  We study the stability threshold of the 2D Couette flow in Sobolev spaces at
high Reynolds number $Re$. We prove that if the initial vorticity $\Omega_{in}$
satisfies $\|\Omega_{in}-(-1)\|_{H^{\sigma}}\leq \epsilon Re^{-1/3}$, then the
solution of the 2D Navier-Stokes equation approaches to some shear flow which
is also close to Couette flow for time $t\gg Re^{1/3}$ by a mixing-enhanced
dissipation effect and then converges back to Couette flow when $t\to +\infty$.
