  In this paper, we consider the stability threshold of the 2D shear flow
$(U(y),0)^{\top}$ of the Navier-Stokes equation at high Reynolds number $Re$.
When the shear flow is near in Sobolev norm to the Couette flow $(y,0)^{\top}$
in some sense, we prove that if the initial data $u_0$ satisfies
$\|u_0-(U(y),0)^{\top}\|\leq \epsilon Re^{-1/3}$, then the solution of the 2D
Navier-Stokes equation approaches to some shear flow which is also close to the
Couette flow for $t\gg Re^{1/3}$, as $t\to\infty$.
