On the Rayleigh theorem for inflectional velocity instability of inviscid flows

It is exactly proved that the classical Rayleigh Theorem on inflectional velocity instability is wrong which states that the necessary condition for instability of inviscid flow is the existence of an inflection point on the velocity profile. It is shown that the disturbance amplified in 2D inviscid flows is necessarily 3D. After the break down of T-S wave in 2D parallel flows, the disturbance becomes a type of spiral waves which proceed along the streamwise direction. This is just the origin of formation of streamwise vortices.