  We prove the instability of the Couette flow if the disturbances is less
smooth than the Gevrey space of class 2. This shows that this is the critical
regularity for this problem since it was proved in [5] that stability and
inviscid damping hold for disturbances which are smoother than the Gevrey space
of class 2. A big novelty is that this critical space is due to an instability
mechanism which is completely nonlinear and is due to some energy cascade.
