|\omega_0\|_{L^2}\leq
c_0\nu^{\frac{3}{4}},$$ for some small constant $c_0>0$ independent of the
viscosity $\nu$, then the solution dose not transition away from the Poiseuille
flow for any time.
