Let $\boldsymbol{u} = U(z)\,\mathbf{e}_x$ be the velocity profile of an inviscid parallel flow. Rayleigh's inflection point theorem states that this flow may be linearly unstable to perturbations only if $ U $ has an inflection point $z_*$, with $U''(z_*) = 0$. (This is a necessary, not sufficient, condition.)

What is the physical significance of a shear flow having an inflection point? Is it correct to think of the possible instability as a 'smoothed-out' version of the Kelvin–Helmholtz instability, with the shear flow being a 'smoothed-out' vortex sheet? Or is there a different physical mechanism?


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