Fjørtoft theorem

For a smooth inviscid parallel shear profile with an exponentially growing mode, let $U_s$ be its velocity at an inflection point. The real and imaginary parts of the integrated Rayleigh equation for inviscid shear flow imply $\int U^{\prime \prime }(U-U_s)|\psi {|}^2/|U-c{|}^2=-\int (|{\psi }^{\prime }{|}^2+k^2|\psi {|}^2)<0$. Consequently $U^{\prime \prime }(U-U_s)<0$ somewhere in the channel. This strengthens Rayleigh's inflection-point theorem but is still only a necessary condition, not a sufficient instability criterion.